Implicit surface reconstruction with radial basis functions via PDEs

Xiao Yan Liu; Hui Wang; C. S. Chen; Qing Wang; Xiaoshuang Zhou; Yong Wang

doi:10.1016/j.enganabound.2019.09.021

Implicit surface reconstruction with radial basis functions via PDEs

Xiao Yan Liu, Hui Wang, C. S. Chen, Qing Wang, Xiaoshuang Zhou, Yong Wang

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We propose a partial differential equations-based algorithm for the 3D implicit surface reconstruction from a set of scattered cloud data. In the solution process, the method of approximate particular solutions with the IMQ radial basis function is employed for solving the modified Helmholtz or Poisson equation with a constant Dirichlet boundary condition. We also consider to repair the surfaces when a certain region of cloud data points are missing. The selection of several parameters is studied for the optimal recovery of the surfaces. Four examples are presented to validate the effectiveness of the proposed method.

Original language	English
Pages (from-to)	95-103
Number of pages	9
Journal	Engineering Analysis with Boundary Elements
Volume	110
DOIs	https://doi.org/10.1016/j.enganabound.2019.09.021
State	Published - Jan 2020

Keywords

Computer graphics
Image reconstruction
Implicit surface
Method of approximate particular solutions
Modified Helmholtz equation
Radial basis function

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10.1016/j.enganabound.2019.09.021

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title = "Implicit surface reconstruction with radial basis functions via PDEs",

abstract = "We propose a partial differential equations-based algorithm for the 3D implicit surface reconstruction from a set of scattered cloud data. In the solution process, the method of approximate particular solutions with the IMQ radial basis function is employed for solving the modified Helmholtz or Poisson equation with a constant Dirichlet boundary condition. We also consider to repair the surfaces when a certain region of cloud data points are missing. The selection of several parameters is studied for the optimal recovery of the surfaces. Four examples are presented to validate the effectiveness of the proposed method.",

keywords = "Computer graphics, Image reconstruction, Implicit surface, Method of approximate particular solutions, Modified Helmholtz equation, Radial basis function",

author = "Liu, {Xiao Yan} and Hui Wang and Chen, {C. S.} and Qing Wang and Xiaoshuang Zhou and Yong Wang",

note = "Publisher Copyright: {\textcopyright} 2019",

year = "2020",

month = jan,

doi = "10.1016/j.enganabound.2019.09.021",

language = "English",

volume = "110",

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journal = "Engineering Analysis with Boundary Elements",

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TY - JOUR

T1 - Implicit surface reconstruction with radial basis functions via PDEs

AU - Liu, Xiao Yan

AU - Wang, Hui

AU - Chen, C. S.

AU - Wang, Qing

AU - Zhou, Xiaoshuang

AU - Wang, Yong

PY - 2020/1

Y1 - 2020/1

N2 - We propose a partial differential equations-based algorithm for the 3D implicit surface reconstruction from a set of scattered cloud data. In the solution process, the method of approximate particular solutions with the IMQ radial basis function is employed for solving the modified Helmholtz or Poisson equation with a constant Dirichlet boundary condition. We also consider to repair the surfaces when a certain region of cloud data points are missing. The selection of several parameters is studied for the optimal recovery of the surfaces. Four examples are presented to validate the effectiveness of the proposed method.

AB - We propose a partial differential equations-based algorithm for the 3D implicit surface reconstruction from a set of scattered cloud data. In the solution process, the method of approximate particular solutions with the IMQ radial basis function is employed for solving the modified Helmholtz or Poisson equation with a constant Dirichlet boundary condition. We also consider to repair the surfaces when a certain region of cloud data points are missing. The selection of several parameters is studied for the optimal recovery of the surfaces. Four examples are presented to validate the effectiveness of the proposed method.

KW - Computer graphics

KW - Image reconstruction

KW - Implicit surface

KW - Method of approximate particular solutions

KW - Modified Helmholtz equation

KW - Radial basis function

UR - http://www.scopus.com/inward/record.url?scp=85074263191&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2019.09.021

DO - 10.1016/j.enganabound.2019.09.021

M3 - Article

AN - SCOPUS:85074263191

SN - 0955-7997

VL - 110

SP - 95

EP - 103

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

ER -

Implicit surface reconstruction with radial basis functions via PDEs

Abstract

Keywords

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