Numerical Analyses of the Boundary Effect of Radial Basis in 3D Surface Reconstruction

[Numerical Analyses of Boundary Effect of RBF]

Xiangqian Jiang, Xiangchao Zhang

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Surface reconstruction is very important for surface characterization and graph processing. Radial basis function has now become a popular method to reconstruct 3D surfaces from scattered data. However, it is relatively inaccurate at the boundary region. To solve this problem, a circle of new centres are added outside the domain of interest. The factors that influence the boundary behaviour are analyzed quantitatively via numerical experiments. It is demonstrated that if the new centres are properly located, the boundary problem can be effectively overcome whilst not reducing the accuracy at the interior area. A modified Graham scan technique is introduced to obtain the boundary points from a scattered point set. These boundary points are extended outside with an appropriate distance, and then uniformized to form the new auxiliary centres.

Original languageEnglish
Pages (from-to)327-339
Number of pages13
JournalNumerical Algorithms
Volume47
Issue number4
DOIs
Publication statusPublished - 1 Apr 2008

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Boundary Effect
Surface Reconstruction
Surface reconstruction
3D Reconstruction
Scattered Data
Boundary Behavior
Boundary Problem
Inaccurate
Radial Functions
Point Sets
Basis Functions
Circle
Interior
Processing
Numerical Experiment
Experiments
Graph in graph theory

Cite this

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abstract = "Surface reconstruction is very important for surface characterization and graph processing. Radial basis function has now become a popular method to reconstruct 3D surfaces from scattered data. However, it is relatively inaccurate at the boundary region. To solve this problem, a circle of new centres are added outside the domain of interest. The factors that influence the boundary behaviour are analyzed quantitatively via numerical experiments. It is demonstrated that if the new centres are properly located, the boundary problem can be effectively overcome whilst not reducing the accuracy at the interior area. A modified Graham scan technique is introduced to obtain the boundary points from a scattered point set. These boundary points are extended outside with an appropriate distance, and then uniformized to form the new auxiliary centres.",
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Numerical Analyses of the Boundary Effect of Radial Basis in 3D Surface Reconstruction : [Numerical Analyses of Boundary Effect of RBF]. / Jiang, Xiangqian; Zhang, Xiangchao.

In: Numerical Algorithms, Vol. 47, No. 4, 01.04.2008, p. 327-339.

Research output: Contribution to journalArticle

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