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Fast and accurate interpolation of large scattered data sets on the sphere

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第5期234卷 1505-1521页

作者： Cavoretto, Roberto De Rossi, Alessandra Univ Turin Dept Math I-10123 Turin Italy

In this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented. The solution method is local and involves a modified spherical Shepard's interpolant, which uses zonal basis functions as local approximants. The associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere. Specifically, this technique is mainly based on the partition of the sphere in a suitable number of spherical zones, the construction of spherical caps as local neighbourhoods for each node, and finally the employment of a spherical zone searching procedure. Computational cost and storage requirements of the spherical algorithm are analyzed. Moreover, several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm. (C) 2010 Elsevier BM. All rights reserved.

关键词： Zonal basis functions Spherical Shepard's formula Local methods Scattered data interpolation interpolation algorithms

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Symmetric matrix polynomial equation: interpolation results

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AUTOMATICA 1998年第7期34卷 811-824页

作者： Henrion, D Sebek, M LAAS CNRS F-31077 Toulouse 4 France Czech Tech Univ Fac Elect Engn Trnka Lab Automat Control Prague Czech Republic Acad Sci Czech Republ Inst Informat Theory & Automat CR-18208 Prague Czech Republic

New numerical procedures are proposed to solve the symmetric matrix polynomial equation A(T)(-s) X(s) + X-T(-s) A(s)= 2B(s) that is frequently encountered in control and signal processing. An interpolation approach is presented that takes full advantage of symmetry properties and leads to an equivalent reduced-size linear system of equations. It results in a simple and general characterization of all solutions of expected column degrees. Several new theoretical results concerning stability theory and reduced Sylvester resultant matrices are also developed and used to conclude a priori on the existence of a solution. By means of numerical experiments, it is shown that our algorithms are more efficient than older methods and, namely, appear to be numerically reliable. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： matrix polynomial equations numerical methods interpolation algorithms efficient algorithms continuous-time systems computer-aided control system design

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THE COMPLEXITY OF SPARSE POLYNOMIAL interpolation OVER FINITE-FIELDS

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 1994年第2期5卷 91-103页

作者： WERTHER, K UNIV BONN INST INFORMAT W-5300 BONN GERMANY

We consider the problem of interpolating and zero testing sparse multivariate polynomials over finite fields from their values given by a black box. We give an estimate of the size of a test set constructed by Clausen, Dress, Grabmeier, and Karpinski [2] and improve the previously known lower bounds on the size of a minimal test set. Further, we present for arbitrary finite fields a new interpolation algorithm that uses only evaluations over the ground field, thereby answering an open question of Dur and Grabmeier [3].

关键词： interpolation algorithms LOWER BOUNDS TEST SETS

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Local regression models for spatial interpolation of urban heat island-an example from Wrocaw, SW Poland

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THEORETICAL AND APPLIED CLIMATOLOGY 2012年第1-2期108卷 53-71页

作者： Szymanowski, Mariusz Kryza, Maciej Univ Wroclaw Inst Geog & Reg Dev PL-50137 Wroclaw Poland

Geographically weighted regression algorithm (GWR) has been applied to derive the spatial structure of urban heat island (UHI) in the city of Wrocaw, SW Poland. Seven UHI cases, measured during various meteorological conditions and characteristic of different seasons, were selected for analysis. GWR results were compared with global regression models (MLR), using various statistical procedures including corrected Akaike Information Criterion, determination coefficient, analysis of variance, and Moran's I index. It was found that GWR is better suited for spatial modeling of UHI than MLR models, as it takes into account non-stationarity of the spatial process. However, Monte Carlo and F3 tests for spatial stationarity of the independent variables suggest that for several spatial predictors a mixed GWR-MLR approach is recommended. Both local and global models were extended by the interpolation of regression residuals and used for spatial interpolation of the UHI structure. The interpolation results were evaluated with the cross-validation approach. It was found that the incorporation of the spatially interpolated residuals leads to significant improvement of the interpolation results for both GWR and MLR approaches. Because GWR is better justified in terms of statistical specification, the combined GWR + interpolated regression residuals (GWR residual kriging;GWRK) approach is recommended for spatial modeling of UHI, instead of widely applied MLR models.

关键词： URBAN heat islands SPATIAL data structures REGRESSION analysis interpolation algorithms

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An algorithm for interpolation with positive rational functions on the imaginary axis

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AUTOMATICA 1997年第12期33卷 2277-2280页

作者： Mosquera, C Perez, F Univ Vigo ETSI Telecomunicac Dept Tecnol Comunicac Vigo 36200 Spain

A procedure is shown to construct a rational transfer function that is real-valued and positive on the imaginary axis. The degree of the solution is lowered with respect to solutions based on existing algorithms. The results can be applied to problems such as the robust strictly positive real problem. (C) 1997 Elsevier Science Ltd.

关键词： adaptive algorithms imaginary axis interpolation algorithms robustness

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A Novel Approach for NURBS interpolation with Minimal Feed Rate Fluctuation Based on Improved Adams-Moulton Method

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MATHEMATICAL PROBLEMS IN ENGINEERING 2017年第1期2017卷 1-10页

作者： Peng, Junquan Liu, Xinhua Si, Lei Liu, Jingjing China Univ Min & Technol Sch Mech & Elect Engn Xuzhou Peoples R China China Univ Min & Technol Sch Informat & Elect Engn Xuzhou Peoples R China

In order to reduce the feed rate fluctuation of interpolation, a novel approach for NURBS interpolation with minimal feed rate fluctuation based on improved Adams-Moulton (IAM) method is proposed. At first, the representation and calculation of NURBS curve interpolation are described. Then, the constraints of feeding step length are firstly given out to calculate the minimal hoping feeding step length and the detailed IAM method of NURBS curve interpolation is presented. Finally, simulations and experiments are carried out to verify the feasibility and applicability of proposed IAM method.

关键词： interpolation algorithms SPLINES NUMERICAL control of machine-tools TRAJECTORIES (Mechanics) QUINTIC curves

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Selection of interpolation parameters depending on the location of measurement points

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GISCIENCE & REMOTE SENSING 2013年第5期50卷 515-526页

作者： Gosciewski, Dariusz Univ Warmia & Mazury Fac Geodesy & Land Management Inst Geodesy PL-10957 Olsztyn Poland

Digital terrain models (DTM) are created increasingly often on the basis of data recorded automatically. In the processing of such sets, there is often a need to organize the measured values and present them in the form of a specific GRID (a regular grid of nodes: the points forming the DTM are located in the corners of squares with a specified side length) or TIN (triangulated irregular network) structure. The correct setting of processing criteria and the proper selection of the structural parameters of a given structure are important factors influencing terrain model accuracy. The GRID structure not only allows data to be organized, but also increases the efficiency of data processing in LIS/GIS (land information systems/geographical information systems). If a large volume of measurement data is acquired, using the GRID structure reduces its volume and eliminates redundancies. To maintain proper DTM quality, it is necessary to set correct processing parameters during the construction of the network forming the GRID structure. This paper analyzes the effect of measurement point distribution on the selection of the structural parameters of a regular square grid used to create the digital bottom model.

关键词： GIS interpolation algorithms digital terrain model regular GRID structure large observation sets data reduction

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interpolation algorithm for asynchronous ADC-data

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ADVANCES IN RADIO SCIENCE 2017年 15卷 163-168页

作者： Bramburger, Stefan Zinke, Benny Killat, Dirk Brandenburg Tech Univ Cottbus Microelect Dept D-03046 Cottbus Germany IHP Technol Pk 25 D-15236 Frankfurt Oder Germany

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.

关键词： DIGITAL signal processing interpolation algorithms TOEPLITZ matrices

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4D Model Flow: Precomputed Appearance Alignment for Real-time 4D Video interpolation

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COMPUTER GRAPHICS FORUM 2015年第7期34卷 173-182页

作者： Casas, Dan Richardt, Christian Collomosse, John Theobalt, Christian Hilton, Adrian Univ Surrey Guildford GU2 5XH Surrey England MPI Informat Saarbrucken Germany Intel Visual Comp Inst Saarbrucken Germany

We introduce the concept of 4D model flow for the precomputed alignment of dynamic surface appearance across 4D video sequences of different motions reconstructed from multi-view video. Precomputed 4D model flow allows the efficient parametrization of surface appearance from the captured videos, which enables efficient real-time rendering of interpolated 4D video sequences whilst accurately reproducing visual dynamics, even when using a coarse underlying geometry. We estimate the 4D model flow using an image-based approach that is guided by available geometry proxies. We propose a novel representation in surface texture space for efficient storage and online parametric interpolation of dynamic appearance. Our 4D model flow overcomes previous requirements for computationally expensive online optical flow computation for data-driven alignment of dynamic surface appearance by precomputing the appearance alignment. This leads to an efficient rendering technique that enables the online interpolation between 4D videos in real time, from arbitrary viewpoints and with visual quality comparable to the state of the art.

关键词： Four-dimensional imaging Video recordings interpolation algorithms Geometry Optical flow Visual perception

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An Oblique-enhanced interpolation Algorithm for Color Image Restoration

An Oblique-enhanced Interpolation Algorithm for Color Image ...

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International Conference on algorithms, High Performance Computing, and Artificial Intelligence (AHPCAI)

作者： Niu, Jiangyuan Nanjing Univ Posts & Telecommun Sch Comp Sci Nanjing 210023 Jiangsu Peoples R China

ISBN: (数字)9781510651890

ISBN: (纸本)9781510651890;9781510651883

Most current digital imaging technologies are based on Bayer color filter array and interpolation algorithms to achieve color image restoration. Common interpolation algorithms include bilinear interpolation algorithm, edge-directed image interpolation algorithm, and so on. Hibbard algorithm, a kind of edge-directed image interpolation algorithm, significantly improves zipper effect and blurred edges through a gradient-based method and constant chromatic aberration ideas compared with the bilinear interpolation algorithm. However, it only considers the possibility of horizontal and vertical edges, ignoring further judgement for edges in other directions. For solving the severe problems, we propose an oblique interpolation algorithm with the addition of oblique direction gradient factors. In this way, we consider the edges in both main diagonal and sub-diagonal directions. The adjacent pixel information in these directions is used to restore the red and blue channels. The experimental results show that images reconstructed by our algorithm are closer to original images. The reconstructed images have a certain improvement on the sharpness and coherence of oblique edges and arc edges. And the problem of false color in edges with an obvious color difference on both sides is weakened.

关键词： digital interpolation algorithms color

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