Software tools using CSRBFs for processing scattered data

Kojekine, Nikita; Hagiwara, Ichiro; Савченко, В. В.

doi:10.1016/s0097-8493(02)00287-x

Cited by 55 publications

(38 citation statements)

References 15 publications

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“…This algorithm has been further improved by Kojekine et al [17] by organizing the sparse matrix into a band-diagonal sparse matrix which can be solved more efficiently by using iterative methods. Unfortunately, the radius of support has to be chosen globally, which means that the method is not robust against highly non-uniformly distributed point sets where the density of the samples may vary significantly.…”

Section: Scattered Data Interpolationmentioning

confidence: 99%

Adaptive hierarchical RBF interpolation for creating smooth digital elevation models

Pouderoux

Gonzato

Tobor

et al. 2004

Proceedings of the 12th Annual ACM International Workshop on Geographic Information Systems

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This paper presents a fast algorithm for smooth digital elevation model interpolation and approximation from scattered elevation data. The global surface is reconstructed by subdividing it into overlapping local subdomains using a perfectly balanced binary tree. In each tree leaf, a smooth local surface is reconstructed using radial basis functions. Finally a hierarchical blending is done to create the final C 1 -continuous surface using a family of functions called Partition of Unity. We present two terrain data sets and show that our method is robust since the number of data points in the Partition of Unity blending areas is explicitly specified.

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Section: Scattered Data Interpolationmentioning

confidence: 99%

Adaptive hierarchical RBF interpolation for creating smooth digital elevation models

Pouderoux

Gonzato

Tobor

et al. 2004

Proceedings of the 12th Annual ACM International Workshop on Geographic Information Systems

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“…As the solution of the system in Eq. (4) is the most time-consuming operation (21) , we propose a system to store the result of step 2. By this way it is not necessary to calculate spline coefficients again for every resolution conversion.…”

Section: 1 Image Resolution Conversionmentioning

confidence: 99%

“…(1) is also proportional to N. The latter becomes significant when N is large and s(x) is evaluated on a fine grid. Fast sorting algorithm (21) is used for image reconstruction at step 4.…”

Section: 2 Image Reconstructionmentioning

confidence: 99%

A Two-Level Iterative Method for Image Reconstruction with Radial Basis Functions

Magoulès

Diago

Hagiwara

2005

JSME Int. J., Ser. C

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Radial basis functions are popular basis for interpolating scattered data during the image reconstruction process in graphic analysis. In this context, the solution of a linear system of equations is required for each color (blue, red, green) and represents the most time-consuming operation. In this paper a two-level iterative algorithm is proposed to solve efficiently these linear systems of equations. This two-level algorithm consists of a preconditioned iterative method which enforces at each iteration a projection of the residual onto a suitable coarse space. This constraint is ensured by solving an auxiliary second-level problem at each iteration. Numerical results illustrate the convergence properties of the proposed method on a wide range of interpolation problems for image reconstruction.

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“…The second group is fast methods for fitting and evaluating RBFs (45) . The third is compactly supported RBFs (47), (48) . Let us notice here about recent outstanding work of Ohtake et al (49) where compactly supported radial basis functions (CSRBS) are used as blending functions.…”

Section: Surface Reconstructionmentioning

confidence: 99%

“…In our software implementation, we employ a standard approach for creating a binary tree from an initial point data set with an additional required parametric value K, which denotes the maximum number of points in a leaf. Such a tree allows to provide an efficient sorting of scattered data (48) that leads to obtaining a band diagonal sub-matrix A; after that Cholesky decomposing and block Gaussian solution are applied.…”

Section: Surface Reconstructionmentioning

confidence: 99%

Trends and Solutions in CAD/CG

Савченко¹

2005

JSME Int. J., Ser. C

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The past and current trends in CAD/CG are discussed. An overview of the approach used in our ongoing project is given. Our final goal is primarily focused on developing a shape modeling system for solving problems of surface generation and enhancement, which includes polygon generation from unorganized points, shape smoothing, simplification, and improvement of mesh quality parameters of 3D polygonal sets.

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Software tools using CSRBFs for processing scattered data

Cited by 55 publications

References 15 publications

Adaptive hierarchical RBF interpolation for creating smooth digital elevation models

Adaptive hierarchical RBF interpolation for creating smooth digital elevation models

A Two-Level Iterative Method for Image Reconstruction with Radial Basis Functions

Trends and Solutions in CAD/CG

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