A FAST METHOD FOR IMPLICIT SURFACE RECONSTRUCTION BASED ON RADIAL BASIS FUNCTIONS NETWORK FROM 3D SCATTERED POINTS

2007 ◽  
Vol 17 (06) ◽  
pp. 459-465 ◽  
Author(s):  
HANBO LIU ◽  
XIN WANG ◽  
WENYI QIANG
Keyword(s):  
Uniform Distribution ◽  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Basis Function ◽  
Basis Functions ◽  
Surface Model ◽  
Fast Method ◽  
Feature Points ◽  
Implicit Surface ◽  
Radial Basis

A method for arbitrary surface reconstruction from 3D large scattered points is proposed in this paper. According to the properties of 3D points, e.g. the non-uniform distribution and unknown topology, an implicit surface model is adopted based on radial basis functions network. And because of the property of locality of radial basis function, the method is fast and robust in surface reconstruction. Furthermore, an adapted K-Means algorithm is used to reduce reconstruction centers. For features completeness, two effective methods are introduced to extract the feature points before the adapted K-Means algorithm. Experiment results show that the presented approach is a good solution for reconstruction from 3D large scattered points.

Implicit surface reconstruction with radial basis functions via PDEs

2020 ◽  
Vol 110 ◽  
pp. 95-103 ◽  
Author(s):  
Xiao-Yan Liu ◽  
Hui Wang ◽  
C.S. Chen ◽  
Qing Wang ◽  
Xiaoshuang Zhou ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Basis Functions ◽  
Implicit Surface ◽  
Radial Basis

Implicit Surface Reconstruction via RBF interpolation: A Review

2021 ◽  
Vol 15 ◽  
Author(s):  
Jiahui Mo ◽  
Huahao Shou ◽  
Wei Chen
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Point Cloud ◽  
Research Direction ◽  
Basis Functions ◽  
Implicit Surface ◽  
Continuity Properties ◽  
Radial Basis ◽  
Application Fields ◽  
Fitting Accuracy

Background: Implicit surface is a kind of surface modeling tool, which is widely used in point cloud reconstruction, deformation, and fusion due to its advantages of good smoothness and Boolean operation. The most typical method is surface reconstruction with radial basis functions (RBF) under normal constraints. RBF has become one of the main methods of point cloud fitting because it has a strong mathematical foundation, an advantage of computation simplicity, and the ability to process nonuniform points. Objective: Techniques and patents of implicit surface reconstruction interpolation with RBF are surveyed. Theory, algorithm, and application are discussed to provide a comprehensive summary for implicit surface reconstruction in RBF and Hermite radial basis functions (HRBF) interpolation. Methods: RBF implicit surface reconstruction interpolation can be divided into RBF interpolation under the constraints of points and HRBF interpolation under the constraints of points and corresponding normals. Results: A total of 125 articles were reviewed in which more than 30% were related to RBF in the last decade. The continuity properties and application fields of the popular globally supported radial basis functions and compactly supported radial basis functions are analyzed. Different methods of RBF and HRBF implicit surface reconstruction are evaluated, and the challenges of these methods are discussed. Conclusion: In future work, implicit surface reconstruction via RBF and HRBF should be further studied for fitting accuracy, computation speed, and other fundamental problems. In addition, it is a more challenging but valuable research direction to construct a new RBF with both compact support and improved fitting accuracy.

scholarly journals Fast Implicit Surface Reconstruction for the Radial Basis Functions Interpolant

2019 ◽  
Vol 9 (24) ◽  
pp. 5335 ◽  
Author(s):  
Deyun Zhong ◽  
Ju Zhang ◽  
Liguan Wang
Keyword(s):  
Radial Basis Functions ◽  
Surface Reconstruction ◽  
Fast Multipole Method ◽  
Single Point ◽  
Basis Functions ◽  
Reconstruction Method ◽  
Implicit Surface ◽  
Point Evaluation ◽  
Radial Basis ◽  
And Performance

In this paper we improve an efficient implicit surface reconstruction method based on the surface following method for the radial basis functions interpolant. The method balances the reconstruction efficiency and the evaluation efficiency in the process of surface following. The growing strategy of the surface following method combines both the evaluation and reconstruction processes. Based on the analysis of the black-box fast multipole method (FMM) operations, we improve the FMM procedures for single point evaluation. The goal is to ensure that one point evaluation of the method obtains an optimum efficiency, so that it can be efficiently applied to the voxel growing method. Combined with the single point FMM, we improve the voxel growing method without manually specifying the seed points, and the leaf growing method is developed to avoid a mass of redundant computation. It ensures a smaller number of evaluation points and a higher evaluation efficiency in surface following. The numerical results of several data sets showed the reliability and performance of the efficient implicit surface reconstruction method. Compared with the existing methods, the improved method performs a better time and space efficiency.

Multilevel RBF collocation method for the fourth-order thin plate problem

2020 ◽  
pp. 2050079
Author(s):  
Lanling Ding ◽  
Zhiyong Liu ◽  
Qiuyan Xu
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Fourth Order ◽  
Basis Function ◽  
Research Method ◽  
Meshfree Method ◽  
Basis Functions ◽  
Radial Basis

The radial basis functions meshfree method is a research method for thin plate problem which has gradually developed into a more mature meshfree method. It includes finite element, radial basis functions meshfree collocation method, etc. In this paper, we introduce the multilevel radial basis function collocation method for the fourth-order thin plate problem. We use nonsymmetric Kansa multilevel radial basis function collocation method to solve the fourth-order thin plate problem. Two numerical examples based on Wendland’s [Formula: see text] and [Formula: see text] functions are given to examine that the convergence of the multilevel radial basis function collocation method which is good for solving the fourth-order thin plate problem.

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