A case study of aerosol data assimilation with the Community Multi-scale Air Quality Model over the contiguous United States using 3D-Var and optimal interpolation methods

Science.gov (United States)

Tang, Youhua; Pagowski, Mariusz; Chai, Tianfeng; Pan, Li; Lee, Pius; Baker, Barry; Kumar, Rajesh; Delle Monache, Luca; Tong, Daniel; Kim, Hyun-Cheol

2017-12-01

This study applies the Gridpoint Statistical Interpolation (GSI) 3D-Var assimilation tool originally developed by the National Centers for Environmental Prediction (NCEP), to improve surface PM2.5 predictions over the contiguous United States (CONUS) by assimilating aerosol optical depth (AOD) and surface PM2.5 in version 5.1 of the Community Multi-scale Air Quality (CMAQ) modeling system. An optimal interpolation (OI) method implemented earlier (Tang et al., 2015) for the CMAQ modeling system is also tested for the same period (July 2011) over the same CONUS. Both GSI and OI methods assimilate surface PM2.5 observations at 00:00, 06:00, 12:00 and 18:00 UTC, and MODIS AOD at 18:00 UTC. The assimilations of observations using both GSI and OI generally help reduce the prediction biases and improve correlation between model predictions and observations. In the GSI experiments, assimilation of surface PM2.5 (particle matter with diameter big differences besides the data assimilation schemes. For instance, the OI uses relatively big model uncertainties, which helps yield smaller mean biases, but sometimes causes the RMSE to increase. We also examine and discuss the sensitivity of the assimilation experiments' results to the AOD forward operators.

Radial basis function interpolation of unstructured, three-dimensional, volumetric particle tracking velocimetry data

International Nuclear Information System (INIS)

Casa, L D C; Krueger, P S

2013-01-01

Unstructured three-dimensional fluid velocity data were interpolated using Gaussian radial basis function (RBF) interpolation. Data were generated to imitate the spatial resolution and experimental uncertainty of a typical implementation of defocusing digital particle image velocimetry. The velocity field associated with a steadily rotating infinite plate was simulated to provide a bounded, fully three-dimensional analytical solution of the Navier–Stokes equations, allowing for robust analysis of the interpolation accuracy. The spatial resolution of the data (i.e. particle density) and the number of RBFs were varied in order to assess the requirements for accurate interpolation. Interpolation constraints, including boundary conditions and continuity, were included in the error metric used for the least-squares minimization that determines the interpolation parameters to explore methods for improving RBF interpolation results. Even spacing and logarithmic spacing of RBF locations were also investigated. Interpolation accuracy was assessed using the velocity field, divergence of the velocity field, and viscous torque on the rotating boundary. The results suggest that for the present implementation, RBF spacing of 0.28 times the boundary layer thickness is sufficient for accurate interpolation, though theoretical error analysis suggests that improved RBF positioning may yield more accurate results. All RBF interpolation results were compared to standard Gaussian weighting and Taylor expansion interpolation methods. Results showed that RBF interpolation improves interpolation results compared to the Taylor expansion method by 60% to 90% based on the average squared velocity error and provides comparable velocity results to Gaussian weighted interpolation in terms of velocity error. RMS accuracy of the flow field divergence was one to two orders of magnitude better for the RBF interpolation compared to the other two methods. RBF interpolation that was applied to

Off-site radiation exposure review project: computer-aided surface interpolation and graphical display

International Nuclear Information System (INIS)

Foley, T.A. Jr.

1981-08-01

This report presents the implementation of an iterative procedure that solves the following bivariate interpolation problem: Given N distinct points in the plane (x/sub i/, y/sub i/) and N real numbers Z/sub i/, construct a function F(x,y) that satisfies F(x/sub i/, y/sub i/) = Z/sub i/, for i = 1, ..., N. This problem can be interpreted as fitting a surface through N points in three dimensional space. The application of primary concern to the Offsite Radiation Exposure Review Project is the characterization of the radionuclide activity resulting from nuclear tests. Samples of activity were measured at various locations. The location of the sample point is represented by (x/sub i/, y/sub i/), and the magnitude of the reading is represented by Z/sub i/. The method presented in this report is constructed to be efficient on large data sets, stable on the large variations of the Z/sub i/ magnitudes, and capable of smoothly filling in areas that are void of data. This globally defined icode was initiateminednitial shock but to two later eriological invaders are Staphylococcus albus, Beta-hemolytic Streptococcus e to the same general semiclassical treatment

A Hybrid Interpolation Method for Geometric Nonlinear Spatial Beam Elements with Explicit Nodal Force

Directory of Open Access Journals (Sweden)

Huiqing Fang

2016-01-01

Full Text Available Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.

Radon-domain interferometric interpolation for reconstruction of the near-offset gap in marine seismic data

Science.gov (United States)

Xu, Zhuo; Sopher, Daniel; Juhlin, Christopher; Han, Liguo; Gong, Xiangbo

2018-04-01

In towed marine seismic data acquisition, a gap between the source and the nearest recording channel is typical. Therefore, extrapolation of the missing near-offset traces is often required to avoid unwanted effects in subsequent data processing steps. However, most existing interpolation methods perform poorly when extrapolating traces. Interferometric interpolation methods are one particular method that have been developed for filling in trace gaps in shot gathers. Interferometry-type interpolation methods differ from conventional interpolation methods as they utilize information from several adjacent shot records to fill in the missing traces. In this study, we aim to improve upon the results generated by conventional time-space domain interferometric interpolation by performing interferometric interpolation in the Radon domain, in order to overcome the effects of irregular data sampling and limited source-receiver aperture. We apply both time-space and Radon-domain interferometric interpolation methods to the Sigsbee2B synthetic dataset and a real towed marine dataset from the Baltic Sea with the primary aim to improve the image of the seabed through extrapolation into the near-offset gap. Radon-domain interferometric interpolation performs better at interpolating the missing near-offset traces than conventional interferometric interpolation when applied to data with irregular geometry and limited source-receiver aperture. We also compare the interferometric interpolated results with those obtained using solely Radon transform (RT) based interpolation and show that interferometry-type interpolation performs better than solely RT-based interpolation when extrapolating the missing near-offset traces. After data processing, we show that the image of the seabed is improved by performing interferometry-type interpolation, especially when Radon-domain interferometric interpolation is applied.

Real-time interpolation for true 3-dimensional ultrasound image volumes.

Science.gov (United States)

Ji, Songbai; Roberts, David W; Hartov, Alex; Paulsen, Keith D

2011-02-01

We compared trilinear interpolation to voxel nearest neighbor and distance-weighted algorithms for fast and accurate processing of true 3-dimensional ultrasound (3DUS) image volumes. In this study, the computational efficiency and interpolation accuracy of the 3 methods were compared on the basis of a simulated 3DUS image volume, 34 clinical 3DUS image volumes from 5 patients, and 2 experimental phantom image volumes. We show that trilinear interpolation improves interpolation accuracy over both the voxel nearest neighbor and distance-weighted algorithms yet achieves real-time computational performance that is comparable to the voxel nearest neighbor algrorithm (1-2 orders of magnitude faster than the distance-weighted algorithm) as well as the fastest pixel-based algorithms for processing tracked 2-dimensional ultrasound images (0.035 seconds per 2-dimesional cross-sectional image [76,800 pixels interpolated, or 0.46 ms/1000 pixels] and 1.05 seconds per full volume with a 1-mm(3) voxel size [4.6 million voxels interpolated, or 0.23 ms/1000 voxels]). On the basis of these results, trilinear interpolation is recommended as a fast and accurate interpolation method for rectilinear sampling of 3DUS image acquisitions, which is required to facilitate subsequent processing and display during operating room procedures such as image-guided neurosurgery.

Gridded precipitation dataset for the Rhine basin made with the genRE interpolation method

NARCIS (Netherlands)

Osnabrugge, van B.; Uijlenhoet, R.

2017-01-01

A high resolution (1.2x1.2km) gridded precipitation dataset with hourly time step that covers the whole Rhine basin for the period 1997-2015. Made from gauge data with the genRE interpolation scheme. See "genRE: A method to extend gridded precipitation climatology datasets in near real-time for

A case study of aerosol data assimilation with the Community Multi-scale Air Quality Model over the contiguous United States using 3D-Var and optimal interpolation methods

Directory of Open Access Journals (Sweden)

Y. Tang

2017-12-01

Full Text Available This study applies the Gridpoint Statistical Interpolation (GSI 3D-Var assimilation tool originally developed by the National Centers for Environmental Prediction (NCEP, to improve surface PM2.5 predictions over the contiguous United States (CONUS by assimilating aerosol optical depth (AOD and surface PM2.5 in version 5.1 of the Community Multi-scale Air Quality (CMAQ modeling system. An optimal interpolation (OI method implemented earlier (Tang et al., 2015 for the CMAQ modeling system is also tested for the same period (July 2011 over the same CONUS. Both GSI and OI methods assimilate surface PM2.5 observations at 00:00, 06:00, 12:00 and 18:00 UTC, and MODIS AOD at 18:00 UTC. The assimilations of observations using both GSI and OI generally help reduce the prediction biases and improve correlation between model predictions and observations. In the GSI experiments, assimilation of surface PM2.5 (particle matter with diameter < 2.5 µm leads to stronger increments in surface PM2.5 compared to its MODIS AOD assimilation at the 550 nm wavelength. In contrast, we find a stronger OI impact of the MODIS AOD on surface aerosols at 18:00 UTC compared to the surface PM2.5 OI method. GSI produces smoother result and yields overall better correlation coefficient and root mean squared error (RMSE. It should be noted that the 3D-Var and OI methods used here have several big differences besides the data assimilation schemes. For instance, the OI uses relatively big model uncertainties, which helps yield smaller mean biases, but sometimes causes the RMSE to increase. We also examine and discuss the sensitivity of the assimilation experiments' results to the AOD forward operators.

Spatio-temporal interpolation of precipitation during monsoon periods in Pakistan

Science.gov (United States)

Hussain, Ijaz; Spöck, Gunter; Pilz, Jürgen; Yu, Hwa-Lung

2010-08-01

Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space-time heterogeneity of rainfall observations make space-time estimation of precipitation a challenging task. In this paper we propose a Box-Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space-time monthly precipitation in the monsoon periods during 1974-2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space-time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method.

A parameterization of observer-based controllers: Bumpless transfer by covariance interpolation

DEFF Research Database (Denmark)

Stoustrup, Jakob; Komareji, Mohammad

2009-01-01

This paper presents an algorithm to interpolate between two observer-based controllers for a linear multivariable system such that the closed loop system remains stable throughout the interpolation. The method interpolates between the inverse Lyapunov functions for the two original state feedback...

Comparison of Interpolation Methods as Applied to Time Synchronous Averaging

National Research Council Canada - National Science Library

Decker, Harry

1999-01-01

Several interpolation techniques were investigated to determine their effect on time synchronous averaging of gear vibration signals and also the effects on standard health monitoring diagnostic parameters...

Monotone piecewise bicubic interpolation

International Nuclear Information System (INIS)

Carlson, R.E.; Fritsch, F.N.

1985-01-01

In a 1980 paper the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone script C 1 piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm. 4 references, 6 figures, 2 tables

Comparative Analysis of Spatial Interpolation Methods in the Mediterranean Area: Application to Temperature in Sicily

Directory of Open Access Journals (Sweden)

Annalisa Di Piazza

2015-04-01

Full Text Available An exhaustive comparison among different spatial interpolation algorithms was carried out in order to derive annual and monthly air temperature maps for Sicily (Italy. Deterministic, data-driven and geostatistics algorithms were used, in some cases adding the elevation information and other physiographic variables to improve the performance of interpolation techniques and the reconstruction of the air temperature field. The dataset is given by air temperature data coming from 84 stations spread around the island of Sicily. The interpolation algorithms were optimized by using a subset of the available dataset, while the remaining subset was used to validate the results in terms of the accuracy and bias of the estimates. Validation results indicate that univariate methods, which neglect the information from physiographic variables, significantly entail the largest errors, while performances improve when such parameters are taken into account. The best results at the annual scale have been obtained using the the ordinary kriging of residuals from linear regression and from the artificial neural network algorithm, while, at the monthly scale, a Fourier-series algorithm has been used to downscale mean annual temperature to reproduce monthly values in the annual cycle.

Energy-Driven Image Interpolation Using Gaussian Process Regression

Directory of Open Access Journals (Sweden)

Lingling Zi

2012-01-01

Full Text Available Image interpolation, as a method of obtaining a high-resolution image from the corresponding low-resolution image, is a classical problem in image processing. In this paper, we propose a novel energy-driven interpolation algorithm employing Gaussian process regression. In our algorithm, each interpolated pixel is predicted by a combination of two information sources: first is a statistical model adopted to mine underlying information, and second is an energy computation technique used to acquire information on pixel properties. We further demonstrate that our algorithm can not only achieve image interpolation, but also reduce noise in the original image. Our experiments show that the proposed algorithm can achieve encouraging performance in terms of image visualization and quantitative measures.

Permanently calibrated interpolating time counter

International Nuclear Information System (INIS)

Jachna, Z; Szplet, R; Kwiatkowski, P; Różyc, K

2015-01-01

We propose a new architecture of an integrated time interval counter that provides its permanent calibration in the background. Time interval measurement and the calibration procedure are based on the use of a two-stage interpolation method and parallel processing of measurement and calibration data. The parallel processing is achieved by a doubling of two-stage interpolators in measurement channels of the counter, and by an appropriate extension of control logic. Such modification allows the updating of transfer characteristics of interpolators without the need to break a theoretically infinite measurement session. We describe the principle of permanent calibration, its implementation and influence on the quality of the counter. The precision of the presented counter is kept at a constant level (below 20 ps) despite significant changes in the ambient temperature (from −10 to 60 °C), which can cause a sevenfold decrease in the precision of the counter with a traditional calibration procedure. (paper)

Study on the algorithm for Newton-Rapson iteration interpolation of NURBS curve and simulation

Science.gov (United States)

Zhang, Wanjun; Gao, Shanping; Cheng, Xiyan; Zhang, Feng

2017-04-01

In order to solve the problems of Newton-Rapson iteration interpolation method of NURBS Curve, Such as interpolation time bigger, calculation more complicated, and NURBS curve step error are not easy changed and so on. This paper proposed a study on the algorithm for Newton-Rapson iteration interpolation method of NURBS curve and simulation. We can use Newton-Rapson iterative that calculate (xi, yi, zi). Simulation results show that the proposed NURBS curve interpolator meet the high-speed and high-accuracy interpolation requirements of CNC systems. The interpolation of NURBS curve should be finished. The simulation results show that the algorithm is correct; it is consistent with a NURBS curve interpolation requirements.

3D Medical Image Interpolation Based on Parametric Cubic Convolution

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

In the process of display, manipulation and analysis of biomedical image data, they usually need to be converted to data of isotropic discretization through the process of interpolation, while the cubic convolution interpolation is widely used due to its good tradeoff between computational cost and accuracy. In this paper, we present a whole concept for the 3D medical image interpolation based on cubic convolution, and the six methods, with the different sharp control parameter, which are formulated in details. Furthermore, we also give an objective comparison for these methods using data sets with the different slice spacing. Each slice in these data sets is estimated by each interpolation method and compared with the original slice using three measures: mean-squared difference, number of sites of disagreement, and largest difference. According to the experimental results, we present a recommendation for 3D medical images under the different situations in the end.

A new method for reducing DNL in nuclear ADCs using an interpolation technique

International Nuclear Information System (INIS)

Vaidya, P.P.; Gopalakrishnan, K.R.; Pethe, V.A.; Anjaneyulu, T.

1986-01-01

The paper describes a new method for reducing the DNL associated with nuclear ADCs. The method named the ''interpolation technique'' is utilized to derive the quantisation steps corresponding to the last n bits of the digital code by dividing quantisation steps due to higher significant bits of the DAC, using a chain of resistors. Using comparators, these quantisation steps are compared with the analog voltage to be digitized, which is applied as a voltage shift at both ends of this chain. The output states of the comparators define the n bit code. The errors due to offset voltages and bias currents of the comparators are statistically neutralized by changing the polarity of quantisation steps as well as the polarity of analog voltage (corresponding to last n bits) for alternate A/D conversion. The effect of averaging on the channel profile can be minimized. A 12 bit ADC was constructured using this technique which gives DNL of less than +-1% over most of the channels for conversion time of nearly 4.5 μs. Gatti's sliding scale technique can be implemented for further reduction of DNL. The interpolation technique has a promising potential of improving the resolution of existing 12 bit ADCs to 16 bit, without degrading the percentage DNL significantly. (orig.)

Interpolation of vector fields from human cardiac DT-MRI

International Nuclear Information System (INIS)

Yang, F; Zhu, Y M; Rapacchi, S; Robini, M; Croisille, P; Luo, J H

2011-01-01

There has recently been increased interest in developing tensor data processing methods for the new medical imaging modality referred to as diffusion tensor magnetic resonance imaging (DT-MRI). This paper proposes a method for interpolating the primary vector fields from human cardiac DT-MRI, with the particularity of achieving interpolation and denoising simultaneously. The method consists of localizing the noise-corrupted vectors using the local statistical properties of vector fields, removing the noise-corrupted vectors and reconstructing them by using the thin plate spline (TPS) model, and finally applying global TPS interpolation to increase the resolution in the spatial domain. Experiments on 17 human hearts show that the proposed method allows us to obtain higher resolution while reducing noise, preserving details and improving direction coherence (DC) of vector fields as well as fiber tracking. Moreover, the proposed method perfectly reconstructs azimuth and elevation angle maps.

Interpolation algorithm for asynchronous ADC-data

Directory of Open Access Journals (Sweden)

S. Bramburger

2017-09-01

Full Text Available This paper presents a modified interpolation algorithm for signals with variable data rate from asynchronous ADCs. The Adaptive weights Conjugate gradient Toeplitz matrix (ACT algorithm is extended to operate with a continuous data stream. An additional preprocessing of data with constant and linear sections and a weighted overlap of step-by-step into spectral domain transformed signals improve the reconstruction of the asycnhronous ADC signal. The interpolation method can be used if asynchronous ADC data is fed into synchronous digital signal processing.

The Diffraction Response Interpolation Method

DEFF Research Database (Denmark)

Jespersen, Søren Kragh; Wilhjelm, Jens Erik; Pedersen, Peder C.

1998-01-01

Computer modeling of the output voltage in a pulse-echo system is computationally very demanding, particularly whenconsidering reflector surfaces of arbitrary geometry. A new, efficient computational tool, the diffraction response interpolationmethod (DRIM), for modeling of reflectors in a fluid...... medium, is presented. The DRIM is based on the velocity potential impulseresponse method, adapted to pulse-echo applications by the use of acoustical reciprocity. Specifically, the DRIM operates bydividing the reflector surface into planar elements, finding the diffraction response at the corners...

Delimiting areas of endemism through kernel interpolation.

Science.gov (United States)

Oliveira, Ubirajara; Brescovit, Antonio D; Santos, Adalberto J

2015-01-01

We propose a new approach for identification of areas of endemism, the Geographical Interpolation of Endemism (GIE), based on kernel spatial interpolation. This method differs from others in being independent of grid cells. This new approach is based on estimating the overlap between the distribution of species through a kernel interpolation of centroids of species distribution and areas of influence defined from the distance between the centroid and the farthest point of occurrence of each species. We used this method to delimit areas of endemism of spiders from Brazil. To assess the effectiveness of GIE, we analyzed the same data using Parsimony Analysis of Endemism and NDM and compared the areas identified through each method. The analyses using GIE identified 101 areas of endemism of spiders in Brazil GIE demonstrated to be effective in identifying areas of endemism in multiple scales, with fuzzy edges and supported by more synendemic species than in the other methods. The areas of endemism identified with GIE were generally congruent with those identified for other taxonomic groups, suggesting that common processes can be responsible for the origin and maintenance of these biogeographic units.

Delimiting areas of endemism through kernel interpolation.

Directory of Open Access Journals (Sweden)

Ubirajara Oliveira

Full Text Available We propose a new approach for identification of areas of endemism, the Geographical Interpolation of Endemism (GIE, based on kernel spatial interpolation. This method differs from others in being independent of grid cells. This new approach is based on estimating the overlap between the distribution of species through a kernel interpolation of centroids of species distribution and areas of influence defined from the distance between the centroid and the farthest point of occurrence of each species. We used this method to delimit areas of endemism of spiders from Brazil. To assess the effectiveness of GIE, we analyzed the same data using Parsimony Analysis of Endemism and NDM and compared the areas identified through each method. The analyses using GIE identified 101 areas of endemism of spiders in Brazil GIE demonstrated to be effective in identifying areas of endemism in multiple scales, with fuzzy edges and supported by more synendemic species than in the other methods. The areas of endemism identified with GIE were generally congruent with those identified for other taxonomic groups, suggesting that common processes can be responsible for the origin and maintenance of these biogeographic units.

Spline Interpolation of Image

OpenAIRE

I. Kuba; J. Zavacky; J. Mihalik

1995-01-01

This paper presents the use of B spline functions in various digital signal processing applications. The theory of one-dimensional B spline interpolation is briefly reviewed, followed by its extending to two dimensions. After presenting of one and two dimensional spline interpolation, the algorithms of image interpolation and resolution increasing were proposed. Finally, experimental results of computer simulations are presented.

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

Science.gov (United States)

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

Smooth Phase Interpolated Keying

Science.gov (United States)

Borah, Deva K.

2007-01-01

Smooth phase interpolated keying (SPIK) is an improved method of computing smooth phase-modulation waveforms for radio communication systems that convey digital information. SPIK is applicable to a variety of phase-shift-keying (PSK) modulation schemes, including quaternary PSK (QPSK), octonary PSK (8PSK), and 16PSK. In comparison with a related prior method, SPIK offers advantages of better performance and less complexity of implementation. In a PSK scheme, the underlying information waveform that one seeks to convey consists of discrete rectangular steps, but the spectral width of such a waveform is excessive for practical radio communication. Therefore, the problem is to smooth the step phase waveform in such a manner as to maintain power and bandwidth efficiency without incurring an unacceptably large error rate and without introducing undesired variations in the amplitude of the affected radio signal. Although the ideal constellation of PSK phasor points does not cause amplitude variations, filtering of the modulation waveform (in which, typically, a rectangular pulse is converted to a square-root raised cosine pulse) causes amplitude fluctuations. If a power-efficient nonlinear amplifier is used in the radio communication system, the fluctuating-amplitude signal can undergo significant spectral regrowth, thus compromising the bandwidth efficiency of the system. In the related prior method, one seeks to solve the problem in a procedure that comprises two major steps: phase-value generation and phase interpolation. SPIK follows the two-step approach of the related prior method, but the details of the steps are different. In the phase-value-generation step, the phase values of symbols in the PSK constellation are determined by a phase function that is said to be maximally smooth and that is chosen to minimize the spectral spread of the modulated signal. In this step, the constellation is divided into two groups by assigning, to information symbols, phase values

Interpolation-Based Condensation Model Reduction Part 1: Frequency Window Reduction Method Application to Structural Acoustics

National Research Council Canada - National Science Library

Ingel, R

1999-01-01

... (which require derivative information) interpolation functions as well as standard Lagrangian functions, which can be linear, quadratic or cubic, have been used to construct the interpolation windows...

Interpolating precipitation and its relation to runoff and non-point source pollution.

Science.gov (United States)

Chang, Chia-Ling; Lo, Shang-Lien; Yu, Shaw-L

2005-01-01

When rainfall spatially varies, complete rainfall data for each region with different rainfall characteristics are very important. Numerous interpolation methods have been developed for estimating unknown spatial characteristics. However, no interpolation method is suitable for all circumstances. In this study, several methods, including the arithmetic average method, the Thiessen Polygons method, the traditional inverse distance method, and the modified inverse distance method, were used to interpolate precipitation. The modified inverse distance method considers not only horizontal distances but also differences between the elevations of the region with no rainfall records and of its surrounding rainfall stations. The results show that when the spatial variation of rainfall is strong, choosing a suitable interpolation method is very important. If the rainfall is uniform, the precipitation estimated using any interpolation method would be quite close to the actual precipitation. When rainfall is heavy in locations with high elevation, the rainfall changes with the elevation. In this situation, the modified inverse distance method is much more effective than any other method discussed herein for estimating the rainfall input for WinVAST to estimate runoff and non-point source pollution (NPSP). When the spatial variation of rainfall is random, regardless of the interpolation method used to yield rainfall input, the estimation errors of runoff and NPSP are large. Moreover, the relationship between the relative error of the predicted runoff and predicted pollutant loading of SS is high. However, the pollutant concentration is affected by both runoff and pollutant export, so the relationship between the relative error of the predicted runoff and the predicted pollutant concentration of SS may be unstable.

Occlusion-Aware View Interpolation

Directory of Open Access Journals (Sweden)

Ince Serdar

2008-01-01

Full Text Available Abstract View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.

Occlusion-Aware View Interpolation

Directory of Open Access Journals (Sweden)

Janusz Konrad

2009-01-01

Full Text Available View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.

EXAMINATION OF THE VISUAL ACUITY ON THE LCD OPTOTYPE WITH WHOLE-LINE AND INTERPOLATION METHOD

OpenAIRE

Zajíček Tomáš; Veselý Petr; Veselý Petr; Synek Svatopluk; Synek Svatopluk

2012-01-01

The goal of this work is to show the possibility of us using the LCD optotype in common optometrist practice. Furthermore two commonly used methods for measuring visual acuity will be compared. 69 respondents were used for the measurements. The respondents were divided into two groups according to the measured LCD optotype. The visual acuity was measured using the whole-line method on modified Snellen charts as well as the interpolation method on ETDRS charts. Measurements were taken on the S...

Modelo digital do terreno através de diferentes interpolações do programa Surfer 12 | Digital terrain model through different interpolations in the surfer 12 software

Directory of Open Access Journals (Sweden)

José Machado

2016-04-01

the MDT interpolation of measured points is required. The use of TDM, 3D surfaces and contours in moving fast computer programs and can create some problems, such as the type of interpolation used. This work aims to analyze the interpolation methods in points quoted from an irregular geometric figure generated by the Surfer program. They used 12 interpolations available (Data Metrics, Inverse Distance, Kriging, Local Polynomial, Minimum Curvature, Modified Shepard Method, Moving Average, Natural Neighbor, Nearest Neighbor, Polynomial Regression, Radial fuction and Triangulation with Linear Interpolation and analyzed the generated topographic maps. The relief was generated graphical representation via the MDT. They were awarded the excellent concepts, excellent, good, average and bad representation of relief and discussed according Relief representations to the listed geometric image. Data Metrics, Polynomial Regression, Moving Average e Local Polynomial (bad; Moving Average e Modified Shepard Method (regular; Nearest Neighbor (media; Inverse Distance (good; Kriging e Radial Function (great e Triangulation With Linear Interpolation e Natural Neighbor (excellent conditions to representation presented dates.

Efficient Algorithms and Design for Interpolation Filters in Digital Receiver

Directory of Open Access Journals (Sweden)

Xiaowei Niu

2014-05-01

Full Text Available Based on polynomial functions this paper introduces a generalized design method for interpolation filters. The polynomial-based interpolation filters can be implemented efficiently by using a modified Farrow structure with an arbitrary frequency response, the filters allow many pass- bands and stop-bands, and for each band the desired amplitude and weight can be set arbitrarily. The optimization coefficients of the interpolation filters in time domain are got by minimizing the weighted mean squared error function, then converting to solve the quadratic programming problem. The optimization coefficients in frequency domain are got by minimizing the maxima (MiniMax of the weighted mean squared error function. The degree of polynomials and the length of interpolation filter can be selected arbitrarily. Numerical examples verified the proposed design method not only can reduce the hardware cost effectively but also guarantee an excellent performance.

Solving eigenvalue problems on curved surfaces using the Closest Point Method

KAUST Repository

Macdonald, Colin B.

2011-06-01

Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach. © 2011 Elsevier Inc.

Multi-dimensional cubic interpolation for ICF hydrodynamics simulation

International Nuclear Information System (INIS)

Aoki, Takayuki; Yabe, Takashi.

1991-04-01

A new interpolation method is proposed to solve the multi-dimensional hyperbolic equations which appear in describing the hydrodynamics of inertial confinement fusion (ICF) implosion. The advection phase of the cubic-interpolated pseudo-particle (CIP) is greatly improved, by assuming the continuities of the second and the third spatial derivatives in addition to the physical value and the first derivative. These derivatives are derived from the given physical equation. In order to evaluate the new method, Zalesak's example is tested, and we obtain successfully good results. (author)

Wideband DOA Estimation through Projection Matrix Interpolation

OpenAIRE

Selva, J.

2017-01-01

This paper presents a method to reduce the complexity of the deterministic maximum likelihood (DML) estimator in the wideband direction-of-arrival (WDOA) problem, which is based on interpolating the array projection matrix in the temporal frequency variable. It is shown that an accurate interpolator like Chebyshev's is able to produce DML cost functions comprising just a few narrowband-like summands. Actually, the number of such summands is far smaller (roughly by factor ten in the numerical ...

Securing Body Sensor Networks with Biometric Methods: A New Key Negotiation Method and a Key Sampling Method for Linear Interpolation Encryption

OpenAIRE

Zhao, Huawei; Chen, Chi; Hu, Jiankun; Qin, Jing

2015-01-01

We present two approaches that exploit biometric data to address security problems in the body sensor networks: a new key negotiation scheme based on the fuzzy extractor technology and an improved linear interpolation encryption method. The first approach designs two attack games to give the formal definition of fuzzy negotiation that forms a new key negotiation scheme based on fuzzy extractor technology. According to the definition, we further define a concrete structure of fuzzy negotiation...

Spectral interpolation - Zero fill or convolution. [image processing

Science.gov (United States)

Forman, M. L.

1977-01-01

Zero fill, or augmentation by zeros, is a method used in conjunction with fast Fourier transforms to obtain spectral spacing at intervals closer than obtainable from the original input data set. In the present paper, an interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies. The technique is shown to operate faster than zero fill, since fewer operations are required. The major advantages of interpolation by repetitive convolution are that efficient use of memory is possible (thus avoiding the difficulties encountered in decimation in time FFTs) and that is is easy to implement.

The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces

KAUST Repository

Chen, Yujia

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. Elliptic partial differential equations are important from both application and analysis points of view. In this paper we apply the closest point method to solve elliptic equations on general curved surfaces. Based on the closest point representation of the underlying surface, we formulate an embedding equation for the surface elliptic problem, then discretize it using standard finite differences and interpolation schemes on banded but uniform Cartesian grids. We prove the convergence of the difference scheme for the Poisson\\'s equation on a smooth closed curve. In order to solve the resulting large sparse linear systems, we propose a specific geometric multigrid method in the setting of the closest point method. Convergence studies in both the accuracy of the difference scheme and the speed of the multigrid algorithm show that our approaches are effective.

Interpolating string field theories

International Nuclear Information System (INIS)

Zwiebach, B.

1992-01-01

This paper reports that a minimal area problem imposing different length conditions on open and closed curves is shown to define a one-parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten's open string field theory capable of incorporating on shell closed strings. The string diagrams of the latter define a new decomposition of the moduli spaces of Riemann surfaces with punctures and boundaries based on quadratic differentials with both first order and second order poles

Interpolation Approaches for Characterizing Spatial Variability of Soil Properties in Tuz Lake Basin of Turkey

Science.gov (United States)

Gorji, Taha; Sertel, Elif; Tanik, Aysegul

2017-12-01

Soil management is an essential concern in protecting soil properties, in enhancing appropriate soil quality for plant growth and agricultural productivity, and in preventing soil erosion. Soil scientists and decision makers require accurate and well-distributed spatially continuous soil data across a region for risk assessment and for effectively monitoring and managing soils. Recently, spatial interpolation approaches have been utilized in various disciplines including soil sciences for analysing, predicting and mapping distribution and surface modelling of environmental factors such as soil properties. The study area selected in this research is Tuz Lake Basin in Turkey bearing ecological and economic importance. Fertile soil plays a significant role in agricultural activities, which is one of the main industries having great impact on economy of the region. Loss of trees and bushes due to intense agricultural activities in some parts of the basin lead to soil erosion. Besides, soil salinization due to both human-induced activities and natural factors has exacerbated its condition regarding agricultural land development. This study aims to compare capability of Local Polynomial Interpolation (LPI) and Radial Basis Functions (RBF) as two interpolation methods for mapping spatial pattern of soil properties including organic matter, phosphorus, lime and boron. Both LPI and RBF methods demonstrated promising results for predicting lime, organic matter, phosphorous and boron. Soil samples collected in the field were used for interpolation analysis in which approximately 80% of data was used for interpolation modelling whereas the remaining for validation of the predicted results. Relationship between validation points and their corresponding estimated values in the same location is examined by conducting linear regression analysis. Eight prediction maps generated from two different interpolation methods for soil organic matter, phosphorus, lime and boron parameters

Trace interpolation by slant-stack migration

International Nuclear Information System (INIS)

Novotny, M.

1990-01-01

The slant-stack migration formula based on the radon transform is studied with respect to the depth steep Δz of wavefield extrapolation. It can be viewed as a generalized trace-interpolation procedure including wave extrapolation with an arbitrary step Δz. For Δz > 0 the formula yields the familiar plane-wave decomposition, while for Δz > 0 it provides a robust tool for migration transformation of spatially under sampled wavefields. Using the stationary phase method, it is shown that the slant-stack migration formula degenerates into the Rayleigh-Sommerfeld integral in the far-field approximation. Consequently, even a narrow slant-stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period

Interpolation functors and interpolation spaces

CERN Document Server

Brudnyi, Yu A

1991-01-01

The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the r...

Improvements in Off Design Aeroengine Performance Prediction Using Analytic Compressor Map Interpolation

Science.gov (United States)

Mist'e, Gianluigi Alberto; Benini, Ernesto

2012-06-01

Compressor map interpolation is usually performed through the introduction of auxiliary coordinates (β). In this paper, a new analytical bivariate β function definition to be used in compressor map interpolation is studied. The function has user-defined parameters that must be adjusted to properly fit to a single map. The analytical nature of β allows for rapid calculations of the interpolation error estimation, which can be used as a quantitative measure of interpolation accuracy and also as a valid tool to compare traditional β function interpolation with new approaches (artificial neural networks, genetic algorithms, etc.). The quality of the method is analyzed by comparing the error output to the one of a well-known state-of-the-art methodology. This comparison is carried out for two different types of compressor and, in both cases, the error output using the method presented in this paper is found to be consistently lower. Moreover, an optimization routine able to locally minimize the interpolation error by shape variation of the β function is implemented. Further optimization introducing other important criteria is discussed.

A fast and accurate dihedral interpolation loop subdivision scheme

Science.gov (United States)

Shi, Zhuo; An, Yalei; Wang, Zhongshuai; Yu, Ke; Zhong, Si; Lan, Rushi; Luo, Xiaonan

2018-04-01

In this paper, we propose a fast and accurate dihedral interpolation Loop subdivision scheme for subdivision surfaces based on triangular meshes. In order to solve the problem of surface shrinkage, we keep the limit condition unchanged, which is important. Extraordinary vertices are handled using modified Butterfly rules. Subdivision schemes are computationally costly as the number of faces grows exponentially at higher levels of subdivision. To address this problem, our approach is to use local surface information to adaptively refine the model. This is achieved simply by changing the threshold value of the dihedral angle parameter, i.e., the angle between the normals of a triangular face and its adjacent faces. We then demonstrate the effectiveness of the proposed method for various 3D graphic triangular meshes, and extensive experimental results show that it can match or exceed the expected results at lower computational cost.

Interpolation methods for creating a scatter radiation exposure map

International Nuclear Information System (INIS)

Gonçalves, Elicardo A. de S.; Gomes, Celio S.; Lopes, Ricardo T.; Oliveira, Luis F. de; Anjos, Marcelino J. dos; Oliveira, Davi F.

2017-01-01

A well know way for best comprehension of radiation scattering during a radiography is to map exposure over the space around the source and sample. This map is done measuring exposure in points regularly spaced, it means, measurement will be placed in localization chosen by increasing a regular steps from a starting point, along the x, y and z axes or even radial and angular coordinates. However, it is not always possible to maintain the accuracy of the steps throughout the entire space, or there will be regions of difficult access where the regularity of the steps will be impaired. This work intended to use some interpolation techniques that work with irregular steps, and to compare their results and their limits. It was firstly done angular coordinates, and tested in lack of some points. Later, in the same data was performed the Delaunay tessellation interpolation ir order to compare. Computational and graphic treatments was done with the GNU OCTAVE software and its image-processing package. Real data was acquired from a bunker where a 6 MeV betatron can be used to produce radiation scattering. (author)

Interpolation methods for creating a scatter radiation exposure map

Energy Technology Data Exchange (ETDEWEB)

Gonçalves, Elicardo A. de S., E-mail: elicardo.goncalves@ifrj.edu.br [Instituto Federal do Rio de Janeiro (IFRJ), Paracambi, RJ (Brazil); Gomes, Celio S.; Lopes, Ricardo T. [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Oliveira, Luis F. de; Anjos, Marcelino J. dos; Oliveira, Davi F. [Universidade do Estado do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto de Física

2017-07-01

A well know way for best comprehension of radiation scattering during a radiography is to map exposure over the space around the source and sample. This map is done measuring exposure in points regularly spaced, it means, measurement will be placed in localization chosen by increasing a regular steps from a starting point, along the x, y and z axes or even radial and angular coordinates. However, it is not always possible to maintain the accuracy of the steps throughout the entire space, or there will be regions of difficult access where the regularity of the steps will be impaired. This work intended to use some interpolation techniques that work with irregular steps, and to compare their results and their limits. It was firstly done angular coordinates, and tested in lack of some points. Later, in the same data was performed the Delaunay tessellation interpolation ir order to compare. Computational and graphic treatments was done with the GNU OCTAVE software and its image-processing package. Real data was acquired from a bunker where a 6 MeV betatron can be used to produce radiation scattering. (author)

A Note on Cubic Convolution Interpolation

OpenAIRE

Meijering, E.; Unser, M.

2003-01-01

We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing.

Economic method for helical gear flank surface characterisation

Science.gov (United States)

Koulin, G.; Reavie, T.; Frazer, R. C.; Shaw, B. A.

2018-03-01

Typically the quality of a gear pair is assessed based on simplified geometric tolerances which do not always correlate with functional performance. In order to identify and quantify functional performance based parameters, further development of the gear measurement approach is required. Methodology for interpolation of the full active helical gear flank surface, from sparse line measurements, is presented. The method seeks to identify the minimum number of line measurements required to sufficiently characterise an active gear flank. In the form ground gear example presented, a single helix and three profile line measurements was considered to be acceptable. The resulting surfaces can be used to simulate the meshing engagement of a gear pair and therefore provide insight into functional performance based parameters. Therefore the assessment of the quality can be based on the predicted performance in the context of an application.

Patch-based frame interpolation for old films via the guidance of motion paths

Science.gov (United States)

Xia, Tianran; Ding, Youdong; Yu, Bing; Huang, Xi

2018-04-01

Due to improper preservation, traditional films will appear frame loss after digital. To deal with this problem, this paper presents a new adaptive patch-based method of frame interpolation via the guidance of motion paths. Our method is divided into three steps. Firstly, we compute motion paths between two reference frames using optical flow estimation. Then, the adaptive bidirectional interpolation with holes filled is applied to generate pre-intermediate frames. Finally, using patch match to interpolate intermediate frames with the most similar patches. Since the patch match is based on the pre-intermediate frames that contain the motion paths constraint, we show a natural and inartificial frame interpolation. We test different types of old film sequences and compare with other methods, the results prove that our method has a desired performance without hole or ghost effects.

Preprocessor with spline interpolation for converting stereolithography into cutter location source data

Science.gov (United States)

Nagata, Fusaomi; Okada, Yudai; Sakamoto, Tatsuhiko; Kusano, Takamasa; Habib, Maki K.; Watanabe, Keigo

2017-06-01

The authors have developed earlier an industrial machining robotic system for foamed polystyrene materials. The developed robotic CAM system provided a simple and effective interface without the need to use any robot language between operators and the machining robot. In this paper, a preprocessor for generating Cutter Location Source data (CLS data) from Stereolithography (STL data) is first proposed for robotic machining. The preprocessor enables to control the machining robot directly using STL data without using any commercially provided CAM system. The STL deals with a triangular representation for a curved surface geometry. The preprocessor allows machining robots to be controlled through a zigzag or spiral path directly calculated from STL data. Then, a smart spline interpolation method is proposed and implemented for smoothing coarse CLS data. The effectiveness and potential of the developed approaches are demonstrated through experiments on actual machining and interpolation.

Lagrange polynomial interpolation method applied in the calculation of the J({xi},{beta}) function

Energy Technology Data Exchange (ETDEWEB)

Fraga, Vinicius Munhoz; Palma, Daniel Artur Pinheiro [Centro Federal de Educacao Tecnologica de Quimica de Nilopolis, RJ (Brazil)]. E-mails: munhoz.vf@gmail.com; dpalma@cefeteq.br; Martinez, Aquilino Senra [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE) (COPPE). Programa de Engenharia Nuclear]. E-mail: aquilino@lmp.ufrj.br

2008-07-01

The explicit dependence of the Doppler broadening function creates difficulties in the obtaining an analytical expression for J function . The objective of this paper is to present a method for the quick and accurate calculation of J function based on the recent advances in the calculation of the Doppler broadening function and on a systematic analysis of its integrand. The methodology proposed, of a semi-analytical nature, uses the Lagrange polynomial interpolation method and the Frobenius formulation in the calculation of Doppler broadening function . The results have proven satisfactory from the standpoint of accuracy and processing time. (author)

Lagrange polynomial interpolation method applied in the calculation of the J(ξ,β) function

International Nuclear Information System (INIS)

Fraga, Vinicius Munhoz; Palma, Daniel Artur Pinheiro; Martinez, Aquilino Senra

2008-01-01

The explicit dependence of the Doppler broadening function creates difficulties in the obtaining an analytical expression for J function . The objective of this paper is to present a method for the quick and accurate calculation of J function based on the recent advances in the calculation of the Doppler broadening function and on a systematic analysis of its integrand. The methodology proposed, of a semi-analytical nature, uses the Lagrange polynomial interpolation method and the Frobenius formulation in the calculation of Doppler broadening function . The results have proven satisfactory from the standpoint of accuracy and processing time. (author)

Interpolation of polytopic control Lyapunov functions for discrete–time linear systems

NARCIS (Netherlands)

Nguyen, T.T.; Lazar, M.; Spinu, V.; Boje, E.; Xia, X.

2014-01-01

This paper proposes a method for interpolating two (or more) polytopic control Lyapunov functions (CLFs) for discrete--time linear systems subject to polytopic constraints, thereby combining different control objectives. The corresponding interpolated CLF is used for synthesis of a stabilizing

An improved local radial point interpolation method for transient heat conduction analysis

Science.gov (United States)

Wang, Feng; Lin, Gao; Zheng, Bao-Jing; Hu, Zhi-Qiang

2013-06-01

The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions.

An improved local radial point interpolation method for transient heat conduction analysis

International Nuclear Information System (INIS)

Wang Feng; Lin Gao; Hu Zhi-Qiang; Zheng Bao-Jing

2013-01-01

The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions

Research of the effectiveness of parallel multithreaded realizations of interpolation methods for scaling raster images

Science.gov (United States)

Vnukov, A. A.; Shershnev, M. B.

2018-01-01

The aim of this work is the software implementation of three image scaling algorithms using parallel computations, as well as the development of an application with a graphical user interface for the Windows operating system to demonstrate the operation of algorithms and to study the relationship between system performance, algorithm execution time and the degree of parallelization of computations. Three methods of interpolation were studied, formalized and adapted to scale images. The result of the work is a program for scaling images by different methods. Comparison of the quality of scaling by different methods is given.

Fast dose kernel interpolation using Fourier transform with application to permanent prostate brachytherapy dosimetry.

Science.gov (United States)

Liu, Derek; Sloboda, Ron S

2014-05-01

Boyer and Mok proposed a fast calculation method employing the Fourier transform (FT), for which calculation time is independent of the number of seeds but seed placement is restricted to calculation grid points. Here an interpolation method is described enabling unrestricted seed placement while preserving the computational efficiency of the original method. The Iodine-125 seed dose kernel was sampled and selected values were modified to optimize interpolation accuracy for clinically relevant doses. For each seed, the kernel was shifted to the nearest grid point via convolution with a unit impulse, implemented in the Fourier domain. The remaining fractional shift was performed using a piecewise third-order Lagrange filter. Implementation of the interpolation method greatly improved FT-based dose calculation accuracy. The dose distribution was accurate to within 2% beyond 3 mm from each seed. Isodose contours were indistinguishable from explicit TG-43 calculation. Dose-volume metric errors were negligible. Computation time for the FT interpolation method was essentially the same as Boyer's method. A FT interpolation method for permanent prostate brachytherapy TG-43 dose calculation was developed which expands upon Boyer's original method and enables unrestricted seed placement. The proposed method substantially improves the clinically relevant dose accuracy with negligible additional computation cost, preserving the efficiency of the original method.

The Convergence Acceleration of Two-Dimensional Fourier Interpolation

Directory of Open Access Journals (Sweden)

Anry Nersessian

2008-07-01

Full Text Available Hereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.

Image Interpolation with Geometric Contour Stencils

Directory of Open Access Journals (Sweden)

Pascal Getreuer

2011-09-01

Full Text Available We consider the image interpolation problem where given an image vm,n with uniformly-sampled pixels vm,n and point spread function h, the goal is to find function u(x,y satisfying vm,n = (h*u(m,n for all m,n in Z. This article improves upon the IPOL article Image Interpolation with Contour Stencils. In the previous work, contour stencils are used to estimate the image contours locally as short line segments. This article begins with a continuous formulation of total variation integrated over a collection of curves and defines contour stencils as a consistent discretization. This discretization is more reliable than the previous approach and can effectively distinguish contours that are locally shaped like lines, curves, corners, and circles. These improved contour stencils sense more of the geometry in the image. Interpolation is performed using an extension of the method described in the previous article. Using the improved contour stencils, there is an increase in image quality while maintaining similar computational efficiency.

MAGIC: A Tool for Combining, Interpolating, and Processing Magnetograms

Science.gov (United States)

Allred, Joel

2012-01-01

Transients in the solar coronal magnetic field are ultimately the source of space weather. Models which seek to track the evolution of the coronal field require magnetogram images to be used as boundary conditions. These magnetograms are obtained by numerous instruments with different cadences and resolutions. A tool is required which allows modelers to fmd all available data and use them to craft accurate and physically consistent boundary conditions for their models. We have developed a software tool, MAGIC (MAGnetogram Interpolation and Composition), to perform exactly this function. MAGIC can manage the acquisition of magneto gram data, cast it into a source-independent format, and then perform the necessary spatial and temporal interpolation to provide magnetic field values as requested onto model-defined grids. MAGIC has the ability to patch magneto grams from different sources together providing a more complete picture of the Sun's field than is possible from single magneto grams. In doing this, care must be taken so as not to introduce nonphysical current densities along the seam between magnetograms. We have designed a method which minimizes these spurious current densities. MAGIC also includes a number of post-processing tools which can provide additional information to models. For example, MAGIC includes an interface to the DA VE4VM tool which derives surface flow velocities from the time evolution of surface magnetic field. MAGIC has been developed as an application of the KAMELEON data formatting toolkit which has been developed by the CCMC.

Wavelet-Smoothed Interpolation of Masked Scientific Data for JPEG 2000 Compression

Energy Technology Data Exchange (ETDEWEB)

Brislawn, Christopher M. [Los Alamos National Laboratory

2012-08-13

How should we manage scientific data with 'holes'? Some applications, like JPEG 2000, expect logically rectangular data, but some sources, like the Parallel Ocean Program (POP), generate data that isn't defined on certain subsets. We refer to grid points that lack well-defined, scientifically meaningful sample values as 'masked' samples. Wavelet-smoothing is a highly scalable interpolation scheme for regions with complex boundaries on logically rectangular grids. Computation is based on forward/inverse discrete wavelet transforms, so runtime complexity and memory scale linearly with respect to sample count. Efficient state-of-the-art minimal realizations yield small constants (O(10)) for arithmetic complexity scaling, and in-situ implementation techniques make optimal use of memory. Implementation in two dimensions using tensor product filter banks is straighsorward and should generalize routinely to higher dimensions. No hand-tuning required when the interpolation mask changes, making the method aeractive for problems with time-varying masks. Well-suited for interpolating undefined samples prior to JPEG 2000 encoding. The method outperforms global mean interpolation, as judged by both SNR rate-distortion performance and low-rate artifact mitigation, for data distributions whose histograms do not take the form of sharply peaked, symmetric, unimodal probability density functions. These performance advantages can hold even for data whose distribution differs only moderately from the peaked unimodal case, as demonstrated by POP salinity data. The interpolation method is very general and is not tied to any particular class of applications, could be used for more generic smooth interpolation.

Estimating monthly temperature using point based interpolation techniques

Science.gov (United States)

Saaban, Azizan; Mah Hashim, Noridayu; Murat, Rusdi Indra Zuhdi

2013-04-01

This paper discusses the use of point based interpolation to estimate the value of temperature at an unallocated meteorology stations in Peninsular Malaysia using data of year 2010 collected from the Malaysian Meteorology Department. Two point based interpolation methods which are Inverse Distance Weighted (IDW) and Radial Basis Function (RBF) are considered. The accuracy of the methods is evaluated using Root Mean Square Error (RMSE). The results show that RBF with thin plate spline model is suitable to be used as temperature estimator for the months of January and December, while RBF with multiquadric model is suitable to estimate the temperature for the rest of the months.

Efficient and Adaptive Methods for Computing Accurate Potential Surfaces for Quantum Nuclear Effects: Applications to Hydrogen-Transfer Reactions.

Science.gov (United States)

DeGregorio, Nicole; Iyengar, Srinivasan S

2018-01-09

We present two sampling measures to gauge critical regions of potential energy surfaces. These sampling measures employ (a) the instantaneous quantum wavepacket density, an approximation to the (b) potential surface, its (c) gradients, and (d) a Shannon information theory based expression that estimates the local entropy associated with the quantum wavepacket. These four criteria together enable a directed sampling of potential surfaces that appears to correctly describe the local oscillation frequencies, or the local Nyquist frequency, of a potential surface. The sampling functions are then utilized to derive a tessellation scheme that discretizes the multidimensional space to enable efficient sampling of potential surfaces. The sampled potential surface is then combined with four different interpolation procedures, namely, (a) local Hermite curve interpolation, (b) low-pass filtered Lagrange interpolation, (c) the monomial symmetrization approximation (MSA) developed by Bowman and co-workers, and (d) a modified Shepard algorithm. The sampling procedure and the fitting schemes are used to compute (a) potential surfaces in highly anharmonic hydrogen-bonded systems and (b) study hydrogen-transfer reactions in biogenic volatile organic compounds (isoprene) where the transferring hydrogen atom is found to demonstrate critical quantum nuclear effects. In the case of isoprene, the algorithm discussed here is used to derive multidimensional potential surfaces along a hydrogen-transfer reaction path to gauge the effect of quantum-nuclear degrees of freedom on the hydrogen-transfer process. Based on the decreased computational effort, facilitated by the optimal sampling of the potential surfaces through the use of sampling functions discussed here, and the accuracy of the associated potential surfaces, we believe the method will find great utility in the study of quantum nuclear dynamics problems, of which application to hydrogen-transfer reactions and hydrogen

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology

Science.gov (United States)

Allen, P. A.; Wells, D. N.

2013-01-01

No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.

Edge-detect interpolation for direct digital periapical images

International Nuclear Information System (INIS)

Song, Nam Kyu; Koh, Kwang Joon

1998-01-01

The purpose of this study was to aid in the use of the digital images by edge-detect interpolation for direct digital periapical images using edge-deted interpolation. This study was performed by image processing of 20 digital periapical images; pixel replication, linear non-interpolation, linear interpolation, and edge-sensitive interpolation. The obtained results were as follows ; 1. Pixel replication showed blocking artifact and serious image distortion. 2. Linear interpolation showed smoothing effect on the edge. 3. Edge-sensitive interpolation overcame the smoothing effect on the edge and showed better image.

Enhancement of low sampling frequency recordings for ECG biometric matching using interpolation.

Science.gov (United States)

Sidek, Khairul Azami; Khalil, Ibrahim

2013-01-01

Electrocardiogram (ECG) based biometric matching suffers from high misclassification error with lower sampling frequency data. This situation may lead to an unreliable and vulnerable identity authentication process in high security applications. In this paper, quality enhancement techniques for ECG data with low sampling frequency has been proposed for person identification based on piecewise cubic Hermite interpolation (PCHIP) and piecewise cubic spline interpolation (SPLINE). A total of 70 ECG recordings from 4 different public ECG databases with 2 different sampling frequencies were applied for development and performance comparison purposes. An analytical method was used for feature extraction. The ECG recordings were segmented into two parts: the enrolment and recognition datasets. Three biometric matching methods, namely, Cross Correlation (CC), Percent Root-Mean-Square Deviation (PRD) and Wavelet Distance Measurement (WDM) were used for performance evaluation before and after applying interpolation techniques. Results of the experiments suggest that biometric matching with interpolated ECG data on average achieved higher matching percentage value of up to 4% for CC, 3% for PRD and 94% for WDM. These results are compared with the existing method when using ECG recordings with lower sampling frequency. Moreover, increasing the sample size from 56 to 70 subjects improves the results of the experiment by 4% for CC, 14.6% for PRD and 0.3% for WDM. Furthermore, higher classification accuracy of up to 99.1% for PCHIP and 99.2% for SPLINE with interpolated ECG data as compared of up to 97.2% without interpolation ECG data verifies the study claim that applying interpolation techniques enhances the quality of the ECG data. Crown Copyright © 2012. Published by Elsevier Ireland Ltd. All rights reserved.

Interpolation of rational matrix functions

CERN Document Server

Ball, Joseph A; Rodman, Leiba

1990-01-01

This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an indepe...

C1 Rational Quadratic Trigonometric Interpolation Spline for Data Visualization

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Shengjun Liu

2015-01-01

Full Text Available A new C1 piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated as O(h3. Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.

Comparison of Spatial Interpolation Schemes for Rainfall Data and Application in Hydrological Modeling

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Tao Chen

2017-05-01

Full Text Available The spatial distribution of precipitation is an important aspect of water-related research. The use of different interpolation schemes in the same catchment may cause large differences and deviations from the actual spatial distribution of rainfall. Our study analyzes different methods of spatial rainfall interpolation at annual, daily, and hourly time scales to provide a comprehensive evaluation. An improved regression-based scheme is proposed using principal component regression with residual correction (PCRR and is compared with inverse distance weighting (IDW and multiple linear regression (MLR interpolation methods. In this study, the meso-scale catchment of the Fuhe River in southeastern China was selected as a typical region. Furthermore, a hydrological model HEC-HMS was used to calculate streamflow and to evaluate the impact of rainfall interpolation methods on the results of the hydrological model. Results show that the PCRR method performed better than the other methods tested in the study and can effectively eliminate the interpolation anomalies caused by terrain differences between observation points and surrounding areas. Simulated streamflow showed different characteristics based on the mean, maximum, minimum, and peak flows. The results simulated by PCRR exhibited the lowest streamflow error and highest correlation with measured values at the daily time scale. The application of the PCRR method is found to be promising because it considers multicollinearity among variables.

Data interpolation for vibration diagnostics using two-variable correlations

International Nuclear Information System (INIS)

Branagan, L.

1991-01-01

This paper reports that effective machinery vibration diagnostics require a clear differentiation between normal vibration changes caused by plant process conditions and those caused by degradation. The normal relationship between vibration and a process parameter can be quantified by developing the appropriate correlation. The differences in data acquisition requirements between dynamic signals (vibration spectra) and static signals (pressure, temperature, etc.) result in asynchronous data acquisition; the development of any correlation must then be based on some form of interpolated data. This interpolation can reproduce or distort the original measured quantity depending on the characteristics of the data and the interpolation technique. Relevant data characteristics, such as acquisition times, collection cycle times, compression method, storage rate, and the slew rate of the measured variable, are dependent both on the data handling and on the measured variable. Linear and staircase interpolation, along with the use of clustering and filtering, provide the necessary options to develop accurate correlations. The examples illustrate the appropriate application of these options

Validation study of an interpolation method for calculating whole lung volumes and masses from reduced numbers of CT-images in ponies.

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Reich, H; Moens, Y; Braun, C; Kneissl, S; Noreikat, K; Reske, A

2014-12-01

Quantitative computer tomographic analysis (qCTA) is an accurate but time intensive method used to quantify volume, mass and aeration of the lungs. The aim of this study was to validate a time efficient interpolation technique for application of qCTA in ponies. Forty-one thoracic computer tomographic (CT) scans obtained from eight anaesthetised ponies positioned in dorsal recumbency were included. Total lung volume and mass and their distribution into four compartments (non-aerated, poorly aerated, normally aerated and hyperaerated; defined based on the attenuation in Hounsfield Units) were determined for the entire lung from all 5 mm thick CT-images, 59 (55-66) per animal. An interpolation technique validated for use in humans was then applied to calculate qCTA results for lung volumes and masses from only 10, 12, and 14 selected CT-images per scan. The time required for both procedures was recorded. Results were compared statistically using the Bland-Altman approach. The bias ± 2 SD for total lung volume calculated from interpolation of 10, 12, and 14 CT-images was -1.2 ± 5.8%, 0.1 ± 3.5%, and 0.0 ± 2.5%, respectively. The corresponding results for total lung mass were -1.1 ± 5.9%, 0.0 ± 3.5%, and 0.0 ± 3.0%. The average time for analysis of one thoracic CT-scan using the interpolation method was 1.5-2 h compared to 8 h for analysis of all images of one complete thoracic CT-scan. The calculation of pulmonary qCTA data by interpolation from 12 CT-images was applicable for equine lung CT-scans and reduced the time required for analysis by 75%. Copyright © 2014 Elsevier Ltd. All rights reserved.

Fast digital zooming system using directionally adaptive image interpolation and restoration.

Science.gov (United States)

Kang, Wonseok; Jeon, Jaehwan; Yu, Soohwan; Paik, Joonki

2014-01-01

This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then selectively used according to the refined edge orientation for removing jagged artifacts in the slanted edge region. A novel image restoration algorithm is also presented for removing blurring artifacts caused by the linear or cubic-spline interpolation using the directionally adaptive truncated constrained least squares (TCLS) filter. Both proposed steerable filter-based interpolation and the TCLS-based restoration filters have a finite impulse response (FIR) structure for real time processing in an image signal processing (ISP) chain. Experimental results show that the proposed digital zooming system provides high-quality magnified images with FIR filter-based fast computational structure.

An integral conservative gridding--algorithm using Hermitian curve interpolation.

Science.gov (United States)

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K

2008-11-07

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to

An integral conservative gridding-algorithm using Hermitian curve interpolation

International Nuclear Information System (INIS)

Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K

2008-01-01

The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to

Generalized interpolative quantum statistics

International Nuclear Information System (INIS)

Ramanathan, R.

1992-01-01

A generalized interpolative quantum statistics is presented by conjecturing a certain reordering of phase space due to the presence of possible exotic objects other than bosons and fermions. Such an interpolation achieved through a Bose-counting strategy predicts the existence of an infinite quantum Boltzmann-Gibbs statistics akin to the one discovered by Greenberg recently

Adapting Better Interpolation Methods to Model Amphibious MT Data Along the Cascadian Subduction Zone.

Science.gov (United States)

Parris, B. A.; Egbert, G. D.; Key, K.; Livelybrooks, D.

2016-12-01

Magnetotellurics (MT) is an electromagnetic technique used to model the inner Earth's electrical conductivity structure. MT data can be analyzed using iterative, linearized inversion techniques to generate models imaging, in particular, conductive partial melts and aqueous fluids that play critical roles in subduction zone processes and volcanism. For example, the Magnetotelluric Observations of Cascadia using a Huge Array (MOCHA) experiment provides amphibious data useful for imaging subducted fluids from trench to mantle wedge corner. When using MOD3DEM(Egbert et al. 2012), a finite difference inversion package, we have encountered problems inverting, particularly, sea floor stations due to the strong, nearby conductivity gradients. As a work-around, we have found that denser, finer model grids near the land-sea interface produce better inversions, as characterized by reduced data residuals. This is partly to be due to our ability to more accurately capture topography and bathymetry. We are experimenting with improved interpolation schemes that more accurately track EM fields across cell boundaries, with an eye to enhancing the accuracy of the simulated responses and, thus, inversion results. We are adapting how MOD3DEM interpolates EM fields in two ways. The first seeks to improve weighting functions for interpolants to better address current continuity across grid boundaries. Electric fields are interpolated using a tri-linear spline technique, where the eight nearest electrical field estimates are each given weights determined by the technique, a kind of weighted average. We are modifying these weights to include cross-boundary conductivity ratios to better model current continuity. We are also adapting some of the techniques discussed in Shantsev et al (2014) to enhance the accuracy of the interpolated fields calculated by our forward solver, as well as to better approximate the sensitivities passed to the software's Jacobian that are used to generate a new

Spatial interpolation schemes of daily precipitation for hydrologic modeling

Science.gov (United States)

Hwang, Y.; Clark, M.R.; Rajagopalan, B.; Leavesley, G.

2012-01-01

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs. ?? 2011 Springer-Verlag.

Importance of interpolation and coincidence errors in data fusion

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S. Ceccherini

2018-02-01

Full Text Available The complete data fusion (CDF method is applied to ozone profiles obtained from simulated measurements in the ultraviolet and in the thermal infrared in the framework of the Sentinel 4 mission of the Copernicus programme. We observe that the quality of the fused products is degraded when the fusing profiles are either retrieved on different vertical grids or referred to different true profiles. To address this shortcoming, a generalization of the complete data fusion method, which takes into account interpolation and coincidence errors, is presented. This upgrade overcomes the encountered problems and provides products of good quality when the fusing profiles are both retrieved on different vertical grids and referred to different true profiles. The impact of the interpolation and coincidence errors on number of degrees of freedom and errors of the fused profile is also analysed. The approach developed here to account for the interpolation and coincidence errors can also be followed to include other error components, such as forward model errors.

Importance of interpolation and coincidence errors in data fusion

Science.gov (United States)

Ceccherini, Simone; Carli, Bruno; Tirelli, Cecilia; Zoppetti, Nicola; Del Bianco, Samuele; Cortesi, Ugo; Kujanpää, Jukka; Dragani, Rossana

2018-02-01

The complete data fusion (CDF) method is applied to ozone profiles obtained from simulated measurements in the ultraviolet and in the thermal infrared in the framework of the Sentinel 4 mission of the Copernicus programme. We observe that the quality of the fused products is degraded when the fusing profiles are either retrieved on different vertical grids or referred to different true profiles. To address this shortcoming, a generalization of the complete data fusion method, which takes into account interpolation and coincidence errors, is presented. This upgrade overcomes the encountered problems and provides products of good quality when the fusing profiles are both retrieved on different vertical grids and referred to different true profiles. The impact of the interpolation and coincidence errors on number of degrees of freedom and errors of the fused profile is also analysed. The approach developed here to account for the interpolation and coincidence errors can also be followed to include other error components, such as forward model errors.

Evaluation of various interpolants available in DICE

Energy Technology Data Exchange (ETDEWEB)

Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Reu, Phillip L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Crozier, Paul [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-02-01

This report evaluates several interpolants implemented in the Digital Image Correlation Engine (DICe), an image correlation software package developed by Sandia. By interpolants we refer to the basis functions used to represent discrete pixel intensity data as a continuous signal. Interpolation is used to determine intensity values in an image at non - pixel locations. It is also used, in some cases, to evaluate the x and y gradients of the image intensities. Intensity gradients subsequently guide the optimization process. The goal of this report is to inform analysts as to the characteristics of each interpolant and provide guidance towards the best interpolant for a given dataset. This work also serves as an initial verification of each of the interpolants implemented.

Multivariate Birkhoff interpolation

CERN Document Server

Lorentz, Rudolph A

1992-01-01

The subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well a...

Gaussian Process Interpolation for Uncertainty Estimation in Image Registration

Science.gov (United States)

Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William

2014-01-01

Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127

Depth-time interpolation of feature trends extracted from mobile microelectrode data with kernel functions.

Science.gov (United States)

Wong, Stephen; Hargreaves, Eric L; Baltuch, Gordon H; Jaggi, Jurg L; Danish, Shabbar F

2012-01-01

Microelectrode recording (MER) is necessary for precision localization of target structures such as the subthalamic nucleus during deep brain stimulation (DBS) surgery. Attempts to automate this process have produced quantitative temporal trends (feature activity vs. time) extracted from mobile MER data. Our goal was to evaluate computational methods of generating spatial profiles (feature activity vs. depth) from temporal trends that would decouple automated MER localization from the clinical procedure and enhance functional localization in DBS surgery. We evaluated two methods of interpolation (standard vs. kernel) that generated spatial profiles from temporal trends. We compared interpolated spatial profiles to true spatial profiles that were calculated with depth windows, using correlation coefficient analysis. Excellent approximation of true spatial profiles is achieved by interpolation. Kernel-interpolated spatial profiles produced superior correlation coefficient values at optimal kernel widths (r = 0.932-0.940) compared to standard interpolation (r = 0.891). The choice of kernel function and kernel width resulted in trade-offs in smoothing and resolution. Interpolation of feature activity to create spatial profiles from temporal trends is accurate and can standardize and facilitate MER functional localization of subcortical structures. The methods are computationally efficient, enhancing localization without imposing additional constraints on the MER clinical procedure during DBS surgery. Copyright © 2012 S. Karger AG, Basel.

An Improved Minimum Error Interpolator of CNC for General Curves Based on FPGA

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Jiye HUANG

2014-05-01

Full Text Available This paper presents an improved minimum error interpolation algorithm for general curves generation in computer numerical control (CNC. Compared with the conventional interpolation algorithms such as the By-Point Comparison method, the Minimum- Error method and the Digital Differential Analyzer (DDA method, the proposed improved Minimum-Error interpolation algorithm can find a balance between accuracy and efficiency. The new algorithm is applicable for the curves of linear, circular, elliptical and parabolic. The proposed algorithm is realized on a field programmable gate array (FPGA with Verilog HDL language, and simulated by the ModelSim software, and finally verified on a two-axis CNC lathe. The algorithm has the following advantages: firstly, the maximum interpolation error is only half of the minimum step-size; and secondly the computing time is only two clock cycles of the FPGA. Simulations and actual tests have proved that the high accuracy and efficiency of the algorithm, which shows that it is highly suited for real-time applications.

Numerical analysis for multi-group neutron-diffusion equation using Radial Point Interpolation Method (RPIM)

International Nuclear Information System (INIS)

Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong

2017-01-01

Highlights: • Employing the Radial Point Interpolation Method (RPIM) in numerical analysis of multi-group neutron-diffusion equation. • Establishing mathematical formation of modified multi-group neutron-diffusion equation by RPIM. • Performing the numerical analysis for 2D critical problem. - Abstract: A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the Point Interpolation Method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and

Interpolation theory

CERN Document Server

Lunardi, Alessandra

2018-01-01

This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.

Time-interpolator

International Nuclear Information System (INIS)

Blok, M. de; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

1990-01-01

This report describes a time-interpolator with which time differences can be measured using digital and analog techniques. It concerns a maximum measuring time of 6.4 μs with a resolution of 100 ps. Use is made of Emitter Coupled Logic (ECL) and analogues of high-frequency techniques. The difficulty which accompanies the use of ECL-logic is keeping as short as possible the mutual connections and closing properly the outputs in order to avoid reflections. The digital part of the time-interpolator consists of a continuous running clock and logic which converts an input signal into a start- and stop signal. The analog part consists of a Time to Amplitude Converter (TAC) and an analog to digital converter. (author). 3 refs.; 30 figs

Performance of an Interpolated Stochastic Weather Generator in Czechia and Nebraska

Science.gov (United States)

Dubrovsky, M.; Trnka, M.; Hayes, M. J.; Svoboda, M. D.; Semeradova, D.; Metelka, L.; Hlavinka, P.

2008-12-01

Met&Roll is a WGEN-like parametric four-variate daily weather generator (WG), with an optional extension allowing the user to generate additional variables (i.e. wind and water vapor pressure). It is designed to produce synthetic weather series representing present and/or future climate conditions to be used as an input into various models (e.g. crop growth and rainfall runoff models). The present contribution will summarize recent experiments, in which we tested the performance of the interpolated WG, with the aim to examine whether the WG may be used to produce synthetic weather series even for sites having no meteorological observations. The experiments being discussed include: (1) the comparison of various interpolation methods where the performance of the candidate methods is compared in terms of the accuracy of the interpolation for selected WG parameters; (2) assessing the ability of the interpolated WG in the territories of Czechia and Nebraska to reproduce extreme temperature and precipitation characteristics; (3) indirect validation of the interpolated WG in terms of the modeled crop yields simulated by STICS crop growth model (in Czechia); and (4) indirect validation of interpolated WG in terms of soil climate regime characteristics simulated by the SoilClim model (Czechia and Nebraska). The experiments are based on observed daily weather series from two regions: Czechia (area = 78864 km2, 125 stations available) and Nebraska (area = 200520 km2, 28 stations available). Even though Nebraska exhibits a much lower density of stations, this is offset by the state's relatively flat topography, which is an advantage in using the interpolated WG. Acknowledgements: The present study is supported by the AMVIS-KONTAKT project (ME 844) and the GAAV Grant Agency (project IAA300420806).

Fast Inverse Distance Weighting-Based Spatiotemporal Interpolation: A Web-Based Application of Interpolating Daily Fine Particulate Matter PM2.5 in the Contiguous U.S. Using Parallel Programming and k-d Tree

Directory of Open Access Journals (Sweden)

Lixin Li

2014-09-01

Full Text Available Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5 exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously, using the so-called extension approach. Time values are calculated with the help of a factor under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. Various IDW-based spatiotemporal interpolation methods with different parameter configurations are evaluated by cross-validation. In addition, this study explores computational issues (computer processing speed faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure, named k-d tree, are adapted in this paper to address the computational challenges. Significant computational improvement has been achieved. Finally, a web-based spatiotemporal IDW-based interpolation application is designed and implemented where users can visualize and animate

Fast Inverse Distance Weighting-Based Spatiotemporal Interpolation: A Web-Based Application of Interpolating Daily Fine Particulate Matter PM2.5 in the Contiguous U.S. Using Parallel Programming and k-d Tree

Science.gov (United States)

Li, Lixin; Losser, Travis; Yorke, Charles; Piltner, Reinhard

2014-01-01

Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5 exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously, using the so-called extension approach. Time values are calculated with the help of a factor under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. Various IDW-based spatiotemporal interpolation methods with different parameter configurations are evaluated by cross-validation. In addition, this study explores computational issues (computer processing speed) faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure, named k-d tree, are adapted in this paper to address the computational challenges. Significant computational improvement has been achieved. Finally, a web-based spatiotemporal IDW-based interpolation application is designed and implemented where users can visualize and animate spatiotemporal interpolation

Fast inverse distance weighting-based spatiotemporal interpolation: a web-based application of interpolating daily fine particulate matter PM2:5 in the contiguous U.S. using parallel programming and k-d tree.

Science.gov (United States)

Li, Lixin; Losser, Travis; Yorke, Charles; Piltner, Reinhard

2014-09-03

Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5 exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. Traditionally, when handling spatiotemporal interpolation, researchers tend to treat space and time separately and reduce the spatiotemporal interpolation problems to a sequence of snapshots of spatial interpolations. In this paper, PM2.5 data interpolation is conducted in the continuous space-time domain by integrating space and time simultaneously, using the so-called extension approach. Time values are calculated with the help of a factor under the assumption that spatial and temporal dimensions are equally important when interpolating a continuous changing phenomenon in the space-time domain. Various IDW-based spatiotemporal interpolation methods with different parameter configurations are evaluated by cross-validation. In addition, this study explores computational issues (computer processing speed) faced during implementation of spatiotemporal interpolation for huge data sets. Parallel programming techniques and an advanced data structure, named k-d tree, are adapted in this paper to address the computational challenges. Significant computational improvement has been achieved. Finally, a web-based spatiotemporal IDW-based interpolation application is designed and implemented where users can visualize and animate spatiotemporal interpolation

Computer aided surface representation

Energy Technology Data Exchange (ETDEWEB)

Barnhill, R E

1987-11-01

The aims of this research are the creation of new surface forms and the determination of geometric and physical properties of surfaces. The full sweep from constructive mathematics through the implementation of algorithms and the interactive computer graphics display of surfaces is utilized. Both three-dimensional and multi- dimensional surfaces are considered. Particular emphasis is given to the scientific computing solution of Department of Energy problems. The methods that we have developed and that we are proposing to develop allow applications such as: Producing smooth contour maps from measured data, such as weather maps. Modeling the heat distribution inside a furnace from sample measurements. Terrain modeling based on satellite pictures. The investigation of new surface forms includes the topics of triangular interpolants, multivariate interpolation, surfaces defined on surfaces and monotone and/or convex surfaces. The geometric and physical properties considered include contours, the intersection of surfaces, curvatures as a interrogation tool, and numerical integration.

A disposition of interpolation techniques

NARCIS (Netherlands)

Knotters, M.; Heuvelink, G.B.M.

2010-01-01

A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated

Spatial interpolation of GPS PWV and meteorological variables over the west coast of Peninsular Malaysia during 2013 Klang Valley Flash Flood

Science.gov (United States)

Suparta, Wayan; Rahman, Rosnani

2016-02-01

Global Positioning System (GPS) receivers are widely installed throughout the Peninsular Malaysia, but the implementation for monitoring weather hazard system such as flash flood is still not optimal. To increase the benefit for meteorological applications, the GPS system should be installed in collocation with meteorological sensors so the precipitable water vapor (PWV) can be measured. The distribution of PWV is a key element to the Earth's climate for quantitative precipitation improvement as well as flash flood forecasts. The accuracy of this parameter depends on a large extent on the number of GPS receiver installations and meteorological sensors in the targeted area. Due to cost constraints, a spatial interpolation method is proposed to address these issues. In this paper, we investigated spatial distribution of GPS PWV and meteorological variables (surface temperature, relative humidity, and rainfall) by using thin plate spline (tps) and ordinary kriging (Krig) interpolation techniques over the Klang Valley in Peninsular Malaysia (longitude: 99.5°-102.5°E and latitude: 2.0°-6.5°N). Three flash flood cases in September, October, and December 2013 were studied. The analysis was performed using mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R2) to determine the accuracy and reliability of the interpolation techniques. Results at different phases (pre, onset, and post) that were evaluated showed that tps interpolation technique is more accurate, reliable, and highly correlated in estimating GPS PWV and relative humidity, whereas Krig is more reliable for predicting temperature and rainfall during pre-flash flood events. During the onset of flash flood events, both methods showed good interpolation in estimating all meteorological parameters with high accuracy and reliability. The finding suggests that the proposed method of spatial interpolation techniques are capable of handling limited data sources with high

Improving the visualization of electron-microscopy data through optical flow interpolation

KAUST Repository

Carata, Lucian

2013-01-01

Technical developments in neurobiology have reached a point where the acquisition of high resolution images representing individual neurons and synapses becomes possible. For this, the brain tissue samples are sliced using a diamond knife and imaged with electron-microscopy (EM). However, the technique achieves a low resolution in the cutting direction, due to limitations of the mechanical process, making a direct visualization of a dataset difficult. We aim to increase the depth resolution of the volume by adding new image slices interpolated from the existing ones, without requiring modifications to the EM image-capturing method. As classical interpolation methods do not provide satisfactory results on this type of data, the current paper proposes a re-framing of the problem in terms of motion volumes, considering the depth axis as a temporal axis. An optical flow method is adapted to estimate the motion vectors of pixels in the EM images, and this information is used to compute and insert multiple new images at certain depths in the volume. We evaluate the visualization results in comparison with interpolation methods currently used on EM data, transforming the highly anisotropic original dataset into a dataset with a larger depth resolution. The interpolation based on optical flow better reveals neurite structures with realistic undistorted shapes, and helps to easier map neuronal connections. © 2011 ACM.

Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals.

Science.gov (United States)

Guven, Onur; Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G

2016-06-01

This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors' previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp-p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat.

Interpolation of diffusion weighted imaging datasets

DEFF Research Database (Denmark)

Dyrby, Tim B; Lundell, Henrik; Burke, Mark W

2014-01-01

anatomical details and signal-to-noise-ratio for reliable fibre reconstruction. We assessed the potential benefits of interpolating DWI datasets to a higher image resolution before fibre reconstruction using a diffusion tensor model. Simulations of straight and curved crossing tracts smaller than or equal......Diffusion weighted imaging (DWI) is used to study white-matter fibre organisation, orientation and structural connectivity by means of fibre reconstruction algorithms and tractography. For clinical settings, limited scan time compromises the possibilities to achieve high image resolution for finer...... interpolation methods fail to disentangle fine anatomical details if PVE is too pronounced in the original data. As for validation we used ex-vivo DWI datasets acquired at various image resolutions as well as Nissl-stained sections. Increasing the image resolution by a factor of eight yielded finer geometrical...

Node insertion in Coalescence Fractal Interpolation Function

International Nuclear Information System (INIS)

Prasad, Srijanani Anurag

2013-01-01

The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed

Homography Propagation and Optimization for Wide-Baseline Street Image Interpolation.

Science.gov (United States)

Nie, Yongwei; Zhang, Zhensong; Sun, Hanqiu; Su, Tan; Li, Guiqing

2017-10-01

Wide-baseline street image interpolation is useful but very challenging. Existing approaches either rely on heavyweight 3D reconstruction or computationally intensive deep networks. We present a lightweight and efficient method which uses simple homography computing and refining operators to estimate piecewise smooth homographies between input views. To achieve the goal, we show how to combine homography fitting and homography propagation together based on reliable and unreliable superpixel discrimination. Such a combination, other than using homography fitting only, dramatically increases the accuracy and robustness of the estimated homographies. Then, we integrate the concepts of homography and mesh warping, and propose a novel homography-constrained warping formulation which enforces smoothness between neighboring homographies by utilizing the first-order continuity of the warped mesh. This further eliminates small artifacts of overlapping, stretching, etc. The proposed method is lightweight and flexible, allows wide-baseline interpolation. It improves the state of the art and demonstrates that homography computation suffices for interpolation. Experiments on city and rural datasets validate the efficiency and effectiveness of our method.

Dynamic Stability Analysis Using High-Order Interpolation

Directory of Open Access Journals (Sweden)

Juarez-Toledo C.

2012-10-01

Full Text Available A non-linear model with robust precision for transient stability analysis in multimachine power systems is proposed. The proposed formulation uses the interpolation of Lagrange and Newton's Divided Difference. The High-Order Interpolation technique developed can be used for evaluation of the critical conditions of the dynamic system.The technique is applied to a 5-area 45-machine model of the Mexican interconnected system. As a particular case, this paper shows the application of the High-Order procedure for identifying the slow-frequency mode for a critical contingency. Numerical examples illustrate the method and demonstrate the ability of the High-Order technique to isolate and extract temporal modal behavior.

Effect of raingage density, position and interpolation on rainfall-discharge modelling

Science.gov (United States)

Ly, S.; Sohier, C.; Charles, C.; Degré, A.

2012-04-01

Precipitation traditionally observed using raingages or weather stations, is one of the main parameters that have direct impact on runoff production. Precipitation data require a preliminary spatial interpolation prior to hydrological modeling. The accuracy of modelling result depends on the accuracy of the interpolated spatial rainfall which differs according to different interpolation methods. The accuracy of the interpolated spatial rainfall is usually determined by cross-validation method. The objective of this study is to assess the different interpolation methods of daily rainfall at the watershed scale through hydrological modelling and to explore the best methods that provide a good long term simulation. Four versions of geostatistics: Ordinary Kriging (ORK), Universal Kriging (UNK), Kriging with External Dridft (KED) and Ordinary Cokriging (OCK) and two types of deterministic methods: Thiessen polygon (THI) and Inverse Distance Weighting (IDW) are used to produce 30-year daily rainfall inputs for a distributed physically-based hydrological model (EPIC-GRID). This work is conducted in the Ourthe and Ambleve nested catchments, located in the Ardennes hilly landscape in the Walloon region, Belgium. The total catchment area is 2908 km2, lies between 67 and 693 m in elevation. The multivariate geostatistics (KED and OCK) are also used by incorporating elevation as external data to improve the rainfall prediction. This work also aims at analysing the effect of different raingage densities and position used for interpolation, on the stream flow modelled to get insight in terms of the capability and limitation of the geostatistical methods. The number of raingage varies from 70, 60, 50, 40, 30, 20, 8 to 4 stations located in and surrounding the catchment area. In the latter case, we try to use different positions: around the catchment and only a part of the catchment. The result shows that the simple method like THI fails to capture the rainfall and to produce

COMPARISONS BETWEEN DIFFERENT INTERPOLATION TECHNIQUES

Directory of Open Access Journals (Sweden)

G. Garnero

2014-01-01

In the present study different algorithms will be analysed in order to spot an optimal interpolation methodology. The availability of the recent digital model produced by the Regione Piemonte with airborne LIDAR and the presence of sections of testing realized with higher resolutions and the presence of independent digital models on the same territory allow to set a series of analysis with consequent determination of the best methodologies of interpolation. The analysis of the residuals on the test sites allows to calculate the descriptive statistics of the computed values: all the algorithms have furnished interesting results; all the more interesting, notably for dense models, the IDW (Inverse Distance Weighing algorithm results to give best results in this study case. Moreover, a comparative analysis was carried out by interpolating data at different input point density, with the purpose of highlighting thresholds in input density that may influence the quality reduction of the final output in the interpolation phase.

Research progress and hotspot analysis of spatial interpolation

Science.gov (United States)

Jia, Li-juan; Zheng, Xin-qi; Miao, Jin-li

2018-02-01

In this paper, the literatures related to spatial interpolation between 1982 and 2017, which are included in the Web of Science core database, are used as data sources, and the visualization analysis is carried out according to the co-country network, co-category network, co-citation network, keywords co-occurrence network. It is found that spatial interpolation has experienced three stages: slow development, steady development and rapid development; The cross effect between 11 clustering groups, the main convergence of spatial interpolation theory research, the practical application and case study of spatial interpolation and research on the accuracy and efficiency of spatial interpolation. Finding the optimal spatial interpolation is the frontier and hot spot of the research. Spatial interpolation research has formed a theoretical basis and research system framework, interdisciplinary strong, is widely used in various fields.

Sparse representation based image interpolation with nonlocal autoregressive modeling.

Science.gov (United States)

Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming

2013-04-01

Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.

Development of high fidelity soot aerosol dynamics models using method of moments with interpolative closure

KAUST Repository

Roy, Subrata P.

2014-01-28

The method of moments with interpolative closure (MOMIC) for soot formation and growth provides a detailed modeling framework maintaining a good balance in generality, accuracy, robustness, and computational efficiency. This study presents several computational issues in the development and implementation of the MOMIC-based soot modeling for direct numerical simulations (DNS). The issues of concern include a wide dynamic range of numbers, choice of normalization, high effective Schmidt number of soot particles, and realizability of the soot particle size distribution function (PSDF). These problems are not unique to DNS, but they are often exacerbated by the high-order numerical schemes used in DNS. Four specific issues are discussed in this article: the treatment of soot diffusion, choice of interpolation scheme for MOMIC, an approach to deal with strongly oxidizing environments, and realizability of the PSDF. General, robust, and stable approaches are sought to address these issues, minimizing the use of ad hoc treatments such as clipping. The solutions proposed and demonstrated here are being applied to generate new physical insight into complex turbulence-chemistry-soot-radiation interactions in turbulent reacting flows using DNS. © 2014 Copyright Taylor and Francis Group, LLC.

Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

Science.gov (United States)

Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

2017-11-01

Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

Analysis of velocity planning interpolation algorithm based on NURBS curve

Science.gov (United States)

Zhang, Wanjun; Gao, Shanping; Cheng, Xiyan; Zhang, Feng

2017-04-01

To reduce interpolation time and Max interpolation error in NURBS (Non-Uniform Rational B-Spline) inter-polation caused by planning Velocity. This paper proposed a velocity planning interpolation algorithm based on NURBS curve. Firstly, the second-order Taylor expansion is applied on the numerator in NURBS curve representation with parameter curve. Then, velocity planning interpolation algorithm can meet with NURBS curve interpolation. Finally, simulation results show that the proposed NURBS curve interpolator meet the high-speed and high-accuracy interpolation requirements of CNC systems. The interpolation of NURBS curve should be finished.

Angular interpolations and splice options for three-dimensional transport computations

International Nuclear Information System (INIS)

Abu-Shumays, I.K.; Yehnert, C.E.

1996-01-01

New, accurate and mathematically rigorous angular Interpolation strategies are presented. These strategies preserve flow and directionality separately over each octant of the unit sphere, and are based on a combination of spherical harmonics expansions and least squares algorithms. Details of a three-dimensional to three-dimensional (3-D to 3-D) splice method which utilizes the new angular interpolations are summarized. The method has been implemented in a multidimensional discrete ordinates transport computer program. Various features of the splice option are illustrated by several applications to a benchmark Dog-Legged Void Neutron (DLVN) streaming and transport experimental assembly

Time Reversal Reconstruction Algorithm Based on PSO Optimized SVM Interpolation for Photoacoustic Imaging

Directory of Open Access Journals (Sweden)

Mingjian Sun

2015-01-01

Full Text Available Photoacoustic imaging is an innovative imaging technique to image biomedical tissues. The time reversal reconstruction algorithm in which a numerical model of the acoustic forward problem is run backwards in time is widely used. In the paper, a time reversal reconstruction algorithm based on particle swarm optimization (PSO optimized support vector machine (SVM interpolation method is proposed for photoacoustics imaging. Numerical results show that the reconstructed images of the proposed algorithm are more accurate than those of the nearest neighbor interpolation, linear interpolation, and cubic convolution interpolation based time reversal algorithm, which can provide higher imaging quality by using significantly fewer measurement positions or scanning times.

Digital x-ray tomosynthesis with interpolated projection data for thin slab objects

Science.gov (United States)

Ha, S.; Yun, J.; Kim, H. K.

2017-11-01

In relation with a thin slab-object inspection, we propose a digital tomosynthesis reconstruction with fewer numbers of measured projections in combinations with additional virtual projections, which are produced by interpolating the measured projections. Hence we can reconstruct tomographic images with less few-view artifacts. The projection interpolation assumes that variations in cone-beam ray path-lengths through an object are negligible and the object is rigid. The interpolation is performed in the projection-space domain. Pixel values in the interpolated projection are the weighted sum of pixel values of the measured projections considering their projection angles. The experimental simulation shows that the proposed method can enhance the contrast-to-noise performance in reconstructed images while sacrificing the spatial resolving power.

Accuration of Time Series and Spatial Interpolation Method for Prediction of Precipitation Distribution on the Geographical Information System

Science.gov (United States)

Prasetyo, S. Y. J.; Hartomo, K. D.

2018-01-01

The Spatial Plan of the Province of Central Java 2009-2029 identifies that most regencies or cities in Central Java Province are very vulnerable to landslide disaster. The data are also supported by other data from Indonesian Disaster Risk Index (In Indonesia called Indeks Risiko Bencana Indonesia) 2013 that suggest that some areas in Central Java Province exhibit a high risk of natural disasters. This research aims to develop an application architecture and analysis methodology in GIS to predict and to map rainfall distribution. We propose our GIS architectural application of “Multiplatform Architectural Spatiotemporal” and data analysis methods of “Triple Exponential Smoothing” and “Spatial Interpolation” as our significant scientific contribution. This research consists of 2 (two) parts, namely attribute data prediction using TES method and spatial data prediction using Inverse Distance Weight (IDW) method. We conduct our research in 19 subdistricts in the Boyolali Regency, Central Java Province, Indonesia. Our main research data is the biweekly rainfall data in 2000-2016 Climatology, Meteorology, and Geophysics Agency (In Indonesia called Badan Meteorologi, Klimatologi, dan Geofisika) of Central Java Province and Laboratory of Plant Disease Observations Region V Surakarta, Central Java. The application architecture and analytical methodology of “Multiplatform Architectural Spatiotemporal” and spatial data analysis methodology of “Triple Exponential Smoothing” and “Spatial Interpolation” can be developed as a GIS application framework of rainfall distribution for various applied fields. The comparison between the TES and IDW methods show that relative to time series prediction, spatial interpolation exhibit values that are approaching actual. Spatial interpolation is closer to actual data because computed values are the rainfall data of the nearest location or the neighbour of sample values. However, the IDW’s main weakness is that some

Optimum quantization and interpolation of projections in X-ray computerized tomography

International Nuclear Information System (INIS)

Vajnberg, Eh.I.; Fajngojz, M.L.

1984-01-01

Two methods to increase the accuracy of image reconstruction due to optimization of quantization and interpolation of proections with separate reduction of the main types of errors are described and experimentally studied. A high metrological and calculation efficiency of increasing the count frequency in the reconstructed tomogram 2-4 times is found. The optimum structure of interpolation functions of a minimum extent is calculated

Interpolative Boolean Networks

Directory of Open Access Journals (Sweden)

Vladimir Dobrić

2017-01-01

Full Text Available Boolean networks are used for modeling and analysis of complex systems of interacting entities. Classical Boolean networks are binary and they are relevant for modeling systems with complex switch-like causal interactions. More descriptive power can be provided by the introduction of gradation in this model. If this is accomplished by using conventional fuzzy logics, the generalized model cannot secure the Boolean frame. Consequently, the validity of the model’s dynamics is not secured. The aim of this paper is to present the Boolean consistent generalization of Boolean networks, interpolative Boolean networks. The generalization is based on interpolative Boolean algebra, the [0,1]-valued realization of Boolean algebra. The proposed model is adaptive with respect to the nature of input variables and it offers greater descriptive power as compared with traditional models. For illustrative purposes, IBN is compared to the models based on existing real-valued approaches. Due to the complexity of the most systems to be analyzed and the characteristics of interpolative Boolean algebra, the software support is developed to provide graphical and numerical tools for complex system modeling and analysis.

Pricing and simulation for real estate index options: Radial basis point interpolation

Science.gov (United States)

Gong, Pu; Zou, Dong; Wang, Jiayue

2018-06-01

This study employs the meshfree radial basis point interpolation (RBPI) for pricing real estate derivatives contingent on real estate index. This method combines radial and polynomial basis functions, which can guarantee the interpolation scheme with Kronecker property and effectively improve accuracy. An exponential change of variables, a mesh refinement algorithm and the Richardson extrapolation are employed in this study to implement the RBPI. Numerical results are presented to examine the computational efficiency and accuracy of our method.

Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

Science.gov (United States)

Ren, Maodong; Liang, Jin; Wei, Bin

2016-12-01

An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

Image interpolation and denoising for division of focal plane sensors using Gaussian processes.

Science.gov (United States)

Gilboa, Elad; Cunningham, John P; Nehorai, Arye; Gruev, Viktor

2014-06-16

Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimates of sensor noise are used to improve the accuracy of the estimated pixel information. We further exploit the inherent grid structure of this data to create a fast exact algorithm that operates in ����(N(3/2)) (vs. the naive ���� (N³)), thus making the Gaussian process method computationally tractable for image data. This modeling advance and the enabling computational advance combine to produce significant improvements over previously published interpolation methods for polarimeters, which is most pronounced in cases of low signal-to-noise ratio (SNR). We provide the comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter.

Energy band structure of Cr by the Slater-Koster interpolation scheme

International Nuclear Information System (INIS)

Seifu, D.; Mikusik, P.

1986-04-01

The matrix elements of the Hamiltonian between nine localized wave-functions in tight-binding formalism are derived. The symmetry adapted wave-functions and the secular equations are formed by the group theory method for high symmetry points in the Brillouin zone. A set of interaction integrals is chosen on physical ground and fitted via the Slater-Koster interpolation scheme to the abinito band structure of chromium calculated by the Green function method. Then the energy band structure of chromium is interpolated and extrapolated in the Brillouin zone. (author)

Fast interpolation for Global Positioning System (GPS) satellite orbits

OpenAIRE

Clynch, James R.; Sagovac, Christopher Patrick; Danielson, D. A. (Donald A.); Neta, Beny

1995-01-01

In this report, we discuss and compare several methods for polynomial interpolation of Global Positioning Systems ephemeris data. We show that the use of difference tables is more efficient than the method currently in use to construct and evaluate the Lagrange polynomials.

An Improved Rotary Interpolation Based on FPGA

Directory of Open Access Journals (Sweden)

Mingyu Gao

2014-08-01

Full Text Available This paper presents an improved rotary interpolation algorithm, which consists of a standard curve interpolation module and a rotary process module. Compared to the conventional rotary interpolation algorithms, the proposed rotary interpolation algorithm is simpler and more efficient. The proposed algorithm was realized on a FPGA with Verilog HDL language, and simulated by the ModelSim software, and finally verified on a two-axis CNC lathe, which uses rotary ellipse and rotary parabolic as an example. According to the theoretical analysis and practical process validation, the algorithm has the following advantages: firstly, less arithmetic items is conducive for interpolation operation; and secondly the computing time is only two clock cycles of the FPGA. Simulations and actual tests have proved that the high accuracy and efficiency of the algorithm, which shows that it is highly suited for real-time applications.

Comparison of multimesh hp-FEM to interpolation and projection methods for spatial coupling of thermal and neutron diffusion calculations

International Nuclear Information System (INIS)

Dubcova, Lenka; Solin, Pavel; Hansen, Glen; Park, HyeongKae

2011-01-01

Multiphysics solution challenges are legion within the field of nuclear reactor design and analysis. One major issue concerns the coupling between heat and neutron flow (neutronics) within the reactor assembly. These phenomena are usually very tightly interdependent, as large amounts of heat are quickly produced with an increase in fission events within the fuel, which raises the temperature that affects the neutron cross section of the fuel. Furthermore, there typically is a large diversity of time and spatial scales between mathematical models of heat and neutronics. Indeed, the different spatial resolution requirements often lead to the use of very different meshes for the two phenomena. As the equations are coupled, one must take care in exchanging solution data between them, or significant error can be introduced into the coupled problem. We propose a novel approach to the discretization of the coupled problem on different meshes based on an adaptive multimesh higher-order finite element method (hp-FEM), and compare it to popular interpolation and projection methods. We show that the multimesh hp-FEM method is significantly more accurate than the interpolation and projection approaches considered in this study.

Interpolant Tree Automata and their Application in Horn Clause Verification

Directory of Open Access Journals (Sweden)

Bishoksan Kafle

2016-07-01

Full Text Available This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this paper. The role of an interpolant tree automaton is to provide a generalisation of a spurious counterexample during refinement, capturing a possibly infinite set of spurious counterexample traces. In our approach these traces are then eliminated using a transformation of the Horn clauses. We compare this approach with two other methods; one of them uses interpolant tree automata in an algorithm for trace abstraction and refinement, while the other uses abstract interpretation over the domain of convex polyhedra without the generalisation step. Evaluation of the results of experiments on a number of Horn clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead.

Kriging interpolation in seismic attribute space applied to the South Arne Field, North Sea

DEFF Research Database (Denmark)

Hansen, Thomas Mejer; Mosegaard, Klaus; Schiøtt, Christian

2010-01-01

Seismic attributes can be used to guide interpolation in-between and extrapolation away from well log locations using for example linear regression, neural networks, and kriging. Kriging-based estimation methods (and most other types of interpolation/extrapolation techniques) are intimately linke...

Calculation of reactivity without Lagrange interpolation

International Nuclear Information System (INIS)

Suescun D, D.; Figueroa J, J. H.; Rodriguez R, K. C.; Villada P, J. P.

2015-09-01

A new method to solve numerically the inverse equation of punctual kinetics without using Lagrange interpolating polynomial is formulated; this method uses a polynomial approximation with N points based on a process of recurrence for simulating different forms of nuclear power. The results show a reliable accuracy. Furthermore, the method proposed here is suitable for real-time measurements of reactivity, with step sizes of calculations greater that Δt = 0.3 s; due to its precision can be used to implement a digital meter of reactivity in real time. (Author)

Precipitation interpolation in mountainous areas

Science.gov (United States)

Kolberg, Sjur

2015-04-01

Different precipitation interpolation techniques as well as external drift covariates are tested and compared in a 26000 km2 mountainous area in Norway, using daily data from 60 stations. The main method of assessment is cross-validation. Annual precipitation in the area varies from below 500 mm to more than 2000 mm. The data were corrected for wind-driven undercatch according to operational standards. While temporal evaluation produce seemingly acceptable at-station correlation values (on average around 0.6), the average daily spatial correlation is less than 0.1. Penalising also bias, Nash-Sutcliffe R2 values are negative for spatial correspondence, and around 0.15 for temporal. Despite largely violated assumptions, plain Kriging produces better results than simple inverse distance weighting. More surprisingly, the presumably 'worst-case' benchmark of no interpolation at all, simply averaging all 60 stations for each day, actually outperformed the standard interpolation techniques. For logistic reasons, high altitudes are under-represented in the gauge network. The possible effect of this was investigated by a) fitting a precipitation lapse rate as an external drift, and b) applying a linear model of orographic enhancement (Smith and Barstad, 2004). These techniques improved the results only marginally. The gauge density in the region is one for each 433 km2; higher than the overall density of the Norwegian national network. Admittedly the cross-validation technique reduces the gauge density, still the results suggest that we are far from able to provide hydrological models with adequate data for the main driving force.

Convergence of trajectories in fractal interpolation of stochastic processes

International Nuclear Information System (INIS)

MaIysz, Robert

2006-01-01

The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation

Improved Visualization of Gastrointestinal Slow Wave Propagation Using a Novel Wavefront-Orientation Interpolation Technique.

Science.gov (United States)

Mayne, Terence P; Paskaranandavadivel, Niranchan; Erickson, Jonathan C; OGrady, Gregory; Cheng, Leo K; Angeli, Timothy R

2018-02-01

High-resolution mapping of gastrointestinal (GI) slow waves is a valuable technique for research and clinical applications. Interpretation of high-resolution GI mapping data relies on animations of slow wave propagation, but current methods remain as rudimentary, pixelated electrode activation animations. This study aimed to develop improved methods of visualizing high-resolution slow wave recordings that increases ease of interpretation. The novel method of "wavefront-orientation" interpolation was created to account for the planar movement of the slow wave wavefront, negate any need for distance calculations, remain robust in atypical wavefronts (i.e., dysrhythmias), and produce an appropriate interpolation boundary. The wavefront-orientation method determines the orthogonal wavefront direction and calculates interpolated values as the mean slow wave activation-time (AT) of the pair of linearly adjacent electrodes along that direction. Stairstep upsampling increased smoothness and clarity. Animation accuracy of 17 human high-resolution slow wave recordings (64-256 electrodes) was verified by visual comparison to the prior method showing a clear improvement in wave smoothness that enabled more accurate interpretation of propagation, as confirmed by an assessment of clinical applicability performed by eight GI clinicians. Quantitatively, the new method produced accurate interpolation values compared to experimental data (mean difference 0.02 ± 0.05 s) and was accurate when applied solely to dysrhythmic data (0.02 ± 0.06 s), both within the error in manual AT marking (mean 0.2 s). Mean interpolation processing time was 6.0 s per wave. These novel methods provide a validated visualization platform that will improve analysis of high-resolution GI mapping in research and clinical translation.

Two-dimensional interpolation with experimental data smoothing

International Nuclear Information System (INIS)

Trejbal, Z.

1989-01-01

A method of two-dimensional interpolation with smoothing of time statistically deflected points is developed for processing of magnetic field measurements at the U-120M field measurements at the U-120M cyclotron. Mathematical statement of initial requirements and the final result of relevant algebraic transformations are given. 3 refs

Reconstruction of reflectance data using an interpolation technique.

Science.gov (United States)

Abed, Farhad Moghareh; Amirshahi, Seyed Hossein; Abed, Mohammad Reza Moghareh

2009-03-01

A linear interpolation method is applied for reconstruction of reflectance spectra of Munsell as well as ColorChecker SG color chips from the corresponding colorimetric values under a given set of viewing conditions. Hence, different types of lookup tables (LUTs) have been created to connect the colorimetric and spectrophotometeric data as the source and destination spaces in this approach. To optimize the algorithm, different color spaces and light sources have been used to build different types of LUTs. The effects of applied color datasets as well as employed color spaces are investigated. Results of recovery are evaluated by the mean and the maximum color difference values under other sets of standard light sources. The mean and the maximum values of root mean square (RMS) error between the reconstructed and the actual spectra are also calculated. Since the speed of reflectance reconstruction is a key point in the LUT algorithm, the processing time spent for interpolation of spectral data has also been measured for each model. Finally, the performance of the suggested interpolation technique is compared with that of the common principal component analysis method. According to the results, using the CIEXYZ tristimulus values as a source space shows priority over the CIELAB color space. Besides, the colorimetric position of a desired sample is a key point that indicates the success of the approach. In fact, because of the nature of the interpolation technique, the colorimetric position of the desired samples should be located inside the color gamut of available samples in the dataset. The resultant spectra that have been reconstructed by this technique show considerable improvement in terms of RMS error between the actual and the reconstructed reflectance spectra as well as CIELAB color differences under the other light source in comparison with those obtained from the standard PCA technique.

Generation of response functions of a NaI detector by using an interpolation technique

International Nuclear Information System (INIS)

Tominaga, Shoji

1983-01-01

A computer method is developed for generating response functions of a NaI detector to monoenergetic γ-rays. The method is based on an interpolation between measured response curves by a detector. The computer programs are constructed for Heath's response spectral library. The principle of the basic mathematics used for interpolation, which was reported previously by the author, et al., is that response curves can be decomposed into a linear combination of intrinsic-component patterns, and thereby the interpolation of curves is reduced to a simple interpolation of weighting coefficients needed to combine the component patterns. This technique has some advantages of data compression, reduction in computation time, and stability of the solution, in comparison with the usual functional fitting method. The processing method of segmentation of a spectrum is devised to generate useful and precise response curves. A spectral curve, obtained for each γ-ray source, is divided into some regions defined by the physical processes, such as the photopeak area, the Compton continuum area, the backscatter peak area, and so on. Each segment curve then is processed separately for interpolation. Lastly the estimated curves to the respective areas are connected on one channel scale. The generation programs are explained briefly. It is shown that the generated curve represents the overall shape of a response spectrum including not only its photopeak but also the corresponding Compton area, with a sufficient accuracy. (author)

Discrete Orthogonal Transforms and Neural Networks for Image Interpolation

Directory of Open Access Journals (Sweden)

J. Polec

1999-09-01

Full Text Available In this contribution we present transform and neural network approaches to the interpolation of images. From transform point of view, the principles from [1] are modified for 1st and 2nd order interpolation. We present several new interpolation discrete orthogonal transforms. From neural network point of view, we present interpolation possibilities of multilayer perceptrons. We use various configurations of neural networks for 1st and 2nd order interpolation. The results are compared by means of tables.

Subsurface temperature maps in French sedimentary basins: new data compilation and interpolation

International Nuclear Information System (INIS)

Bonte, D.; Guillou-Frottier, L.; Garibaldi, C.; Bourgine, B.; Lopez, S.; Bouchot, V.; Garibaldi, C.; Lucazeau, F.

2010-01-01

Assessment of the underground geothermal potential requires the knowledge of deep temperatures (1-5 km). Here, we present new temperature maps obtained from oil boreholes in the French sedimentary basins. Because of their origin, the data need to be corrected, and their local character necessitates spatial interpolation. Previous maps were obtained in the 1970's using empirical corrections and manual interpolation. In this study, we update the number of measurements by using values collected during the last thirty years, correct the temperatures for transient perturbations and carry out statistical analyses before modelling the 3D distribution of temperatures. This dataset provides 977 temperatures corrected for transient perturbations in 593 boreholes located in the French sedimentary basins. An average temperature gradient of 30.6 deg. C/km is obtained for a representative surface temperature of 10 deg. C. When surface temperature is not accounted for, deep measurements are best fitted with a temperature gradient of 25.7 deg. C/km. We perform a geostatistical analysis on a residual temperature dataset (using a drift of 25.7 deg. C/km) to constrain the 3D interpolation kriging procedure with horizontal and vertical models of variograms. The interpolated residual temperatures are added to the country-scale averaged drift in order to get a three dimensional thermal structure of the French sedimentary basins. The 3D thermal block enables us to extract isothermal surfaces and 2D sections (iso-depth maps and iso-longitude cross-sections). A number of anomalies with a limited depth and spatial extension have been identified, from shallow in the Rhine graben and Aquitanian basin, to deep in the Provence basin. Some of these anomalies (Paris basin, Alsace, south of the Provence basin) may be partly related to thick insulating sediments, while for some others (southwestern Aquitanian basin, part of the Provence basin) large-scale fluid circulation may explain superimposed

Application of validation data for assessing spatial interpolation methods for 8-h ozone or other sparsely monitored constituents.

Science.gov (United States)

Joseph, John; Sharif, Hatim O; Sunil, Thankam; Alamgir, Hasanat

2013-07-01

The adverse health effects of high concentrations of ground-level ozone are well-known, but estimating exposure is difficult due to the sparseness of urban monitoring networks. This sparseness discourages the reservation of a portion of the monitoring stations for validation of interpolation techniques precisely when the risk of overfitting is greatest. In this study, we test a variety of simple spatial interpolation techniques for 8-h ozone with thousands of randomly selected subsets of data from two urban areas with monitoring stations sufficiently numerous to allow for true validation. Results indicate that ordinary kriging with only the range parameter calibrated in an exponential variogram is the generally superior method, and yields reliable confidence intervals. Sparse data sets may contain sufficient information for calibration of the range parameter even if the Moran I p-value is close to unity. R script is made available to apply the methodology to other sparsely monitored constituents. Copyright © 2013 Elsevier Ltd. All rights reserved.

Interpolation Inequalities and Spectral Estimates for Magnetic Operators

Science.gov (United States)

Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael

2018-05-01

We prove magnetic interpolation inequalities and Keller-Lieb-Thir-ring estimates for the principal eigenvalue of magnetic Schr{\\"o}dinger operators. We establish explicit upper and lower bounds for the best constants and show by numerical methods that our theoretical estimates are accurate.

Image interpolation used in three-dimensional range data compression.

Science.gov (United States)

Zhang, Shaoze; Zhang, Jianqi; Huang, Xi; Liu, Delian

2016-05-20

Advances in the field of three-dimensional (3D) scanning have made the acquisition of 3D range data easier and easier. However, with the large size of 3D range data comes the challenge of storing and transmitting it. To address this challenge, this paper presents a framework to further compress 3D range data using image interpolation. We first use a virtual fringe-projection system to store 3D range data as images, and then apply the interpolation algorithm to the images to reduce their resolution to further reduce the data size. When the 3D range data are needed, the low-resolution image is scaled up to its original resolution by applying the interpolation algorithm, and then the scaled-up image is decoded and the 3D range data are recovered according to the decoded result. Experimental results show that the proposed method could further reduce the data size while maintaining a low rate of error.

Comparing interpolation schemes in dynamic receive ultrasound beamforming

DEFF Research Database (Denmark)

Kortbek, Jacob; Andresen, Henrik; Nikolov, Svetoslav

2005-01-01

In medical ultrasound interpolation schemes are of- ten applied in receive focusing for reconstruction of image points. This paper investigates the performance of various interpolation scheme by means of ultrasound simulations of point scatterers in Field II. The investigation includes conventional...... B-mode imaging and synthetic aperture (SA) imaging using a 192-element, 7 MHz linear array transducer with λ pitch as simulation model. The evaluation consists primarily of calculations of the side lobe to main lobe ratio, SLMLR, and the noise power of the interpolation error. When using...... conventional B-mode imaging and linear interpolation, the difference in mean SLMLR is 6.2 dB. With polynomial interpolation the ratio is in the range 6.2 dB to 0.3 dB using 2nd to 5th order polynomials, and with FIR interpolation the ratio is in the range 5.8 dB to 0.1 dB depending on the filter design...

Spatiotemporal interpolation of elevation changes derived from satellite altimetry for Jakobshavn Isbræ, Greenland

DEFF Research Database (Denmark)

Hurkmans, R.T.W.L.; Bamber, J.L.; Sørensen, Louise Sandberg

2012-01-01

. In those areas, straightforward interpolation of data is unlikely to reflect the true patterns of dH/dt. Here, four interpolation methods are compared and evaluated over Jakobshavn Isbræ, an outlet glacier for which widespread airborne validation data are available from NASA's Airborne Topographic Mapper...

Nuclear data banks generation by interpolation

International Nuclear Information System (INIS)

Castillo M, J. A.

1999-01-01

Nuclear Data Bank generation, is a process in which a great amount of resources is required, both computing and humans. If it is taken into account that at some times it is necessary to create a great amount of those, it is convenient to have a reliable tool that generates Data Banks with the lesser resources, in the least possible time and with a very good approximation. In this work are shown the results obtained during the development of INTPOLBI code, use to generate Nuclear Data Banks employing bicubic polynominal interpolation, taking as independent variables the uranium and gadolinia percents. Two proposal were worked, applying in both cases the finite element method, using one element with 16 nodes to carry out the interpolation. In the first proposals the canonic base was employed, to obtain the interpolating polynomial and later, the corresponding linear equation systems. In the solution of this systems the Gaussian elimination methods with partial pivot was applied. In the second case, the Newton base was used to obtain the mentioned system, resulting in a triangular inferior matrix, which structure, applying elemental operations, to obtain a blocks diagonal matrix, with special characteristics and easier to work with. For the validation tests, a comparison was made between the values obtained with INTPOLBI and INTERTEG (create at the Instituto de Investigaciones Electricas (MX) with the same purpose) codes, and Data Banks created through the conventional process, that is, with nuclear codes normally used. Finally, it is possible to conclude that the Nuclear Data Banks generated with INTPOLBI code constitute a very good approximation that, even though do not wholly replace conventional process, however are helpful in cases when it is necessary to create a great amount of Data Banks

Building Input Adaptive Parallel Applications: A Case Study of Sparse Grid Interpolation

KAUST Repository

Murarasu, Alin

2012-12-01

The well-known power wall resulting in multi-cores requires special techniques for speeding up applications. In this sense, parallelization plays a crucial role. Besides standard serial optimizations, techniques such as input specialization can also bring a substantial contribution to the speedup. By identifying common patterns in the input data, we propose new algorithms for sparse grid interpolation that accelerate the state-of-the-art non-specialized version. Sparse grid interpolation is an inherently hierarchical method of interpolation employed for example in computational steering applications for decompressing highdimensional simulation data. In this context, improving the speedup is essential for real-time visualization. Using input specialization, we report a speedup of up to 9x over the nonspecialized version. The paper covers the steps we took to reach this speedup by means of input adaptivity. Our algorithms will be integrated in fastsg, a library for fast sparse grid interpolation. © 2012 IEEE.

Interpolation of fuzzy data | Khodaparast | Journal of Fundamental ...

African Journals Online (AJOL)

Considering the many applications of mathematical functions in different ways, it is essential to have a defining function. In this study, we used Fuzzy Lagrangian interpolation and natural fuzzy spline polynomials to interpolate the fuzzy data. In the current world and in the field of science and technology, interpolation issues ...

Sample Data Synchronization and Harmonic Analysis Algorithm Based on Radial Basis Function Interpolation

Directory of Open Access Journals (Sweden)

Huaiqing Zhang

2014-01-01

Full Text Available The spectral leakage has a harmful effect on the accuracy of harmonic analysis for asynchronous sampling. This paper proposed a time quasi-synchronous sampling algorithm which is based on radial basis function (RBF interpolation. Firstly, a fundamental period is evaluated by a zero-crossing technique with fourth-order Newton’s interpolation, and then, the sampling sequence is reproduced by the RBF interpolation. Finally, the harmonic parameters can be calculated by FFT on the synchronization of sampling data. Simulation results showed that the proposed algorithm has high accuracy in measuring distorted and noisy signals. Compared to the local approximation schemes as linear, quadric, and fourth-order Newton interpolations, the RBF is a global approximation method which can acquire more accurate results while the time-consuming is about the same as Newton’s.

A comparison of spatial interpolation methods for soil temperature over a complex topographical region

Science.gov (United States)

Wu, Wei; Tang, Xiao-Ping; Ma, Xue-Qing; Liu, Hong-Bin

2016-08-01

Soil temperature variability data provide valuable information on understanding land-surface ecosystem processes and climate change. This study developed and analyzed a spatial dataset of monthly mean soil temperature at a depth of 10 cm over a complex topographical region in southwestern China. The records were measured at 83 stations during the period of 1961-2000. Nine approaches were compared for interpolating soil temperature. The accuracy indicators were root mean square error (RMSE), modelling efficiency (ME), and coefficient of residual mass (CRM). The results indicated that thin plate spline with latitude, longitude, and elevation gave the best performance with RMSE varying between 0.425 and 0.592 °C, ME between 0.895 and 0.947, and CRM between -0.007 and 0.001. A spatial database was developed based on the best model. The dataset showed that larger seasonal changes of soil temperature were from autumn to winter over the region. The northern and eastern areas with hilly and low-middle mountains experienced larger seasonal changes.

Interpolation between multi-dimensional histograms using a new non-linear moment morphing method

NARCIS (Netherlands)

Baak, M.; Gadatsch, S.; Harrington, R.; Verkerke, W.

2015-01-01

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model׳s parameters and transformed according to a specific

Stokes vector based interpolation method to improve the efficiency of bio-inspired polarization-difference imaging in turbid media

Science.gov (United States)

Guan, Jinge; Ren, Wei; Cheng, Yaoyu

2018-04-01

We demonstrate an efficient polarization-difference imaging system in turbid conditions by using the Stokes vector of light. The interaction of scattered light with the polarizer is analyzed by the Stokes-Mueller formalism. An interpolation method is proposed to replace the mechanical rotation of the polarization axis of the analyzer theoretically, and its performance is verified by the experiment at different turbidity levels. We show that compared with direct imaging, the Stokes vector based imaging method can effectively reduce the effect of light scattering and enhance the image contrast.

A GPU-Accelerated Parameter Interpolation Thermodynamic Integration Free Energy Method.

Science.gov (United States)

Giese, Timothy J; York, Darrin M

2018-03-13

There has been a resurgence of interest in free energy methods motivated by the performance enhancements offered by molecular dynamics (MD) software written for specialized hardware, such as graphics processing units (GPUs). In this work, we exploit the properties of a parameter-interpolated thermodynamic integration (PI-TI) method to connect states by their molecular mechanical (MM) parameter values. This pathway is shown to be better behaved for Mg 2+ → Ca 2+ transformations than traditional linear alchemical pathways (with and without soft-core potentials). The PI-TI method has the practical advantage that no modification of the MD code is required to propagate the dynamics, and unlike with linear alchemical mixing, only one electrostatic evaluation is needed (e.g., single call to particle-mesh Ewald) leading to better performance. In the case of AMBER, this enables all the performance benefits of GPU-acceleration to be realized, in addition to unlocking the full spectrum of features available within the MD software, such as Hamiltonian replica exchange (HREM). The TI derivative evaluation can be accomplished efficiently in a post-processing step by reanalyzing the statistically independent trajectory frames in parallel for high throughput. We also show how one can evaluate the particle mesh Ewald contribution to the TI derivative evaluation without needing to perform two reciprocal space calculations. We apply the PI-TI method with HREM on GPUs in AMBER to predict p K a values in double stranded RNA molecules and make comparison with experiments. Convergence to under 0.25 units for these systems required 100 ns or more of sampling per window and coupling of windows with HREM. We find that MM charges derived from ab initio QM/MM fragment calculations improve the agreement between calculation and experimental results.

Multiresolution Motion Estimation for Low-Rate Video Frame Interpolation

Directory of Open Access Journals (Sweden)

Hezerul Abdul Karim

2004-09-01

Full Text Available Interpolation of video frames with the purpose of increasing the frame rate requires the estimation of motion in the image so as to interpolate pixels along the path of the objects. In this paper, the specific challenges of low-rate video frame interpolation are illustrated by choosing one well-performing algorithm for high-frame-rate interpolation (Castango 1996 and applying it to low frame rates. The degradation of performance is illustrated by comparing the original algorithm, the algorithm adapted to low frame rate, and simple averaging. To overcome the particular challenges of low-frame-rate interpolation, two algorithms based on multiresolution motion estimation are developed and compared on objective and subjective basis and shown to provide an elegant solution to the specific challenges of low-frame-rate video interpolation.

Spatio-Temporal Interpolation of Cloudy SST Fields Using Conditional Analog Data Assimilation

Directory of Open Access Journals (Sweden)

Ronan Fablet

2018-02-01

Full Text Available The ever increasing geophysical data streams pouring from earth observation satellite missions and numerical simulations along with the development of dedicated big data infrastructure advocate for truly exploiting the potential of these datasets, through novel data-driven strategies, to deliver enhanced satellite-derived gapfilled geophysical products from partial satellite observations. We here demonstrate the relevance of the analog data assimilation (AnDA for an application to the reconstruction of cloud-free level-4 gridded Sea Surface Temperature (SST. We propose novel AnDA models which exploit auxiliary variables such as sea surface currents and significantly reduce the computational complexity of AnDA. Numerical experiments benchmark the proposed models with respect to state-of-the-art interpolation techniques such as optimal interpolation and EOF-based schemes. We report relative improvement up to 40%/50% in terms of RMSE and also show a good parallelization performance, which supports the feasibility of an upscaling on a global scale.

Improvement of Hydrological Simulations by Applying Daily Precipitation Interpolation Schemes in Meso-Scale Catchments

Directory of Open Access Journals (Sweden)

Mateusz Szcześniak

2015-02-01

Full Text Available Ground-based precipitation data are still the dominant input type for hydrological models. Spatial variability in precipitation can be represented by spatially interpolating gauge data using various techniques. In this study, the effect of daily precipitation interpolation methods on discharge simulations using the semi-distributed SWAT (Soil and Water Assessment Tool model over a 30-year period is examined. The study was carried out in 11 meso-scale (119–3935 km2 sub-catchments lying in the Sulejów reservoir catchment in central Poland. Four methods were tested: the default SWAT method (Def based on the Nearest Neighbour technique, Thiessen Polygons (TP, Inverse Distance Weighted (IDW and Ordinary Kriging (OK. =The evaluation of methods was performed using a semi-automated calibration program SUFI-2 (Sequential Uncertainty Fitting Procedure Version 2 with two objective functions: Nash-Sutcliffe Efficiency (NSE and the adjusted R2 coefficient (bR2. The results show that: (1 the most complex OK method outperformed other methods in terms of NSE; and (2 OK, IDW, and TP outperformed Def in terms of bR2. The median difference in daily/monthly NSE between OK and Def/TP/IDW calculated across all catchments ranged between 0.05 and 0.15, while the median difference between TP/IDW/OK and Def ranged between 0.05 and 0.07. The differences between pairs of interpolation methods were, however, spatially variable and a part of this variability was attributed to catchment properties: catchments characterised by low station density and low coefficient of variation of daily flows experienced more pronounced improvement resulting from using interpolation methods. Methods providing higher precipitation estimates often resulted in a better model performance. The implication from this study is that appropriate consideration of spatial precipitation variability (often neglected by model users that can be achieved using relatively simple interpolation methods can

An Improved Local Gradient Method for Sea Surface Wind Direction Retrieval from SAR Imagery

Directory of Open Access Journals (Sweden)

Lizhang Zhou

2017-06-01

Full Text Available Sea surface wind affects the fluxes of energy, mass and momentum between the atmosphere and ocean, and therefore regional and global weather and climate. With various satellite microwave sensors, sea surface wind can be measured with large spatial coverage in almost all-weather conditions, day or night. Like any other remote sensing measurements, sea surface wind measurement is also indirect. Therefore, it is important to develop appropriate wind speed and direction retrieval models for different types of microwave instruments. In this paper, a new sea surface wind direction retrieval method from synthetic aperture radar (SAR imagery is developed. In the method, local gradients are computed in frequency domain by combining the operation of smoothing and computing local gradients in one step to simplify the process and avoid the difference approximation. This improved local gradients (ILG method is compared with the traditional two-dimensional fast Fourier transform (2D FFT method and local gradients (LG method, using interpolating wind directions from the European Centre for Medium-Range Weather Forecast (ECMWF reanalysis data and the Cross-Calibrated Multi-Platform (CCMP wind vector product. The sensitivities to the salt-and-pepper noise, the additive noise and the multiplicative noise are analyzed. The ILG method shows a better performance of retrieval wind directions than the other two methods.

Differential Interpolation Effects in Free Recall

Science.gov (United States)

Petrusic, William M.; Jamieson, Donald G.

1978-01-01

Attempts to determine whether a sufficiently demanding and difficult interpolated task (shadowing, i.e., repeating aloud) would decrease recall for earlier-presented items as well as for more recent items. Listening to music was included as a second interpolated task. Results support views that serial position effects reflect a single process.…

A method of image improvement in three-dimensional imaging

International Nuclear Information System (INIS)

Suto, Yasuzo; Huang, Tewen; Furuhata, Kentaro; Uchino, Masafumi.

1988-01-01

In general, image interpolation is required when the surface configurations of such structures as bones and organs are three-dimensionally constructed from the multi-sliced images obtained by CT. Image interpolation is a processing method whereby an artificial image is inserted between two adjacent slices to make spatial resolution equal to slice resolution in appearance. Such image interpolation makes it possible to increase the image quality of the constructed three-dimensional image. In our newly-developed algorithm, we have converted the presently and subsequently sliced images to distance images, and generated the interpolation images from these two distance images. As a result, compared with the previous method, three-dimensional images with better image quality have been constructed. (author)

EBSDinterp 1.0: A MATLAB® Program to Perform Microstructurally Constrained Interpolation of EBSD Data.

Science.gov (United States)

Pearce, Mark A

2015-08-01

EBSDinterp is a graphic user interface (GUI)-based MATLAB® program to perform microstructurally constrained interpolation of nonindexed electron backscatter diffraction data points. The area available for interpolation is restricted using variations in pattern quality or band contrast (BC). Areas of low BC are not available for interpolation, and therefore cannot be erroneously filled by adjacent grains "growing" into them. Points with the most indexed neighbors are interpolated first and the required number of neighbors is reduced with each successive round until a minimum number of neighbors is reached. Further iterations allow more data points to be filled by reducing the BC threshold. This method ensures that the best quality points (those with high BC and most neighbors) are interpolated first, and that the interpolation is restricted to grain interiors before adjacent grains are grown together to produce a complete microstructure. The algorithm is implemented through a GUI, taking advantage of MATLAB®'s parallel processing toolbox to perform the interpolations rapidly so that a variety of parameters can be tested to ensure that the final microstructures are robust and artifact-free. The software is freely available through the CSIRO Data Access Portal (doi:10.4225/08/5510090C6E620) as both a compiled Windows executable and as source code.

SAR image formation with azimuth interpolation after azimuth transform

Science.gov (United States)

Doerry,; Armin W. , Martin; Grant D. , Holzrichter; Michael, W [Albuquerque, NM

2008-07-08

Two-dimensional SAR data can be processed into a rectangular grid format by subjecting the SAR data to a Fourier transform operation, and thereafter to a corresponding interpolation operation. Because the interpolation operation follows the Fourier transform operation, the interpolation operation can be simplified, and the effect of interpolation errors can be diminished. This provides for the possibility of both reducing the re-grid processing time, and improving the image quality.

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model.

Science.gov (United States)

Chen, Zhaoxue; Chen, Hao

2014-01-01

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.

Selection of a Geostatistical Method to Interpolate Soil Properties of the State Crop Testing Fields using Attributes of a Digital Terrain Model

Science.gov (United States)

Sahabiev, I. A.; Ryazanov, S. S.; Kolcova, T. G.; Grigoryan, B. R.

2018-03-01

The three most common techniques to interpolate soil properties at a field scale—ordinary kriging (OK), regression kriging with multiple linear regression drift model (RK + MLR), and regression kriging with principal component regression drift model (RK + PCR)—were examined. The results of the performed study were compiled into an algorithm of choosing the most appropriate soil mapping technique. Relief attributes were used as the auxiliary variables. When spatial dependence of a target variable was strong, the OK method showed more accurate interpolation results, and the inclusion of the auxiliary data resulted in an insignificant improvement in prediction accuracy. According to the algorithm, the RK + PCR method effectively eliminates multicollinearity of explanatory variables. However, if the number of predictors is less than ten, the probability of multicollinearity is reduced, and application of the PCR becomes irrational. In that case, the multiple linear regression should be used instead.

Image interpolation via graph-based Bayesian label propagation.

Science.gov (United States)

Xianming Liu; Debin Zhao; Jiantao Zhou; Wen Gao; Huifang Sun

2014-03-01

In this paper, we propose a novel image interpolation algorithm via graph-based Bayesian label propagation. The basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices, then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones. This process can be posed as a Bayesian inference, in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation. Specially, our algorithm first constructs a set of local interpolation models, which predict the intensity labels of all image samples, and a loss term will be minimized to keep the predicted labels of the available low-resolution (LR) samples sufficiently close to the original ones. Then, all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples. Moreover, a graph-Laplacian-based manifold regularization term is incorporated to penalize the global smoothness of intensity labels, such smoothing can alleviate the insufficient training of the local models and make them more robust. Finally, we construct a unified objective function to combine together the global loss of the locally linear regression, square error of prediction bias on the available LR samples, and the manifold regularization term. It can be solved with a closed-form solution as a convex optimization problem. Experimental results demonstrate that the proposed method achieves competitive performance with the state-of-the-art image interpolation algorithms.

Evaluation of interpolation methods for TG-43 dosimetric parameters based on comparison with Monte Carlo data for high-energy brachytherapy sources.

Science.gov (United States)

Pujades-Claumarchirant, Ma Carmen; Granero, Domingo; Perez-Calatayud, Jose; Ballester, Facundo; Melhus, Christopher; Rivard, Mark

2010-03-01

The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spatial locations not included in the radial dose function g L ( r ) and 2D anisotropy function F ( r , θ ) table entries for radial distance r and polar angle θ . The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive g L ( r ) and F ( r , θ ) from the reported data; 2) to determine the minimum number of entries in g L ( r ) and F ( r , θ ) that allow reproduction of dose distributions with sufficient accuracy. Four high-energy photon-emitting brachytherapy sources were studied: 60 Co model Co0.A86, 137 Cs model CSM-3, 192 Ir model Ir2.A85-2, and 169 Yb hypothetical model. The mesh used for r was: 0.25, 0.5, 0.75, 1, 1.5, 2-8 (integer steps) and 10 cm. Four different angular steps were evaluated for F ( r , θ ): 1°, 2°, 5° and 10°. Linear-linear and logarithmic-linear interpolation was evaluated for g L ( r ). Linear-linear interpolation was used to obtain F ( r , θ ) with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC) calculations for the four sources with the same grid. Linear interpolation of g L ( r ) provided differences ≤ 0.5% compared to MC for all four sources. Bilinear interpolation of F ( r , θ ) using 1° and 2° angular steps resulted in agreement ≤ 0.5% with MC for 60 Co, 192 Ir, and 169 Yb, while 137 Cs agreement was ≤ 1.5% for θ energy brachytherapy sources, and was similar to commonly found examples in the published literature. For F ( r , θ ) close to the source longitudinal-axis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.

Novel true-motion estimation algorithm and its application to motion-compensated temporal frame interpolation.

Science.gov (United States)

Dikbas, Salih; Altunbasak, Yucel

2013-08-01

In this paper, a new low-complexity true-motion estimation (TME) algorithm is proposed for video processing applications, such as motion-compensated temporal frame interpolation (MCTFI) or motion-compensated frame rate up-conversion (MCFRUC). Regular motion estimation, which is often used in video coding, aims to find the motion vectors (MVs) to reduce the temporal redundancy, whereas TME aims to track the projected object motion as closely as possible. TME is obtained by imposing implicit and/or explicit smoothness constraints on the block-matching algorithm. To produce better quality-interpolated frames, the dense motion field at interpolation time is obtained for both forward and backward MVs; then, bidirectional motion compensation using forward and backward MVs is applied by mixing both elegantly. Finally, the performance of the proposed algorithm for MCTFI is demonstrated against recently proposed methods and smoothness constraint optical flow employed by a professional video production suite. Experimental results show that the quality of the interpolated frames using the proposed method is better when compared with the MCFRUC techniques.

Efficient GPU-based texture interpolation using uniform B-splines

NARCIS (Netherlands)

Ruijters, D.; Haar Romenij, ter B.M.; Suetens, P.

2008-01-01

This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and

Shape Preserving Interpolation Using C2 Rational Cubic Spline

Directory of Open Access Journals (Sweden)

Samsul Ariffin Abdul Karim

2016-01-01

Full Text Available This paper discusses the construction of new C2 rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parameters αi, βi, and γi. The sufficient conditions for the positivity are derived on one parameter γi while the other two parameters αi and βi are free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation with C2 continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion and C2 continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivatives di, i=1,…,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the new C2 rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated is ft∈C3t0,tn is also investigated in detail.

Interpolation of Missing Precipitation Data Using Kernel Estimations for Hydrologic Modeling

Directory of Open Access Journals (Sweden)

Hyojin Lee

2015-01-01

Full Text Available Precipitation is the main factor that drives hydrologic modeling; therefore, missing precipitation data can cause malfunctions in hydrologic modeling. Although interpolation of missing precipitation data is recognized as an important research topic, only a few methods follow a regression approach. In this study, daily precipitation data were interpolated using five different kernel functions, namely, Epanechnikov, Quartic, Triweight, Tricube, and Cosine, to estimate missing precipitation data. This study also presents an assessment that compares estimation of missing precipitation data through Kth nearest neighborhood (KNN regression to the five different kernel estimations and their performance in simulating streamflow using the Soil Water Assessment Tool (SWAT hydrologic model. The results show that the kernel approaches provide higher quality interpolation of precipitation data compared with the KNN regression approach, in terms of both statistical data assessment and hydrologic modeling performance.

Transfinite C2 interpolant over triangles

International Nuclear Information System (INIS)

Alfeld, P.; Barnhill, R.E.

1984-01-01

A transfinite C 2 interpolant on a general triangle is created. The required data are essentially C 2 , no compatibility conditions arise, and the precision set includes all polynomials of degree less than or equal to eight. The symbol manipulation language REDUCE is used to derive the scheme. The scheme is discretized to two different finite dimensional C 2 interpolants in an appendix

Single image interpolation via adaptive nonlocal sparsity-based modeling.

Science.gov (United States)

Romano, Yaniv; Protter, Matan; Elad, Michael

2014-07-01

Single image interpolation is a central and extensively studied problem in image processing. A common approach toward the treatment of this problem in recent years is to divide the given image into overlapping patches and process each of them based on a model for natural image patches. Adaptive sparse representation modeling is one such promising image prior, which has been shown to be powerful in filling-in missing pixels in an image. Another force that such algorithms may use is the self-similarity that exists within natural images. Processing groups of related patches together exploits their correspondence, leading often times to improved results. In this paper, we propose a novel image interpolation method, which combines these two forces-nonlocal self-similarities and sparse representation modeling. The proposed method is contrasted with competitive and related algorithms, and demonstrated to achieve state-of-the-art results.

Interpolating Spline Curve-Based Perceptual Encryption for 3D Printing Models

Directory of Open Access Journals (Sweden)

Giao N. Pham

2018-02-01

Full Text Available With the development of 3D printing technology, 3D printing has recently been applied to many areas of life including healthcare and the automotive industry. Due to the benefit of 3D printing, 3D printing models are often attacked by hackers and distributed without agreement from the original providers. Furthermore, certain special models and anti-weapon models in 3D printing must be protected against unauthorized users. Therefore, in order to prevent attacks and illegal copying and to ensure that all access is authorized, 3D printing models should be encrypted before being transmitted and stored. A novel perceptual encryption algorithm for 3D printing models for secure storage and transmission is presented in this paper. A facet of 3D printing model is extracted to interpolate a spline curve of degree 2 in three-dimensional space that is determined by three control points, the curvature coefficients of degree 2, and an interpolating vector. Three control points, the curvature coefficients, and interpolating vector of the spline curve of degree 2 are encrypted by a secret key. The encrypted features of the spline curve are then used to obtain the encrypted 3D printing model by inverse interpolation and geometric distortion. The results of experiments and evaluations prove that the entire 3D triangle model is altered and deformed after the perceptual encryption process. The proposed algorithm is responsive to the various formats of 3D printing models. The results of the perceptual encryption process is superior to those of previous methods. The proposed algorithm also provides a better method and more security than previous methods.

Geostatistical interpolation of available copper in orchard soil as influenced by planting duration.

Science.gov (United States)

Fu, Chuancheng; Zhang, Haibo; Tu, Chen; Li, Lianzhen; Luo, Yongming

2018-01-01

Mapping the spatial distribution of available copper (A-Cu) in orchard soils is important in agriculture and environmental management. However, data on the distribution of A-Cu in orchard soils is usually highly variable and severely skewed due to the continuous input of fungicides. In this study, ordinary kriging combined with planting duration (OK_PD) is proposed as a method for improving the interpolation of soil A-Cu. Four normal distribution transformation methods, namely, the Box-Cox, Johnson, rank order, and normal score methods, were utilized prior to interpolation. A total of 317 soil samples were collected in the orchards of the Northeast Jiaodong Peninsula. Moreover, 1472 orchards were investigated to obtain a map of planting duration using Voronoi tessellations. The soil A-Cu content ranged from 0.09 to 106.05 with a mean of 18.10 mg kg -1 , reflecting the high availability of Cu in the soils. Soil A-Cu concentrations exhibited a moderate spatial dependency and increased significantly with increasing planting duration. All the normal transformation methods successfully decreased the skewness and kurtosis of the soil A-Cu and the associated residuals, and also computed more robust variograms. OK_PD could generate better spatial prediction accuracy than ordinary kriging (OK) for all transformation methods tested, and it also provided a more detailed map of soil A-Cu. Normal score transformation produced satisfactory accuracy and showed an advantage in ameliorating smoothing effect derived from the interpolation methods. Thus, normal score transformation prior to kriging combined with planting duration (NSOK_PD) is recommended for the interpolation of soil A-Cu in this area.

Imaging system design and image interpolation based on CMOS image sensor

Science.gov (United States)

Li, Yu-feng; Liang, Fei; Guo, Rui

2009-11-01

An image acquisition system is introduced, which consists of a color CMOS image sensor (OV9620), SRAM (CY62148), CPLD (EPM7128AE) and DSP (TMS320VC5509A). The CPLD implements the logic and timing control to the system. SRAM stores the image data, and DSP controls the image acquisition system through the SCCB (Omni Vision Serial Camera Control Bus). The timing sequence of the CMOS image sensor OV9620 is analyzed. The imaging part and the high speed image data memory unit are designed. The hardware and software design of the image acquisition and processing system is given. CMOS digital cameras use color filter arrays to sample different spectral components, such as red, green, and blue. At the location of each pixel only one color sample is taken, and the other colors must be interpolated from neighboring samples. We use the edge-oriented adaptive interpolation algorithm for the edge pixels and bilinear interpolation algorithm for the non-edge pixels to improve the visual quality of the interpolated images. This method can get high processing speed, decrease the computational complexity, and effectively preserve the image edges.

Real-time image-based B-mode ultrasound image simulation of needles using tensor-product interpolation.

Science.gov (United States)

Zhu, Mengchen; Salcudean, Septimiu E

2011-07-01

In this paper, we propose an interpolation-based method for simulating rigid needles in B-mode ultrasound images in real time. We parameterize the needle B-mode image as a function of needle position and orientation. We collect needle images under various spatial configurations in a water-tank using a needle guidance robot. Then we use multidimensional tensor-product interpolation to simulate images of needles with arbitrary poses and positions using collected images. After further processing, the interpolated needle and seed images are superimposed on top of phantom or tissue image backgrounds. The similarity between the simulated and the real images is measured using a correlation metric. A comparison is also performed with in vivo images obtained during prostate brachytherapy. Our results, carried out for both the convex (transverse plane) and linear (sagittal/para-sagittal plane) arrays of a trans-rectal transducer indicate that our interpolation method produces good results while requiring modest computing resources. The needle simulation method we present can be extended to the simulation of ultrasound images of other wire-like objects. In particular, we have shown that the proposed approach can be used to simulate brachytherapy seeds.

Effect of interpolation on parameters extracted from seating interface pressure arrays.

Science.gov (United States)

Wininger, Michael; Crane, Barbara

2014-01-01

Interpolation is a common data processing step in the study of interface pressure data collected at the wheelchair seating interface. However, there has been no focused study on the effect of interpolation on features extracted from these pressure maps, nor on whether these parameters are sensitive to the manner in which the interpolation is implemented. Here, two different interpolation paradigms, bilinear versus bicubic spline, are tested for their influence on parameters extracted from pressure array data and compared against a conventional low-pass filtering operation. Additionally, analysis of the effect of tandem filtering and interpolation, as well as the interpolation degree (interpolating to 2, 4, and 8 times sampling density), was undertaken. The following recommendations are made regarding approaches that minimized distortion of features extracted from the pressure maps: (1) filter prior to interpolate (strong effect); (2) use of cubic interpolation versus linear (slight effect); and (3) nominal difference between interpolation orders of 2, 4, and 8 times (negligible effect). We invite other investigators to perform similar benchmark analyses on their own data in the interest of establishing a community consensus of best practices in pressure array data processing.

An efficient interpolation filter VLSI architecture for HEVC standard

Science.gov (United States)

Zhou, Wei; Zhou, Xin; Lian, Xiaocong; Liu, Zhenyu; Liu, Xiaoxiang

2015-12-01

The next-generation video coding standard of High-Efficiency Video Coding (HEVC) is especially efficient for coding high-resolution video such as 8K-ultra-high-definition (UHD) video. Fractional motion estimation in HEVC presents a significant challenge in clock latency and area cost as it consumes more than 40 % of the total encoding time and thus results in high computational complexity. With aims at supporting 8K-UHD video applications, an efficient interpolation filter VLSI architecture for HEVC is proposed in this paper. Firstly, a new interpolation filter algorithm based on the 8-pixel interpolation unit is proposed in this paper. It can save 19.7 % processing time on average with acceptable coding quality degradation. Based on the proposed algorithm, an efficient interpolation filter VLSI architecture, composed of a reused data path of interpolation, an efficient memory organization, and a reconfigurable pipeline interpolation filter engine, is presented to reduce the implement hardware area and achieve high throughput. The final VLSI implementation only requires 37.2k gates in a standard 90-nm CMOS technology at an operating frequency of 240 MHz. The proposed architecture can be reused for either half-pixel interpolation or quarter-pixel interpolation, which can reduce the area cost for about 131,040 bits RAM. The processing latency of our proposed VLSI architecture can support the real-time processing of 4:2:0 format 7680 × 4320@78fps video sequences.

Geostatistical interpolation model selection based on ArcGIS and spatio-temporal variability analysis of groundwater level in piedmont plains, northwest China.

Science.gov (United States)

Xiao, Yong; Gu, Xiaomin; Yin, Shiyang; Shao, Jingli; Cui, Yali; Zhang, Qiulan; Niu, Yong

2016-01-01

Based on the geo-statistical theory and ArcGIS geo-statistical module, datas of 30 groundwater level observation wells were used to estimate the decline of groundwater level in Beijing piedmont. Seven different interpolation methods (inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, tension spline interpolation, ordinary Kriging interpolation, simple Kriging interpolation and universal Kriging interpolation) were used for interpolating groundwater level between 2001 and 2013. Cross-validation, absolute error and coefficient of determination (R(2)) was applied to evaluate the accuracy of different methods. The result shows that simple Kriging method gave the best fit. The analysis of spatial and temporal variability suggest that the nugget effects from 2001 to 2013 were increasing, which means the spatial correlation weakened gradually under the influence of human activities. The spatial variability in the middle areas of the alluvial-proluvial fan is relatively higher than area in top and bottom. Since the changes of the land use, groundwater level also has a temporal variation, the average decline rate of groundwater level between 2007 and 2013 increases compared with 2001-2006. Urban development and population growth cause over-exploitation of residential and industrial areas. The decline rate of the groundwater level in residential, industrial and river areas is relatively high, while the decreasing of farmland area and development of water-saving irrigation reduce the quantity of water using by agriculture and decline rate of groundwater level in agricultural area is not significant.

Validation of China-wide interpolated daily climate variables from 1960 to 2011

Science.gov (United States)

Yuan, Wenping; Xu, Bing; Chen, Zhuoqi; Xia, Jiangzhou; Xu, Wenfang; Chen, Yang; Wu, Xiaoxu; Fu, Yang

2015-02-01

Temporally and spatially continuous meteorological variables are increasingly in demand to support many different types of applications related to climate studies. Using measurements from 600 climate stations, a thin-plate spline method was applied to generate daily gridded climate datasets for mean air temperature, maximum temperature, minimum temperature, relative humidity, sunshine duration, wind speed, atmospheric pressure, and precipitation over China for the period 1961-2011. A comprehensive evaluation of interpolated climate was conducted at 150 independent validation sites. The results showed superior performance for most of the estimated variables. Except for wind speed, determination coefficients ( R 2) varied from 0.65 to 0.90, and interpolations showed high consistency with observations. Most of the estimated climate variables showed relatively consistent accuracy among all seasons according to the root mean square error, R 2, and relative predictive error. The interpolated data correctly predicted the occurrence of daily precipitation at validation sites with an accuracy of 83 %. Moreover, the interpolation data successfully explained the interannual variability trend for the eight meteorological variables at most validation sites. Consistent interannual variability trends were observed at 66-95 % of the sites for the eight meteorological variables. Accuracy in distinguishing extreme weather events differed substantially among the meteorological variables. The interpolated data identified extreme events for the three temperature variables, relative humidity, and sunshine duration with an accuracy ranging from 63 to 77 %. However, for wind speed, air pressure, and precipitation, the interpolation model correctly identified only 41, 48, and 58 % of extreme events, respectively. The validation indicates that the interpolations can be applied with high confidence for the three temperatures variables, as well as relative humidity and sunshine duration based

Biased motion vector interpolation for reduced video artifacts.

NARCIS (Netherlands)

2011-01-01

In a video processing system where motion vectors are estimated for a subset of the blocks of data forming a video frame, and motion vectors are interpolated for the remainder of the blocks of the frame, a method includes determining, for at least at least one block of the current frame for which a

Interpolation solution of the single-impurity Anderson model

International Nuclear Information System (INIS)

Kuzemsky, A.L.

1990-10-01

The dynamical properties of the single-impurity Anderson model (SIAM) is studied using a novel Irreducible Green's Function method (IGF). The new solution for one-particle GF interpolating between the strong and weak correlation limits is obtained. The unified concept of relevant mean-field renormalizations is indispensable for strong correlation limit. (author). 21 refs

Generation of nuclear data banks through interpolation

International Nuclear Information System (INIS)

Castillo M, J.A.

1999-01-01

Nuclear Data Bank generation, is a process in which a great amount of resources is required, both computing and humans. If it is taken into account that at some times it is necessary to create a great amount of those, it is convenient to have a reliable tool that generates Data Banks with the lesser resources, in the least possible time and with a very good approximation. In this work are shown the results obtained during the development of INTPOLBI code, used to generate Nuclear Data Banks employing bi cubic polynomial interpolation, taking as independent variables the uranium and gadolinium percents. Two proposals were worked, applying in both cases the finite element method, using one element with 16 nodes to carry out the interpolation. In the first proposals the canonic base was employed to obtain the interpolating polynomial and later, the corresponding linear equations system. In the solution of this system the Gaussian elimination method with partial pivot was applied. In the second case, the Newton base was used to obtain the mentioned system, resulting in a triangular inferior matrix, which structure, applying elemental operations, to obtain a blocks diagonal matrix, with special characteristics and easier to work with. For the validations test, a comparison was made between the values obtained with INTPOLBI and INTERTEG (created at the Instituto de Investigaciones Electricas with the same purpose) codes, and Data Banks created through the conventional process, that is, with nuclear codes normally used. Finally, it is possible to conclude that the Nuclear Data Banks generated with INTPOLBI code constitute a very good approximation that, even though do not wholly replace conventional process, however are helpful in cases when it is necessary to create a great amount of Data Banks. (Author)

Scalable Intersample Interpolation Architecture for High-channel-count Beamformers

DEFF Research Database (Denmark)

Tomov, Borislav Gueorguiev; Nikolov, Svetoslav I; Jensen, Jørgen Arendt

2011-01-01

Modern ultrasound scanners utilize digital beamformers that operate on sampled and quantized echo signals. Timing precision is of essence for achieving good focusing. The direct way to achieve it is through the use of high sampling rates, but that is not economical, so interpolation between echo...... samples is used. This paper presents a beamformer architecture that combines a band-pass filter-based interpolation algorithm with the dynamic delay-and-sum focusing of a digital beamformer. The reduction in the number of multiplications relative to a linear perchannel interpolation and band-pass per......-channel interpolation architecture is respectively 58 % and 75 % beamformer for a 256-channel beamformer using 4-tap filters. The approach allows building high channel count beamformers while maintaining high image quality due to the use of sophisticated intersample interpolation....

Cardinal Basis Piecewise Hermite Interpolation on Fuzzy Data

Directory of Open Access Journals (Sweden)

H. Vosoughi

2016-01-01

Full Text Available A numerical method along with explicit construction to interpolation of fuzzy data through the extension principle results by widely used fuzzy-valued piecewise Hermite polynomial in general case based on the cardinal basis functions, which satisfy a vanishing property on the successive intervals, has been introduced here. We have provided a numerical method in full detail using the linear space notions for calculating the presented method. In order to illustrate the method in computational examples, we take recourse to three prime cases: linear, cubic, and quintic.

Solving the Schroedinger equation using Smolyak interpolants

International Nuclear Information System (INIS)

Avila, Gustavo; Carrington, Tucker Jr.

2013-01-01

In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased

Interpolation-Based Condensation Model Reduction Part 1: Frequency Window Reduction Method Application to Structural Acoustics

National Research Council Canada - National Science Library

Ingel, R

1999-01-01

.... Projection operators are employed for the model reduction or condensation process. Interpolation is then introduced over a user defined frequency window, which can have real and imaginary boundaries and be quite large. Hermitian...

Application of Spatial Interpolation in Asphalt Pavement Climate Zoning: A Case of Temperature Parameter%空间插值算法在沥青路面气候分区中的应用研究——以温度参数为例

Institute of Scientific and Technical Information of China (English)

杨彦海; 侯博; 韦洪峰; 那达慕

2017-01-01

Temperature is one of the important indicators of the asphalt pavement climatic zoning,its accuracy of the interpolation results has great influence on the asphalt pavement climate zoning.Based on three general interpolation methods and three trend surface simulation and residual interpolation methods based on digital elevation model (DEM) respectively,interpolated annual average temperature in the hottest and coldest month of 14 years in Liaoning province.The results of the interpolation space distribution,precision and its impact on the climate zoning of asphalt pavement were analyzed and compared in detail.The results showed that:three trend surface simulation and residual interpolation methods based on DEM could reflect temperature change trend with elevation and topographic features,but three general interpolation methods couldnt be,and the accuracy of the former was about higher than the latter 1 times.At the same time,the accuracy of trend surface simulation and residual interpolation methods based on DEM in inverse distance weight was highest,the accuracy of general interpolation method in spline was lowest.Last but not the least,the higher the accuracy of the interpolation,the more close to the temperature data obtained by interpolation and the actual temperature data,the more accurate the zoning results.%温度是沥青路面气候分区的重要指标之一,其插值结果的精度对沥青路面气候分区影响极大.论文分别基于3种一般插值法及3种基于数字高程模型(DEM)的趋势面模拟+残差内插法对辽宁省14 a累年最热、冷月平均温度进行插值研究,对插值结果的空间分布、精度及其对沥青路面气候分区影响进行了详细的分析比较.研究结果表明:3种基于DEM的趋势面模拟+残值内插法均能反映温度随海拔高度等地形特征的变化趋势,而一般插值法则不能,且前者的精度约高于后者1�

Adaptive Surface Modeling of Soil Properties in Complex Landforms

Directory of Open Access Journals (Sweden)

Wei Liu

2017-06-01

Full Text Available Abstract: Spatial discontinuity often causes poor accuracy when a single model is used for the surface modeling of soil properties in complex geomorphic areas. Here we present a method for adaptive surface modeling of combined secondary variables to improve prediction accuracy during the interpolation of soil properties (ASM-SP. Using various secondary variables and multiple base interpolation models, ASM-SP was used to interpolate soil K+ in a typical complex geomorphic area (Qinghai Lake Basin, China. Five methods, including inverse distance weighting (IDW, ordinary kriging (OK, and OK combined with different secondary variables (e.g., OK-Landuse, OK-Geology, and OK-Soil, were used to validate the proposed method. The mean error (ME, mean absolute error (MAE, root mean square error (RMSE, mean relative error (MRE, and accuracy (AC were used as evaluation indicators. Results showed that: (1 The OK interpolation result is spatially smooth and has a weak bull's-eye effect, and the IDW has a stronger ‘bull’s-eye’ effect, relatively. They both have obvious deficiencies in depicting spatial variability of soil K+. (2 The methods incorporating combinations of different secondary variables (e.g., ASM-SP, OK-Landuse, OK-Geology, and OK-Soil were associated with lower estimation bias. Compared with IDW, OK, OK-Landuse, OK-Geology, and OK-Soil, the accuracy of ASM-SP increased by 13.63%, 10.85%, 9.98%, 8.32%, and 7.66%, respectively. Furthermore, ASM-SP was more stable, with lower MEs, MAEs, RMSEs, and MREs. (3 ASM-SP presents more details than others in the abrupt boundary, which can render the result consistent with the true secondary variables. In conclusion, ASM-SP can not only consider the nonlinear relationship between secondary variables and soil properties, but can also adaptively combine the advantages of multiple models, which contributes to making the spatial interpolation of soil K+ more reasonable.

Interpolation for a subclass of H

Indian Academy of Sciences (India)

|g(zm)| ≤ c |zm − zm |, ∀m ∈ N. Thus it is natural to pose the following interpolation problem for H. ∞. : DEFINITION 4. We say that (zn) is an interpolating sequence in the weak sense for H. ∞ if given any sequence of complex numbers (λn) verifying. |λn| ≤ c ψ(zn,z. ∗ n) |zn − zn |, ∀n ∈ N,. (4) there exists a product fg ∈ H.

Spatial and spectral interpolation of ground-motion intensity measure observations

Science.gov (United States)

Worden, Charles; Thompson, Eric M.; Baker, Jack W.; Bradley, Brendon A.; Luco, Nicolas; Wilson, David

2018-01-01

Following a significant earthquake, ground‐motion observations are available for a limited set of locations and intensity measures (IMs). Typically, however, it is desirable to know the ground motions for additional IMs and at locations where observations are unavailable. Various interpolation methods are available, but because IMs or their logarithms are normally distributed, spatially correlated, and correlated with each other at a given location, it is possible to apply the conditional multivariate normal (MVN) distribution to the problem of estimating unobserved IMs. In this article, we review the MVN and its application to general estimation problems, and then apply the MVN to the specific problem of ground‐motion IM interpolation. In particular, we present (1) a formulation of the MVN for the simultaneous interpolation of IMs across space and IM type (most commonly, spectral response at different oscillator periods) and (2) the inclusion of uncertain observation data in the MVN formulation. These techniques, in combination with modern empirical ground‐motion models and correlation functions, provide a flexible framework for estimating a variety of IMs at arbitrary locations.

Impact of rain gauge quality control and interpolation on streamflow simulation: an application to the Warwick catchment, Australia

Science.gov (United States)

Liu, Shulun; Li, Yuan; Pauwels, Valentijn R. N.; Walker, Jeffrey P.

2017-12-01

Rain gauges are widely used to obtain temporally continuous point rainfall records, which are then interpolated into spatially continuous data to force hydrological models. However, rainfall measurements and interpolation procedure are subject to various uncertainties, which can be reduced by applying quality control and selecting appropriate spatial interpolation approaches. Consequently, the integrated impact of rainfall quality control and interpolation on streamflow simulation has attracted increased attention but not been fully addressed. This study applies a quality control procedure to the hourly rainfall measurements obtained in the Warwick catchment in eastern Australia. The grid-based daily precipitation from the Australian Water Availability Project was used as a reference. The Pearson correlation coefficient between the daily accumulation of gauged rainfall and the reference data was used to eliminate gauges with significant quality issues. The unrealistic outliers were censored based on a comparison between gauged rainfall and the reference. Four interpolation methods, including the inverse distance weighting (IDW), nearest neighbors (NN), linear spline (LN), and ordinary Kriging (OK), were implemented. The four methods were firstly assessed through a cross-validation using the quality-controlled rainfall data. The impacts of the quality control and interpolation on streamflow simulation were then evaluated through a semi-distributed hydrological model. The results showed that the Nash–Sutcliffe model efficiency coefficient (NSE) and Bias of the streamflow simulations were significantly improved after quality control. In the cross-validation, the IDW and OK methods resulted in good interpolation rainfall, while the NN led to the worst result. In term of the impact on hydrological prediction, the IDW led to the most consistent streamflow predictions with the observations, according to the validation at five streamflow-gauged locations. The OK method

Evaluation of interpolation effects on upsampling and accuracy of cost functions-based optimized automatic image registration.

Science.gov (United States)

Mahmoudzadeh, Amir Pasha; Kashou, Nasser H

2013-01-01

Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.

Evaluation of Interpolation Effects on Upsampling and Accuracy of Cost Functions-Based Optimized Automatic Image Registration

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Amir Pasha Mahmoudzadeh

2013-01-01

Full Text Available Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order and to compare the effect of cost functions (least squares (LS, normalized mutual information (NMI, normalized cross correlation (NCC, and correlation ratio (CR for optimized automatic image registration (OAIR on 3D spoiled gradient recalled (SPGR magnetic resonance images (MRI of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.

Research Note : Near-surface layer replacement for sparse data: Is interpolation needed?

NARCIS (Netherlands)

Sun, Yimin; Verschuur, D.J.; Luo, Yi

2017-01-01

Near-surface problem is a common challenge faced by land seismic data processing, where often, due to near-surface anomalies, events of interest are obscured. One method to handle this challenge is near-surface layer replacement, which is a wavefield reconstruction process based on downward

Grade Distribution Modeling within the Bauxite Seams of the Wachangping Mine, China, Using a Multi-Step Interpolation Algorithm

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Shaofeng Wang

2017-05-01

Full Text Available Mineral reserve estimation and mining design depend on a precise modeling of the mineralized deposit. A multi-step interpolation algorithm, including 1D biharmonic spline estimator for interpolating floor altitudes, 2D nearest neighbor, linear, natural neighbor, cubic, biharmonic spline, inverse distance weighted, simple kriging, and ordinary kriging interpolations for grade distribution on the two vertical sections at roadways, and 3D linear interpolation for grade distribution between sections, was proposed to build a 3D grade distribution model of the mineralized seam in a longwall mining panel with a U-shaped layout having two roadways at both sides. Compared to field data from exploratory boreholes, this multi-step interpolation using a natural neighbor method shows an optimal stability and a minimal difference between interpolation and field data. Using this method, the 97,576 m3 of bauxite, in which the mass fraction of Al2O3 (Wa and the mass ratio of Al2O3 to SiO2 (Wa/s are 61.68% and 27.72, respectively, was delimited from the 189,260 m3 mineralized deposit in the 1102 longwall mining panel in the Wachangping mine, Southwest China. The mean absolute errors, the root mean squared errors and the relative standard deviations of errors between interpolated data and exploratory grade data at six boreholes are 2.544, 2.674, and 32.37% of Wa; and 1.761, 1.974, and 67.37% of Wa/s, respectively. The proposed method can be used for characterizing the grade distribution in a mineralized seam between two roadways at both sides of a longwall mining panel.

Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

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E. George Walters III

2015-11-01

Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

Improved Interpolation Kernels for Super-resolution Algorithms

DEFF Research Database (Denmark)

Rasti, Pejman; Orlova, Olga; Tamberg, Gert

2016-01-01

Super resolution (SR) algorithms are widely used in forensics investigations to enhance the resolution of images captured by surveillance cameras. Such algorithms usually use a common interpolation algorithm to generate an initial guess for the desired high resolution (HR) image. This initial guess...... when their original interpolation kernel is replaced by the ones introduced in this work....

Robust super-resolution by fusion of interpolated frames for color and grayscale images

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Barry eKarch

2015-04-01

Full Text Available Multi-frame super-resolution (SR processing seeks to overcome undersampling issues that can lead to undesirable aliasing artifacts. The key to effective multi-frame SR is accurate subpixel inter-frame registration. This accurate registration is challenging when the motion does not obey a simple global translational model and may include local motion. SR processing is further complicated when the camera uses a division-of-focal-plane (DoFP sensor, such as the Bayer color filter array. Various aspects of these SR challenges have been previously investigated. Fast SR algorithms tend to have difficulty accommodating complex motion and DoFP sensors. Furthermore, methods that can tolerate these complexities tend to be iterative in nature and may not be amenable to real-time processing. In this paper, we present a new fast approach for performing SR in the presence of these challenging imaging conditions. We refer to the new approach as Fusion of Interpolated Frames (FIF SR. The FIF SR method decouples the demosaicing, interpolation, and restoration steps to simplify the algorithm. Frames are first individually demosaiced and interpolated to the desired resolution. Next, FIF uses a novel weighted sum of the interpolated frames to fuse them into an improved resolution estimate. Finally, restoration is applied to deconvolve the modeled system PSF. The proposed FIF approach has a lower computational complexity than most iterative methods, making it a candidate for real-time implementation. We provide a detailed description of the FIF SR method and show experimental results using synthetic and real datasets in both constrained and complex imaging scenarios. The experiments include airborne grayscale imagery and Bayer color array images with affine background motion plus local motion.

On Multiple Interpolation Functions of the -Genocchi Polynomials

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Jin Jeong-Hee

2010-01-01

Full Text Available Abstract Recently, many mathematicians have studied various kinds of the -analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009.", Kim defined new generating functions of -Genocchi, -Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type -zeta function. This function interpolates -Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.

Direction-of-Arrival Estimation for Coprime Array Using Compressive Sensing Based Array Interpolation

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Aihua Liu

2017-01-01

Full Text Available A method of direction-of-arrival (DOA estimation using array interpolation is proposed in this paper to increase the number of resolvable sources and improve the DOA estimation performance for coprime array configuration with holes in its virtual array. The virtual symmetric nonuniform linear array (VSNLA of coprime array signal model is introduced, with the conventional MUSIC with spatial smoothing algorithm (SS-MUSIC applied on the continuous lags in the VSNLA; the degrees of freedom (DoFs for DOA estimation are obviously not fully exploited. To effectively utilize the extent of DoFs offered by the coarray configuration, a compressing sensing based array interpolation algorithm is proposed. The compressing sensing technique is used to obtain the coarse initial DOA estimation, and a modified iterative initial DOA estimation based interpolation algorithm (IMCA-AI is then utilized to obtain the final DOA estimation, which maps the sample covariance matrix of the VSNLA to the covariance matrix of a filled virtual symmetric uniform linear array (VSULA with the same aperture size. The proposed DOA estimation method can efficiently improve the DOA estimation performance. The numerical simulations are provided to demonstrate the effectiveness of the proposed method.

Correction of Sample-Time Error for Time-Interleaved Sampling System Using Cubic Spline Interpolation

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Qin Guo-jie

2014-08-01

Full Text Available Sample-time errors can greatly degrade the dynamic range of a time-interleaved sampling system. In this paper, a novel correction technique employing a cubic spline interpolation is proposed for inter-channel sample-time error compensation. The cubic spline interpolation compensation filter is developed in the form of a finite-impulse response (FIR filter structure. The correction method of the interpolation compensation filter coefficients is deduced. A 4GS/s two-channel, time-interleaved ADC prototype system has been implemented to evaluate the performance of the technique. The experimental results showed that the correction technique is effective to attenuate the spurious spurs and improve the dynamic performance of the system.

Improved Coarray Interpolation Algorithms with Additional Orthogonal Constraint for Cyclostationary Signals

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Jinyang Song

2018-01-01

Full Text Available Many modulated signals exhibit a cyclostationarity property, which can be exploited in direction-of-arrival (DOA estimation to effectively eliminate interference and noise. In this paper, our aim is to integrate the cyclostationarity with the spatial domain and enable the algorithm to estimate more sources than sensors. However, DOA estimation with a sparse array is performed in the coarray domain and the holes within the coarray limit the usage of the complete coarray information. In order to use the complete coarray information to increase the degrees-of-freedom (DOFs, sparsity-aware-based methods and the difference coarray interpolation methods have been proposed. In this paper, the coarray interpolation technique is further explored with cyclostationary signals. Besides the difference coarray model and its corresponding Toeplitz completion formulation, we build up a sum coarray model and formulate a Hankel completion problem. In order to further improve the performance of the structured matrix completion, we define the spatial spectrum sampling operations and the derivative (conjugate correlation subspaces, which can be exploited to construct orthogonal constraints for the autocorrelation vectors in the coarray interpolation problem. Prior knowledge of the source interval can also be incorporated into the problem. Simulation results demonstrate that the additional constraints contribute to a remarkable performance improvement.

Image re-sampling detection through a novel interpolation kernel.

Science.gov (United States)

Hilal, Alaa

2018-06-01

Image re-sampling involved in re-size and rotation transformations is an essential element block in a typical digital image alteration. Fortunately, traces left from such processes are detectable, proving that the image has gone a re-sampling transformation. Within this context, we present in this paper two original contributions. First, we propose a new re-sampling interpolation kernel. It depends on five independent parameters that controls its amplitude, angular frequency, standard deviation, and duration. Then, we demonstrate its capacity to imitate the same behavior of the most frequent interpolation kernels used in digital image re-sampling applications. Secondly, the proposed model is used to characterize and detect the correlation coefficients involved in re-sampling transformations. The involved process includes a minimization of an error function using the gradient method. The proposed method is assessed over a large database of 11,000 re-sampled images. Additionally, it is implemented within an algorithm in order to assess images that had undergone complex transformations. Obtained results demonstrate better performance and reduced processing time when compared to a reference method validating the suitability of the proposed approaches. Copyright © 2018 Elsevier B.V. All rights reserved.

Optimized Quasi-Interpolators for Image Reconstruction.

Science.gov (United States)

Sacht, Leonardo; Nehab, Diego

2015-12-01

We propose new quasi-interpolators for the continuous reconstruction of sampled images, combining a narrowly supported piecewise-polynomial kernel and an efficient digital filter. In other words, our quasi-interpolators fit within the generalized sampling framework and are straightforward to use. We go against standard practice and optimize for approximation quality over the entire Nyquist range, rather than focusing exclusively on the asymptotic behavior as the sample spacing goes to zero. In contrast to previous work, we jointly optimize with respect to all degrees of freedom available in both the kernel and the digital filter. We consider linear, quadratic, and cubic schemes, offering different tradeoffs between quality and computational cost. Experiments with compounded rotations and translations over a range of input images confirm that, due to the additional degrees of freedom and the more realistic objective function, our new quasi-interpolators perform better than the state of the art, at a similar computational cost.

Diabat Interpolation for Polymorph Free-Energy Differences.

Science.gov (United States)

Kamat, Kartik; Peters, Baron

2017-02-02

Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.

Using reweighting and free energy surface interpolation to predict solid-solid phase diagrams

Science.gov (United States)

Schieber, Natalie P.; Dybeck, Eric C.; Shirts, Michael R.

2018-04-01

Many physical properties of small organic molecules are dependent on the current crystal packing, or polymorph, of the material, including bioavailability of pharmaceuticals, optical properties of dyes, and charge transport properties of semiconductors. Predicting the most stable crystalline form at a given temperature and pressure requires determining the crystalline form with the lowest relative Gibbs free energy. Effective computational prediction of the most stable polymorph could save significant time and effort in the design of novel molecular crystalline solids or predict their behavior under new conditions. In this study, we introduce a new approach using multistate reweighting to address the problem of determining solid-solid phase diagrams and apply this approach to the phase diagram of solid benzene. For this approach, we perform sampling at a selection of temperature and pressure states in the region of interest. We use multistate reweighting methods to determine the reduced free energy differences between T and P states within a given polymorph and validate this phase diagram using several measures. The relative stability of the polymorphs at the sampled states can be successively interpolated from these points to create the phase diagram by combining these reduced free energy differences with a reference Gibbs free energy difference between polymorphs. The method also allows for straightforward estimation of uncertainties in the phase boundary. We also find that when properly implemented, multistate reweighting for phase diagram determination scales better with the size of the system than previously estimated.

Hörmander spaces, interpolation, and elliptic problems

CERN Document Server

Mikhailets, Vladimir A; Malyshev, Peter V

2014-01-01

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005-2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a

An Algorithmic Comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a Nonlinear Thermal Problem

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Felix Fritzen

2018-02-01

Full Text Available A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete Empirical Interpolation Method (EIM, DEIM. An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (DEIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations.

Input variable selection for interpolating high-resolution climate ...

African Journals Online (AJOL)

Although the primary input data of climate interpolations are usually meteorological data, other related (independent) variables are frequently incorporated in the interpolation process. One such variable is elevation, which is known to have a strong influence on climate. This research investigates the potential of 4 additional ...

A meshless scheme for partial differential equations based on multiquadric trigonometric B-spline quasi-interpolation

International Nuclear Information System (INIS)

Gao Wen-Wu; Wang Zhi-Gang

2014-01-01

Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions. (general)

Extension Of Lagrange Interpolation

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Mousa Makey Krady

2015-01-01

Full Text Available Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.

Interpolation and sampling in spaces of analytic functions

CERN Document Server

Seip, Kristian

2004-01-01

The book is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for H^\\infty, and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem. The book aims at clarifying how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences. Key words for the geometric descriptions are Carleson measures, Beurling densities, the Nyquist rate, and the Helson-Szegő condition. The book is based on six lectures given by the author at the University of Michigan. This is reflected in the exposition, which is a blend of informal explanations with technical details. The book is essentially self-contained. There is an underlying assumption that the reader has a basic knowledge of complex and functional analysis. Beyond that, the reader should have some familiari...

Performance Assessment of Spatial Interpolation of Precipitation for Hydrological Process Simulation in the Three Gorges Basin

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Meiling Cheng

2017-11-01

Full Text Available Accurate assessment of spatial and temporal precipitation is crucial for simulating hydrological processes in basins, but is challenging due to insufficient rain gauges. Our study aims to analyze different precipitation interpolation schemes and their performances in runoff simulation during light and heavy rain periods. In particular, combinations of different interpolation estimates are explored and their performances in runoff simulation are discussed. The study was carried out in the Pengxi River basin of the Three Gorges Basin. Precipitation data from 16 rain gauges were interpolated using the Thiessen Polygon (TP, Inverse Distance Weighted (IDW, and Co-Kriging (CK methods. Results showed that streamflow predictions employing CK inputs demonstrated the best performance in the whole process, in terms of the Nash–Sutcliffe Coefficient (NSE, the coefficient of determination (R2, and the Root Mean Square Error (RMSE indices. The TP, IDW, and CK methods showed good performance in the heavy rain period but poor performance in the light rain period compared with the default method (least sophisticated nearest neighbor technique in Soil and Water Assessment Tool (SWAT. Furthermore, the correlation between the dynamic weight of one method and its performance during runoff simulation followed a parabolic function. The combination of CK and TP achieved a better performance in decreasing the largest and lowest absolute errors compared to any single method, but the IDW method outperformed all methods in terms of the median absolute error. However, it is clear from our findings that interpolation methods should be chosen depending on the amount of precipitation, adaptability of the method, and accuracy of the estimate in different rain periods.

Global sensitivity analysis using sparse grid interpolation and polynomial chaos

International Nuclear Information System (INIS)

Buzzard, Gregery T.

2012-01-01

Sparse grid interpolation is widely used to provide good approximations to smooth functions in high dimensions based on relatively few function evaluations. By using an efficient conversion from the interpolating polynomial provided by evaluations on a sparse grid to a representation in terms of orthogonal polynomials (gPC representation), we show how to use these relatively few function evaluations to estimate several types of sensitivity coefficients and to provide estimates on local minima and maxima. First, we provide a good estimate of the variance-based sensitivity coefficients of Sobol' (1990) [1] and then use the gradient of the gPC representation to give good approximations to the derivative-based sensitivity coefficients described by Kucherenko and Sobol' (2009) [2]. Finally, we use the package HOM4PS-2.0 given in Lee et al. (2008) [3] to determine the critical points of the interpolating polynomial and use these to determine the local minima and maxima of this polynomial. - Highlights: ► Efficient estimation of variance-based sensitivity coefficients. ► Efficient estimation of derivative-based sensitivity coefficients. ► Use of homotopy methods for approximation of local maxima and minima.

Effect of interpolation on parameters extracted from seating interface pressure arrays

OpenAIRE

Michael Wininger, PhD; Barbara Crane, PhD, PT

2015-01-01

Interpolation is a common data processing step in the study of interface pressure data collected at the wheelchair seating interface. However, there has been no focused study on the effect of interpolation on features extracted from these pressure maps, nor on whether these parameters are sensitive to the manner in which the interpolation is implemented. Here, two different interpolation paradigms, bilinear versus bicubic spline, are tested for their influence on parameters extracted from pre...

Geospatial interpolation of reference evapotranspiration (ETo in areas with scarce data: case study in the South of Minas Gerais, Brazil

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Silvio Jorge Coelho Simões

2012-08-01

Full Text Available The reference evapotranspiration is an important hydrometeorological variable; its measurement is scarce in large portions of the Brazilian territory, what demands the search for alternative methods and techniques for its quantification. In this sense, the present work investigated a method for the spatialization of the reference evapotranspiration using the geostatistical method of kriging, in regions with limited data and hydrometeorological stations. The monthly average reference evapotranspiration was calculated by the Penman-Monteith-FAO equation, based on data from three weather stations located in southern Minas Gerais (Itajubá, Lavras and Poços de Caldas, and subsequently interpolated by ordinary point kriging using the approach "calculate and interpolate." The meteorological data for a fourth station (Três Corações located within the area of interpolation were used to validate the reference evapotranspiration interpolated spatially. Due to the reduced number of stations and the consequent impossibility of carrying variographic analyzes, correlation coefficient (r, index of agreement (d, medium bias error (MBE, root mean square error (RMSE and t-test were used for comparison between the calculated and interpolated reference evapotranspiration for the Três Corações station. The results of this comparison indicated that the spatial kriging procedure, even using a few stations, allows to interpolate satisfactorily the reference evapotranspiration, therefore, it is an important tool for agricultural and hydrological applications in regions with lack of data.

Fast Shepard interpolation on graphics processing units: potential energy surfaces and dynamics for H + CH4 → H2 + CH3.

Science.gov (United States)

Welsch, Ralph; Manthe, Uwe

2013-04-28

A strategy for the fast evaluation of Shepard interpolated potential energy surfaces (PESs) utilizing graphics processing units (GPUs) is presented. Speed ups of several orders of magnitude are gained for the title reaction on the ZFWCZ PES [Y. Zhou, B. Fu, C. Wang, M. A. Collins, and D. H. Zhang, J. Chem. Phys. 134, 064323 (2011)]. Thermal rate constants are calculated employing the quantum transition state concept and the multi-layer multi-configurational time-dependent Hartree approach. Results for the ZFWCZ PES are compared to rate constants obtained for other ab initio PESs and problems are discussed. A revised PES is presented. Thermal rate constants obtained for the revised PES indicate that an accurate description of the anharmonicity around the transition state is crucial.

Comparison of spatial interpolation techniques to predict soil properties in the colombian piedmont eastern plains

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Mauricio Castro Franco

2017-07-01

Full Text Available Context: Interpolating soil properties at field-scale in the Colombian piedmont eastern plains is challenging due to: the highly and complex variable nature of some processes; the effects of the soil; the land use; and the management. While interpolation techniques are being adapted to include auxiliary information of these effects, the soil data are often difficult to predict using conventional techniques of spatial interpolation. Method: In this paper, we evaluated and compared six spatial interpolation techniques: Inverse Distance Weighting (IDW, Spline, Ordinary Kriging (KO, Universal Kriging (UK, Cokriging (Ckg, and Residual Maximum Likelihood-Empirical Best Linear Unbiased Predictor (REML-EBLUP, from conditioned Latin Hypercube as a sampling strategy. The ancillary information used in Ckg and REML-EBLUP was indexes calculated from a digital elevation model (MDE. The “Random forest” algorithm was used for selecting the most important terrain index for each soil properties. Error metrics were used to validate interpolations against cross validation. Results: The results support the underlying assumption that HCLc captured adequately the full distribution of variables of ancillary information in the Colombian piedmont eastern plains conditions. They also suggest that Ckg and REML-EBLUP perform best in the prediction in most of the evaluated soil properties. Conclusions: Mixed interpolation techniques having auxiliary soil information and terrain indexes, provided a significant improvement in the prediction of soil properties, in comparison with other techniques.

Optimum and robust 3D facies interpolation strategies in a heterogeneous coal zone (Tertiary As Pontes basin, NW Spain)

Energy Technology Data Exchange (ETDEWEB)

Falivene, Oriol; Cabrera, Lluis; Saez, Alberto [Geomodels Institute, Group of Geodynamics and Basin Analysis, Department of Stratigraphy, Paleontology and Marine Geosciences, Universitat de Barcelona, c/ Marti i Franques s/n, Facultat de Geologia, 08028 Barcelona (Spain)

2007-07-02

Coal exploration and mining in extensively drilled and sampled coal zones can benefit from 3D statistical facies interpolation. Starting from closely spaced core descriptions, and using interpolation methods, a 3D optimum and robust facies distribution model was obtained for a thick, heterogeneous coal zone deposited in the non-marine As Pontes basin (Oligocene-Early Miocene, NW Spain). Several grid layering styles, interpolation methods (truncated inverse squared distance weighting, truncated kriging, truncated kriging with an areal trend, indicator inverse squared distance weighting, indicator kriging, and indicator kriging with an areal trend) and searching conditions were compared. Facies interpolation strategies were evaluated using visual comparison and cross validation. Moreover, robustness of the resultant facies distribution with respect to variations in interpolation method input parameters was verified by taking into account several scenarios of uncertainty. The resultant 3D facies reconstruction improves the understanding of the distribution and geometry of the coal facies. Furthermore, since some coal quality properties (e.g. calorific value or sulphur percentage) display a good statistical correspondence with facies, predicting the distribution of these properties using the reconstructed facies distribution as a template proved to be a powerful approach, yielding more accurate and realistic reconstructions of these properties in the coal zone. (author)

Image interpolation allows accurate quantitative bone morphometry in registered micro-computed tomography scans.

Science.gov (United States)

Schulte, Friederike A; Lambers, Floor M; Mueller, Thomas L; Stauber, Martin; Müller, Ralph

2014-04-01

Time-lapsed in vivo micro-computed tomography is a powerful tool to analyse longitudinal changes in the bone micro-architecture. Registration can overcome problems associated with spatial misalignment between scans; however, it requires image interpolation which might affect the outcome of a subsequent bone morphometric analysis. The impact of the interpolation error itself, though, has not been quantified to date. Therefore, the purpose of this ex vivo study was to elaborate the effect of different interpolator schemes [nearest neighbour, tri-linear and B-spline (BSP)] on bone morphometric indices. None of the interpolator schemes led to significant differences between interpolated and non-interpolated images, with the lowest interpolation error found for BSPs (1.4%). Furthermore, depending on the interpolator, the processing order of registration, Gaussian filtration and binarisation played a role. Independent from the interpolator, the present findings suggest that the evaluation of bone morphometry should be done with images registered using greyscale information.

Lagrangian Finite-Element Method for the Simulation of K-BKZ Fluids with Third Order Accuracy

DEFF Research Database (Denmark)

Marin, José Manuel Román; Rasmussen, Henrik K.

2009-01-01

system attached to the particles is discretized by ten-node quadratic tetrahedral elements using Cartesian coordinates and the pressure by linear interpolation inside these elements. The spatial discretization of the governing equations follows the mixed Galerkin finite element method. The time integral...... is discretized by a quadratic interpolation in time. The convergence of the method in time and space was demonstrated on the free surface problem of a filament stretched between two plates, considering the axisymmetric case as well as the growth of non-axisymmetric disturbances on the free surface. The scheme...

Joint seismic data denoising and interpolation with double-sparsity dictionary learning

Science.gov (United States)

Zhu, Lingchen; Liu, Entao; McClellan, James H.

2017-08-01

Seismic data quality is vital to geophysical applications, so that methods of data recovery, including denoising and interpolation, are common initial steps in the seismic data processing flow. We present a method to perform simultaneous interpolation and denoising, which is based on double-sparsity dictionary learning. This extends previous work that was for denoising only. The original double-sparsity dictionary learning algorithm is modified to track the traces with missing data by defining a masking operator that is integrated into the sparse representation of the dictionary. A weighted low-rank approximation algorithm is adopted to handle the dictionary updating as a sparse recovery optimization problem constrained by the masking operator. Compared to traditional sparse transforms with fixed dictionaries that lack the ability to adapt to complex data structures, the double-sparsity dictionary learning method learns the signal adaptively from selected patches of the corrupted seismic data, while preserving compact forward and inverse transform operators. Numerical experiments on synthetic seismic data indicate that this new method preserves more subtle features in the data set without introducing pseudo-Gibbs artifacts when compared to other directional multi-scale transform methods such as curvelets.

LINEAR2007, Linear-Linear Interpolation of ENDF Format Cross-Sections

International Nuclear Information System (INIS)

2007-01-01

1 - Description of program or function: LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form. Codes used subsequently need thus to consider only linear-linear data. IAEA1311/15: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. Modifications from previous versions: - Linear VERS. 2007-1 (JAN. 2007): checked against all ENDF/B-VII; increased page size from 60,000 to 600,000 points 2 - Method of solution: Each section of data is considered separately. Each section of File 3, 23, and 27 data consists of a table of cross section versus energy with any of five interpolation laws. LINEAR will replace each section with a new table of energy versus cross section data in which the interpolation law is always linear in energy and cross section. The histogram (constant cross section between two energies) interpolation law is converted to linear-linear by substituting two points for each initial point. The linear-linear is not altered. For the log-linear, linear-log and log- log laws, the cross section data are converted to linear by an interval halving algorithm. Each interval is divided in half until the value at the middle of the interval can be approximated by linear-linear interpolation to within a given accuracy. The LINEAR program uses a multipoint fractional error thinning algorithm to minimize the size of each cross section table

Spatial interpolation of hourly rainfall – effect of additional information, variogram inference and storm properties

Directory of Open Access Journals (Sweden)

A. Verworn

2011-02-01

Full Text Available Hydrological modelling of floods relies on precipitation data with a high resolution in space and time. A reliable spatial representation of short time step rainfall is often difficult to achieve due to a low network density. In this study hourly precipitation was spatially interpolated with the multivariate geostatistical method kriging with external drift (KED using additional information from topography, rainfall data from the denser daily networks and weather radar data. Investigations were carried out for several flood events in the time period between 2000 and 2005 caused by different meteorological conditions. The 125 km radius around the radar station Ummendorf in northern Germany covered the overall study region. One objective was to assess the effect of different approaches for estimation of semivariograms on the interpolation performance of short time step rainfall. Another objective was the refined application of the method kriging with external drift. Special attention was not only given to find the most relevant additional information, but also to combine the additional information in the best possible way. A multi-step interpolation procedure was applied to better consider sub-regions without rainfall.

The impact of different semivariogram types on the interpolation performance was low. While it varied over the events, an averaged semivariogram was sufficient overall. Weather radar data were the most valuable additional information for KED for convective summer events. For interpolation of stratiform winter events using daily rainfall as additional information was sufficient. The application of the multi-step procedure significantly helped to improve the representation of fractional precipitation coverage.

Optimal Interpolation scheme to generate reference crop evapotranspiration

Science.gov (United States)

Tomas-Burguera, Miquel; Beguería, Santiago; Vicente-Serrano, Sergio; Maneta, Marco

2018-05-01

We used an Optimal Interpolation (OI) scheme to generate a reference crop evapotranspiration (ETo) grid, forcing meteorological variables, and their respective error variance in the Iberian Peninsula for the period 1989-2011. To perform the OI we used observational data from the Spanish Meteorological Agency (AEMET) and outputs from a physically-based climate model. To compute ETo we used five OI schemes to generate grids for the five observed climate variables necessary to compute ETo using the FAO-recommended form of the Penman-Monteith equation (FAO-PM). The granularity of the resulting grids are less sensitive to variations in the density and distribution of the observational network than those generated by other interpolation methods. This is because our implementation of the OI method uses a physically-based climate model as prior background information about the spatial distribution of the climatic variables, which is critical for under-observed regions. This provides temporal consistency in the spatial variability of the climatic fields. We also show that increases in the density and improvements in the distribution of the observational network reduces substantially the uncertainty of the climatic and ETo estimates. Finally, a sensitivity analysis of observational uncertainties and network densification suggests the existence of a trade-off between quantity and quality of observations.

LINTAB, Linear Interpolable Tables from any Continuous Variable Function

International Nuclear Information System (INIS)

1988-01-01

1 - Description of program or function: LINTAB is designed to construct linearly interpolable tables from any function. The program will start from any function of a single continuous variable... FUNKY(X). By user input the function can be defined, (1) Over 1 to 100 X ranges. (2) Within each X range the function is defined by 0 to 50 constants. (3) At boundaries between X ranges the function may be continuous or discontinuous (depending on the constants used to define the function within each X range). 2 - Method of solution: LINTAB will construct a table of X and Y values where the tabulated (X,Y) pairs will be exactly equal to the function (Y=FUNKY(X)) and linear interpolation between the tabulated pairs will be within any user specified fractional uncertainty of the function for all values of X within the requested X range

Motion compensated frame interpolation with a symmetric optical flow constraint

DEFF Research Database (Denmark)

Rakêt, Lars Lau; Roholm, Lars; Bruhn, Andrés

2012-01-01

We consider the problem of interpolating frames in an image sequence. For this purpose accurate motion estimation can be very helpful. We propose to move the motion estimation from the surrounding frames directly to the unknown frame by parametrizing the optical flow objective function such that ......We consider the problem of interpolating frames in an image sequence. For this purpose accurate motion estimation can be very helpful. We propose to move the motion estimation from the surrounding frames directly to the unknown frame by parametrizing the optical flow objective function...... methods. The proposed reparametrization is generic and can be applied to almost every existing algorithm. In this paper we illustrate its advantages by considering the classic TV-L1 optical flow algorithm as a prototype. We demonstrate that this widely used method can produce results that are competitive...... with current state-of-the-art methods. Finally we show that the scheme can be implemented on graphics hardware such that it be- comes possible to double the frame rate of 640 × 480 video footage at 30 fps, i.e. to perform frame doubling in realtime....

Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

DEFF Research Database (Denmark)

Fyhn, Karsten; Duarte, Marco F.; Jensen, Søren Holdt

2015-01-01

We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non...... to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super...... interpolation increases the estimation precision....

Three-dimensional reconstruction from cone-beam data using an efficient Fourier technique combined with a special interpolation filter

International Nuclear Information System (INIS)

Magnusson Seger, Maria

1998-01-01

We here present LINCON FAST which is an exact method for 3D reconstruction from cone-beam projection data. The new method is compared to the LINCON method which is known to be fast and to give good image quality. Both methods have O(N 3 log N) complexity and are based on Grangeat's result which states that the derivative of the Radon transform of the object function can be obtained from cone-beam projections. One disadvantage with LINCON is that the rather computationally intensive chirp z-transform is frequently used. In LINCON FAST , FFT and interpolation in the Fourier domain are used instead, which are less computationally demanding. The computation tools involved in LINCON FAST are solely FFT, 1D eight-point interpolation, multiplicative weighting and tri-linear interpolation. We estimate that LINCON FAST will be 2-2.5 times faster than LINCON. The interpolation filter belongs to a special class of filters developed by us. It turns out that the filter must be very carefully designed to keep a good image quality. Visual inspection of experimental results shows that the image quality is almost the same for LINCON and the new method LINCON FAST . However, it should be remembered that LINCON FAST can never give better image quality than LINCON, since LINCON FAST is designed to approximate LINCON as well as possible. (author)

A novel power harmonic analysis method based on Nuttall-Kaiser combination window double spectrum interpolated FFT algorithm

Science.gov (United States)

Jin, Tao; Chen, Yiyang; Flesch, Rodolfo C. C.

2017-11-01

Harmonics pose a great threat to safe and economical operation of power grids. Therefore, it is critical to detect harmonic parameters accurately to design harmonic compensation equipment. The fast Fourier transform (FFT) is widely used for electrical popular power harmonics analysis. However, the barrier effect produced by the algorithm itself and spectrum leakage caused by asynchronous sampling often affects the harmonic analysis accuracy. This paper examines a new approach for harmonic analysis based on deducing the modifier formulas of frequency, phase angle, and amplitude, utilizing the Nuttall-Kaiser window double spectrum line interpolation method, which overcomes the shortcomings in traditional FFT harmonic calculations. The proposed approach is verified numerically and experimentally to be accurate and reliable.

Comparison of the accuracy of kriging and IDW interpolations in estimating groundwater arsenic concentrations in Texas.

Science.gov (United States)

Gong, Gordon; Mattevada, Sravan; O'Bryant, Sid E

2014-04-01

Exposure to arsenic causes many diseases. Most Americans in rural areas use groundwater for drinking, which may contain arsenic above the currently allowable level, 10µg/L. It is cost-effective to estimate groundwater arsenic levels based on data from wells with known arsenic concentrations. We compared the accuracy of several commonly used interpolation methods in estimating arsenic concentrations in >8000 wells in Texas by the leave-one-out-cross-validation technique. Correlation coefficient between measured and estimated arsenic levels was greater with inverse distance weighted (IDW) than kriging Gaussian, kriging spherical or cokriging interpolations when analyzing data from wells in the entire Texas (pgroundwater arsenic level depends on both interpolation methods and wells' geographic distributions and characteristics in Texas. Taking well depth and elevation into regression analysis as covariates significantly increases the accuracy in estimating groundwater arsenic level in Texas with IDW in particular. Published by Elsevier Inc.

BV-norm convergence of interpolation approximations for Frobenius-Perron operators

International Nuclear Information System (INIS)

Ding, J; Rhee, N

2008-01-01

Let S be a chaotic transformation from an interval into itself and let P be the corresponding Frobenius-Perron operator associated with S. In this paper we prove the convergence under the variation norm for a piecewise linear interpolation method that was recently proposed by the authors for computing a stationary density of P

NOAA Daily 25km Global Optimally Interpolated Sea Surface Temperature (OISST) in situ and AVHRR analysis supplemented with AVHRR Pathfinder Version 5.0 climatological SST for inland and coastal pixels, 1981-09-01 through 2010-12-31 (NODC Accession 0071180)

Data.gov (United States)

National Oceanic and Atmospheric Administration, Department of Commerce — This accession contains the daily 25km global Optimally Interpolated Sea Surface Temperature (OISST) in situ and AVHRR analysis, supplemented with AVHRR Pathfinder...

Description of the ECMWF/WMO Global Observational Data Set, and associated data extraction and interpolation procedures

NARCIS (Netherlands)

Potma CJM

1993-01-01

This report presents a description of data-extraction and interpolation procedures using the ECMWF/WMO Global Observational Data Set (ODS), an archive of unvalidated observational meteorological surface data measured at 00, 06, 12 and 18 UT. The archive covers the period 1 January 1980 to 31

Interpolation in Spaces of Functions

Directory of Open Access Journals (Sweden)

K. Mosaleheh

2006-03-01

Full Text Available In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces

Multivariate Hermite interpolation on scattered point sets using tensor-product expo-rational B-splines

Science.gov (United States)

Dechevsky, Lubomir T.; Bang, Børre; Laksa˚, Arne; Zanaty, Peter

2011-12-01

At the Seventh International Conference on Mathematical Methods for Curves and Surfaces, To/nsberg, Norway, in 2008, several new constructions for Hermite interpolation on scattered point sets in domains in Rn,n∈N, combined with smooth convex partition of unity for several general types of partitions of these domains were proposed in [1]. All of these constructions were based on a new type of B-splines, proposed by some of the authors several years earlier: expo-rational B-splines (ERBS) [3]. In the present communication we shall provide more details about one of these constructions: the one for the most general class of domain partitions considered. This construction is based on the use of two separate families of basis functions: one which has all the necessary Hermite interpolation properties, and another which has the necessary properties of a smooth convex partition of unity. The constructions of both of these two bases are well-known; the new part of the construction is the combined use of these bases for the derivation of a new basis which enjoys having all above-said interpolation and unity partition properties simultaneously. In [1] the emphasis was put on the use of radial basis functions in the definitions of the two initial bases in the construction; now we shall put the main emphasis on the case when these bases consist of tensor-product B-splines. This selection provides two useful advantages: (A) it is easier to compute higher-order derivatives while working in Cartesian coordinates; (B) it becomes clear that this construction becomes a far-going extension of tensor-product constructions. We shall provide 3-dimensional visualization of the resulting bivariate bases, using tensor-product ERBS. In the main tensor-product variant, we shall consider also replacement of ERBS with simpler generalized ERBS (GERBS) [2], namely, their simplified polynomial modifications: the Euler Beta-function B-splines (BFBS). One advantage of using BFBS instead of ERBS

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

Science.gov (United States)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-06-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts

Science.gov (United States)

Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf

2018-04-01

For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.

Evaluation of Interpolants in Their Ability to Fit Seismometric Time Series

Directory of Open Access Journals (Sweden)

Kanadpriya Basu

2015-08-01

Full Text Available This article is devoted to the study of the ASARCO demolition seismic data. Two different classes of modeling techniques are explored: First, mathematical interpolation methods and second statistical smoothing approaches for curve fitting. We estimate the characteristic parameters of the propagation medium for seismic waves with multiple mathematical and statistical techniques, and provide the relative advantages of each approach to address fitting of such data. We conclude that mathematical interpolation techniques and statistical curve fitting techniques complement each other and can add value to the study of one dimensional time series seismographic data: they can be use to add more data to the system in case the data set is not large enough to perform standard statistical tests.

Interface information transfer between non-matching, nonconforming interfaces using radial basis function interpolation

CSIR Research Space (South Africa)

Bogaers, Alfred EJ

2016-10-01

Full Text Available words, gB = [ φBA PB ] [ MAA PA P TA 0 ]−1 [ gA 0 ] . (15) NAME: DEFINITION C0 compactly supported piecewise polynomial (C0): (1− (||x|| /r))2+ C2 compactly supported piecewise polynomial (C2): (1− (||x|| /r))4+ (4 (||x|| /r) + 1) Thin-plate spline (TPS... a numerical comparison to Kriging and the moving least-squares method, see Krishnamurthy [16]). RBF interpolation is based on fitting a series of splines, or basis functions to interpolate information from one point cloud to another. Let us assume we...

Sibsonian and non-Sibsonian natural neighbour interpolation of the total electron content value

Science.gov (United States)

Kotulak, Kacper; Froń, Adam; Krankowski, Andrzej; Pulido, German Olivares; Henrandez-Pajares, Manuel

2017-03-01

In radioastronomy the interferometric measurement between radiotelescopes located relatively close to each other helps removing ionospheric effects. Unfortunately, in case of networks such as LOw Frequency ARray (LOFAR), due to long baselines (currently up to 1500 km), interferometric methods fail to provide sufficiently accurate ionosphere delay corrections. Practically it means that systems such as LOFAR need external ionosphere information, coming from Global or Regional Ionospheric Maps (GIMs or RIMs, respectively). Thanks to the technology based on Global Navigation Satellite Systems (GNSS), the scientific community is provided with ionosphere sounding virtually worldwide. In this paper we compare several interpolation methods for RIMs computation based on scattered Vertical Total Electron Content measurements located on one thin ionospheric layer (Ionospheric Pierce Points—IPPs). The results of this work show that methods that take into account the topology of the data distribution (e.g., natural neighbour interpolation) perform better than those based on geometric computation only (e.g., distance-weighted methods).

Interpolation of extensive routine water pollution monitoring datasets: methodology and discussion of implications for aquifer management.

Science.gov (United States)

Yuval, Yuval; Rimon, Yaara; Graber, Ellen R; Furman, Alex

2014-08-01

A large fraction of the fresh water available for human use is stored in groundwater aquifers. Since human activities such as mining, agriculture, industry and urbanisation often result in incursion of various pollutants to groundwater, routine monitoring of water quality is an indispensable component of judicious aquifer management. Unfortunately, groundwater pollution monitoring is expensive and usually cannot cover an aquifer with the spatial resolution necessary for making adequate management decisions. Interpolation of monitoring data is thus an important tool for supplementing monitoring observations. However, interpolating routine groundwater pollution data poses a special problem due to the nature of the observations. The data from a producing aquifer usually includes many zero pollution concentration values from the clean parts of the aquifer but may span a wide range of values (up to a few orders of magnitude) in the polluted areas. This manuscript presents a methodology that can cope with such datasets and use them to produce maps that present the pollution plumes but also delineates the clean areas that are fit for production. A method for assessing the quality of mapping in a way which is suitable to the data's dynamic range of values is also presented. A local variant of inverse distance weighting is employed to interpolate the data. Inclusion zones around the interpolation points ensure that only relevant observations contribute to each interpolated concentration. Using inclusion zones improves the accuracy of the mapping but results in interpolation grid points which are not assigned a value. The inherent trade-off between the interpolation accuracy and coverage is demonstrated using both circular and elliptical inclusion zones. A leave-one-out cross testing is used to assess and compare the performance of the interpolations. The methodology is demonstrated using groundwater pollution monitoring data from the coastal aquifer along the Israeli

Interpolation of extensive routine water pollution monitoring datasets: methodology and discussion of implications for aquifer management

Science.gov (United States)

Yuval; Rimon, Y.; Graber, E. R.; Furman, A.

2013-07-01

A large fraction of the fresh water available for human use is stored in groundwater aquifers. Since human activities such as mining, agriculture, industry and urbanization often result in incursion of various pollutants to groundwater, routine monitoring of water quality is an indispensable component of judicious aquifer management. Unfortunately, groundwater pollution monitoring is expensive and usually cannot cover an aquifer with the spatial resolution necessary for making adequate management decisions. Interpolation of monitoring data between points is thus an important tool for supplementing measured data. However, interpolating routine groundwater pollution data poses a special problem due to the nature of the observations. The data from a producing aquifer usually includes many zero pollution concentration values from the clean parts of the aquifer but may span a wide range (up to a few orders of magnitude) of values in the polluted areas. This manuscript presents a methodology that can cope with such datasets and use them to produce maps that present the pollution plumes but also delineates the clean areas that are fit for production. A method for assessing the quality of mapping in a way which is suitable to the data's dynamic range of values is also presented. Local variant of inverse distance weighting is employed to interpolate the data. Inclusion zones around the interpolation points ensure that only relevant observations contribute to each interpolated concentration. Using inclusion zones improves the accuracy of the mapping but results in interpolation grid points which are not assigned a value. That inherent trade-off between the interpolation accuracy and coverage is demonstrated using both circular and elliptical inclusion zones. A leave-one-out cross testing is used to assess and compare the performance of the interpolations. The methodology is demonstrated using groundwater pollution monitoring data from the Coastal aquifer along the Israeli

Size-Dictionary Interpolation for Robot's Adjustment

Directory of Open Access Journals (Sweden)

Morteza eDaneshmand

2015-05-01

Full Text Available This paper describes the classification and size-dictionary interpolation of the three-dimensional data obtained by a laser scanner to be used in a realistic virtual fitting room, where automatic activation of the chosen mannequin robot, while several mannequin robots of different genders and sizes are simultaneously connected to the same computer, is also considered to make it mimic the body shapes and sizes instantly. The classification process consists of two layers, dealing, respectively, with gender and size. The interpolation procedure tries to find out which set of the positions of the biologically-inspired actuators for activation of the mannequin robots could lead to the closest possible resemblance of the shape of the body of the person having been scanned, through linearly mapping the distances between the subsequent size-templates and the corresponding position set of the bioengineered actuators, and subsequently, calculating the control measures that could maintain the same distance proportions, where minimizing the Euclidean distance between the size-dictionary template vectors and that of the desired body sizes determines the mathematical description. In this research work, the experimental results of the implementation of the proposed method on Fits.me's mannequin robots are visually illustrated, and explanation of the remaining steps towards completion of the whole realistic online fitting package is provided.

Abstract interpolation in vector-valued de Branges-Rovnyak spaces

NARCIS (Netherlands)

Ball, J.A.; Bolotnikov, V.; ter Horst, S.

2011-01-01

Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83–96, Naukova Dumka, Kiev, 1987) for Schur class functions, we study a general metric constrained interpolation problem for functions from a

Kriging for interpolation of sparse and irregularly distributed geologic data

Energy Technology Data Exchange (ETDEWEB)

Campbell, K.

1986-12-31

For many geologic problems, subsurface observations are available only from a small number of irregularly distributed locations, for example from a handful of drill holes in the region of interest. These observations will be interpolated one way or another, for example by hand-drawn stratigraphic cross-sections, by trend-fitting techniques, or by simple averaging which ignores spatial correlation. In this paper we consider an interpolation technique for such situations which provides, in addition to point estimates, the error estimates which are lacking from other ad hoc methods. The proposed estimator is like a kriging estimator in form, but because direct estimation of the spatial covariance function is not possible the parameters of the estimator are selected by cross-validation. Its use in estimating subsurface stratigraphy at a candidate site for geologic waste repository provides an example.

Fast image interpolation for motion estimation using graphics hardware

Science.gov (United States)

Kelly, Francis; Kokaram, Anil

2004-05-01

Motion estimation and compensation is the key to high quality video coding. Block matching motion estimation is used in most video codecs, including MPEG-2, MPEG-4, H.263 and H.26L. Motion estimation is also a key component in the digital restoration of archived video and for post-production and special effects in the movie industry. Sub-pixel accurate motion vectors can improve the quality of the vector field and lead to more efficient video coding. However sub-pixel accuracy requires interpolation of the image data. Image interpolation is a key requirement of many image processing algorithms. Often interpolation can be a bottleneck in these applications, especially in motion estimation due to the large number pixels involved. In this paper we propose using commodity computer graphics hardware for fast image interpolation. We use the full search block matching algorithm to illustrate the problems and limitations of using graphics hardware in this way.

Soil moisture mapping in torrential headwater catchments using a local interpolation method (Draix-Bléone field observatory, South Alps, France)

Science.gov (United States)

Mallet, Florian; Marc, Vincent; Douvinet, Johnny; Rossello, Philippe; Le Bouteiller, Caroline; Malet, Jean-Philippe

2016-04-01

Soil moisture is a key parameter that controls runoff processes at the watershed scale. It is characterized by a high area and time variability, controlled by site properties such as soil texture, topography, vegetation cover and climate. Several recent studies showed that changes in water storage was a key variable to understand the distribution of water residence time and the shape of flood's hydrograph (McDonnell and Beven, 2014; Davies and Beven, 2015). Knowledge of high frequency soil moisture variation across scales is a prerequisite for better understanding the areal distribution of runoff generation. The present study has been carried out in the torrential Draix-Bléone's experimental catchments, where water storage processes are expected to occur mainly on the first meter of soil. The 0,86 km2 Laval marly torrential watershed has a peculiar hydrological behavior during flood events with specific discharge among the highest in the world. To better understand the Laval internal behavior and to identify explanatory parameters of runoff generation, additional field equipment has been setup in sub-basins with various land use and morphological characteristics. From fall 2015 onwards this new instrumentation helped to supplement the routine measurements (rainfall rate, streamflow) and to develop a network of high frequency soil water content sensors (moisture probes, mini lysimeter). Data collected since early May and complementary measurement campaigns (itinerant soil moisture measurements, geophysical measurements) make it now possible to propose a soil water content mapping procedure. We use the LISDQS spatial extrapolation model based on a local interpolation method (Joly et. al, 2008). The interpolation is carried out from different geographical variables which are derived from a high resolution DEM (1m LIDAR) and a land cover image. Unlike conventional interpolation procedure, this method takes into account local forcing parameters such as slope, aspect

DEM-based delineation for improving geostatistical interpolation of rainfall in mountainous region of Central Himalayas, India

Science.gov (United States)

Kumari, Madhuri; Singh, Chander Kumar; Bakimchandra, Oinam; Basistha, Ashoke

2017-10-01

In mountainous region with heterogeneous topography, the geostatistical modeling of the rainfall using global data set may not confirm to the intrinsic hypothesis of stationarity. This study was focused on improving the precision of the interpolated rainfall maps by spatial stratification in complex terrain. Predictions of the normal annual rainfall data were carried out by ordinary kriging, universal kriging, and co-kriging, using 80-point observations in the Indian Himalayas extending over an area of 53,484 km2. A two-step spatial clustering approach is proposed. In the first step, the study area was delineated into two regions namely lowland and upland based on the elevation derived from the digital elevation model. The delineation was based on the natural break classification method. In the next step, the rainfall data was clustered into two groups based on its spatial location in lowland or upland. The terrain ruggedness index (TRI) was incorporated as a co-variable in co-kriging interpolation algorithm. The precision of the kriged and co-kriged maps was assessed by two accuracy measures, root mean square error and Chatfield's percent better. It was observed that the stratification of rainfall data resulted in 5-20 % of increase in the performance efficiency of interpolation methods. Co-kriging outperformed the kriging models at annual and seasonal scale. The result illustrates that the stratification of the study area improves the stationarity characteristic of the point data, thus enhancing the precision of the interpolated rainfall maps derived using geostatistical methods.

Relationships between response surfaces for tablet characteristics of placebo and API-containing tablets manufactured by direct compression method.

Science.gov (United States)

Hayashi, Yoshihiro; Tsuji, Takahiro; Shirotori, Kaede; Oishi, Takuya; Kosugi, Atsushi; Kumada, Shungo; Hirai, Daijiro; Takayama, Kozo; Onuki, Yoshinori

2017-10-30

In this study, we evaluated the correlation between the response surfaces for the tablet characteristics of placebo and active pharmaceutical ingredient (API)-containing tablets. The quantities of lactose, cornstarch, and microcrystalline cellulose were chosen as the formulation factors. Ten tablet formulations were prepared. The tensile strength (TS) and disintegration time (DT) of tablets were measured as tablet characteristics. The response surfaces for TS and DT were estimated using a nonlinear response surface method incorporating multivariate spline interpolation, and were then compared with those of placebo tablets. A correlation was clearly observed for TS and DT of all APIs, although the value of the response surfaces for TS and DT was highly dependent on the type of API used. Based on this knowledge, the response surfaces for TS and DT of API-containing tablets were predicted from only two and four formulations using regression expression and placebo tablet data, respectively. The results from the evaluation of prediction accuracy showed that this method accurately predicted TS and DT, suggesting that it could construct a reliable response surface for TS and DT with a small number of samples. This technique assists in the effective estimation of the relationships between design variables and pharmaceutical responses during pharmaceutical development. Copyright © 2017 Elsevier B.V. All rights reserved.

Hydraulic head interpolation using ANFIS—model selection and sensitivity analysis

Science.gov (United States)

Kurtulus, Bedri; Flipo, Nicolas

2012-01-01

The aim of this study is to investigate the efficiency of ANFIS (adaptive neuro fuzzy inference system) for interpolating hydraulic head in a 40-km 2 agricultural watershed of the Seine basin (France). Inputs of ANFIS are Cartesian coordinates and the elevation of the ground. Hydraulic head was measured at 73 locations during a snapshot campaign on September 2009, which characterizes low-water-flow regime in the aquifer unit. The dataset was then split into three subsets using a square-based selection method: a calibration one (55%), a training one (27%), and a test one (18%). First, a method is proposed to select the best ANFIS model, which corresponds to a sensitivity analysis of ANFIS to the type and number of membership functions (MF). Triangular, Gaussian, general bell, and spline-based MF are used with 2, 3, 4, and 5 MF per input node. Performance criteria on the test subset are used to select the 5 best ANFIS models among 16. Then each is used to interpolate the hydraulic head distribution on a (50×50)-m grid, which is compared to the soil elevation. The cells where the hydraulic head is higher than the soil elevation are counted as "error cells." The ANFIS model that exhibits the less "error cells" is selected as the best ANFIS model. The best model selection reveals that ANFIS models are very sensitive to the type and number of MF. Finally, a sensibility analysis of the best ANFIS model with four triangular MF is performed on the interpolation grid, which shows that ANFIS remains stable to error propagation with a higher sensitivity to soil elevation.

Some observations on interpolating gauges and non-covariant gauges

Indian Academy of Sciences (India)

We discuss the viability of using interpolating gauges to define the non-covariant gauges starting from the covariant ones. We draw attention to the need for a very careful treatment of boundary condition defining term. We show that the boundary condition needed to maintain gauge-invariance as the interpolating parameter ...

A 2.9 ps equivalent resolution interpolating time counter based on multiple independent coding lines

International Nuclear Information System (INIS)

Szplet, R; Jachna, Z; Kwiatkowski, P; Rozyc, K

2013-01-01

We present the design, operation and test results of a time counter that has an equivalent resolution of 2.9 ps, a measurement uncertainty at the level of 6 ps, and a measurement range of 10 s. The time counter has been implemented in a general-purpose reprogrammable device Spartan-6 (Xilinx). To obtain both high precision and wide measurement range the counting of periods of a reference clock is combined with a two-stage interpolation within a single period of the clock signal. The interpolation involves a four-phase clock in the first interpolation stage (FIS) and an equivalent coding line (ECL) in the second interpolation stage (SIS). The ECL is created as a compound of independent discrete time coding lines (TCL). The number of TCLs used to create the virtual ECL has an effect on its resolution. We tested ECLs made from up to 16 TCLs, but the idea may be extended to a larger number of lines. In the presented time counter the coarse resolution of the counting method equal to 2 ns (period of the 500 MHz reference clock) is firstly improved fourfold in the FIS and next even more than 400 times in the SIS. The proposed solution allows us to overcome the technological limitation in achievable resolution and improve the precision of conversion of integrated interpolators based on tapped delay lines. (paper)

DATASPACE - A PROGRAM FOR THE LOGARITHMIC INTERPOLATION OF TEST DATA

Science.gov (United States)

Ledbetter, F. E.

1994-01-01

Scientists and engineers work with the reduction, analysis, and manipulation of data. In many instances, the recorded data must meet certain requirements before standard numerical techniques may be used to interpret it. For example, the analysis of a linear visoelastic material requires knowledge of one of two time-dependent properties, the stress relaxation modulus E(t) or the creep compliance D(t), one of which may be derived from the other by a numerical method if the recorded data points are evenly spaced or increasingly spaced with respect to the time coordinate. The problem is that most laboratory data are variably spaced, making the use of numerical techniques difficult. To ease this difficulty in the case of stress relaxation data analysis, NASA scientists developed DATASPACE (A Program for the Logarithmic Interpolation of Test Data), to establish a logarithmically increasing time interval in the relaxation data. The program is generally applicable to any situation in which a data set needs increasingly spaced abscissa values. DATASPACE first takes the logarithm of the abscissa values, then uses a cubic spline interpolation routine (which minimizes interpolation error) to create an evenly spaced array from the log values. This array is returned from the log abscissa domain to the abscissa domain and written to an output file for further manipulation. As a result of the interpolation in the log abscissa domain, the data is increasingly spaced. In the case of stress relaxation data, the array is closely spaced at short times and widely spaced at long times, thus avoiding the distortion inherent in evenly spaced time coordinates. The interpolation routine gives results which compare favorably with the recorded data. The experimental data curve is retained and the interpolated points reflect the desired spacing. DATASPACE is written in FORTRAN 77 for IBM PC compatibles with a math co-processor running MS-DOS and Apple Macintosh computers running MacOS. With

Estimation of missing values in solar radiation data using piecewise interpolation methods: Case study at Penang city

International Nuclear Information System (INIS)

Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu

2015-01-01

The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique

Estimation of missing values in solar radiation data using piecewise interpolation methods: Case study at Penang city

Science.gov (United States)

Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu

2015-12-01

The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device's development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.

Estimation of missing values in solar radiation data using piecewise interpolation methods: Case study at Penang city

Energy Technology Data Exchange (ETDEWEB)

Zainudin, Mohd Lutfi, E-mail: mdlutfi07@gmail.com [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Institut Matematik Kejuruteraan (IMK), Universiti Malaysia Perlis, 02600 Arau, Perlis (Malaysia); Saaban, Azizan, E-mail: azizan.s@uum.edu.my [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu, E-mail: mohdnazari@perlis.uitm.edu.my [Faculty of Applied Science, Universiti Teknologi Mara, 02600 Arau, Perlis (Malaysia)

2015-12-11

The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.

Interpolation-free scanning and sampling scheme for tomographic reconstructions

International Nuclear Information System (INIS)

Donohue, K.D.; Saniie, J.

1987-01-01

In this paper a sampling scheme is developed for computer tomography (CT) systems that eliminates the need for interpolation. A set of projection angles along with their corresponding sampling rates are derived from the geometry of the Cartesian grid such that no interpolation is required to calculate the final image points for the display grid. A discussion is presented on the choice of an optimal set of projection angles that will maintain a resolution comparable to a sampling scheme of regular measurement geometry, while minimizing the computational load. The interpolation-free scanning and sampling (IFSS) scheme developed here is compared to a typical sampling scheme of regular measurement geometry through a computer simulation

Separation of non-stationary multi-source sound field based on the interpolated time-domain equivalent source method

Science.gov (United States)

Bi, Chuan-Xing; Geng, Lin; Zhang, Xiao-Zheng

2016-05-01

In the sound field with multiple non-stationary sources, the measured pressure is the sum of the pressures generated by all sources, and thus cannot be used directly for studying the vibration and sound radiation characteristics of every source alone. This paper proposes a separation model based on the interpolated time-domain equivalent source method (ITDESM) to separate the pressure field belonging to every source from the non-stationary multi-source sound field. In the proposed method, ITDESM is first extended to establish the relationship between the mixed time-dependent pressure and all the equivalent sources distributed on every source with known location and geometry information, and all the equivalent source strengths at each time step are solved by an iterative solving process; then, the corresponding equivalent source strengths of one interested source are used to calculate the pressure field generated by that source alone. Numerical simulation of two baffled circular pistons demonstrates that the proposed method can be effective in separating the non-stationary pressure generated by every source alone in both time and space domains. An experiment with two speakers in a semi-anechoic chamber further evidences the effectiveness of the proposed method.

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation.

Science.gov (United States)

Välimäki, Vesa; Pekonen, Jussi; Nam, Juhan

2012-01-01

Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz. © 2012 Acoustical Society of America.

Characterization of NiTi shape memory alloys using dual kriging interpolation

International Nuclear Information System (INIS)

Trochu, F.; Sacepe, N.; Volkov, O.; Turenne, S.

1999-01-01

A large number of industrial applications could benefit from the remarkable properties of shape memory alloys (SMA). The development of a general material law is the first important step before reliable design calculations of shape memory devices can be carried out. This paper presents a new phenomenological constitutive law based on dual kriging, which is a powerful mathematical tool used here as interpolation method to simulate the macroscopic mechanical behavior of shape memory alloys. From a set of experimental strain-temperature curves at constant loads, two deformation surfaces are constructed in the stress, strain and temperature space which describe the cooling and heating behaviors of the material for any stress. The response of a specimen subjected to complex thermomechanical loading can be calculated by dual kriging form a general 3-dimensional parametric solid constructed inside the hysteretic domain delimited by the main cooling and heating deformation surfaces. This approach presents the advantage of yielding immediately the explicit equation of any partial cycle inside the main hysteretic domain, thus yielding a general material law for shape memory alloys. Preliminary validation for a set of simple examples demonstrates the potential of this new model that includes in a single formulation superelasticity, rubber-like behavior and shape memory effect. (orig.)

Interpolation between multi-dimensional histograms using a new non-linear moment morphing method

Energy Technology Data Exchange (ETDEWEB)

Baak, M., E-mail: max.baak@cern.ch [CERN, CH-1211 Geneva 23 (Switzerland); Gadatsch, S., E-mail: stefan.gadatsch@nikhef.nl [Nikhef, PO Box 41882, 1009 DB Amsterdam (Netherlands); Harrington, R. [School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, Scotland (United Kingdom); Verkerke, W. [Nikhef, PO Box 41882, 1009 DB Amsterdam (Netherlands)

2015-01-21

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates are often required to model the impact of systematic uncertainties.

Interpolation between multi-dimensional histograms using a new non-linear moment morphing method

International Nuclear Information System (INIS)

Baak, M.; Gadatsch, S.; Harrington, R.; Verkerke, W.

2015-01-01

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates are often required to model the impact of systematic uncertainties

Interpolation between multi-dimensional histograms using a new non-linear moment morphing method

CERN Document Server

Baak, Max; Harrington, Robert; Verkerke, Wouter

2014-01-01

A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates is often required to model the impact of systematic uncertainties.

Interpolation between multi-dimensional histograms using a new non-linear moment morphing method