article

Sparse surface reconstruction with adaptive partition of unity and radial basis functions

Authors:

Alexander Belyaev,

Hans-Peter SeidelAuthors Info & Claims

Graphical Models, Volume 68, Issue 1

Pages 15 - 24

https://doi.org/10.1016/j.gmod.2005.08.001

Published: 01 January 2006 Publication History

Abstract

A new implicit surface fitting method for surface reconstruction from scattered point data is proposed. The method combines an adaptive partition of unity approximation with least-squares RBF fitting and is capable of generating a high quality surface reconstruction. Given a set of points scattered over a smooth surface, first a sparse set of overlapped local approximations is constructed. The partition of unity generated from these local approximants already gives a faithful surface reconstruction. The final reconstruction is obtained by adding compactly supported RBFs. The main feature of the developed approach consists of using various regularization schemes which lead to economical, yet accurate surface reconstruction.

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Sparse surface reconstruction with adaptive partition of unity and radial basis functions

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cover image Graphical Models

Graphical Models Volume 68, Issue 1

Special issue on SMI 2004

January 2006

64 pages

ISSN:1524-0703

Issue’s Table of Contents

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 01 January 2006

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Cited By

Novello TSchardong GSchirmer Lda Silva VLopes HVelho L(2022)Exploring differential geometry in neural implicits▪Computers and Graphics10.1016/j.cag.2022.09.003108:C(49-60)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1016/j.cag.2022.09.003
Bauer BDevroye LKohler MKrzyak AWalk H(2017)Nonparametric estimation of a function from noiseless observations at random pointsJournal of Multivariate Analysis10.1016/j.jmva.2017.05.010160:C(93-104)Online publication date: 1-Aug-2017
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Pan MTong WChen F(2017)Phase-field guided surface reconstruction based on implicit hierarchical B-splinesComputer Aided Geometric Design10.1016/j.cagd.2017.03.00952:C(154-169)Online publication date: 1-Mar-2017
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Crivellaro APerotto SZonca S(2017)Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniquesApplied Numerical Mathematics10.1016/j.apnum.2016.11.003113:C(93-108)Online publication date: 1-Mar-2017
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Li MChen FWang WTu C(2016)Sparse RBF surface representationsComputer Aided Geometric Design10.1016/j.cagd.2016.08.00148:C(49-59)Online publication date: 1-Nov-2016
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Xiao JWang LBoyd J(2015)RBF-vortex methods for the barotropic vorticity equation on a sphereJournal of Computational Physics10.1016/j.jcp.2015.01.005285:C(208-225)Online publication date: 15-Mar-2015
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