Multigrid convergent principal curvature estimators in digital geometry

被引:27
作者
Coeurjolly, David [1 ]
Lachaud, Jacques-Olivier [2 ,3 ]
Levallois, Jeremy [1 ,2 ]
机构
[1] Univ Lyon, CNRS, INSA Lyon, LIRIS,UMR5205, F-69621 Villeurbanne, France
[2] Univ Savoie, CNRS, LAMA, UMR 5127, F-73776 Chambery, France
[3] Univ Grenoble Alpes, CNRS, LJK, UMR 5224, F-38041 Grenoble, France
关键词
Digital geometry; Curvature estimation; Multigrid convergence; Integral invariants; LARGE CONVEX-BODIES; LATTICE POINTS; CONVOLUTIONS; SURFACES; FEATURES;
D O I
10.1016/j.cviu.2014.04.013
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
In many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. In this paper, we investigate a new class of estimators on digital shape boundaries based on integral invariants (Pottmann et al., 2007) [39]. More precisely, we provide both proofs of multigrid convergence of principal curvature estimators and a complete experimental evaluation of their performances. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:27 / 41
页数:15
相关论文
共 46 条
[1]  
Alliez Pierre, 2007, P 5 07, V7, P39, DOI DOI 10.2312/SGP/SGP07/039-048(VERP.39
[2]  
Amenta N., 1998, Computer Graphics. Proceedings. SIGGRAPH 98 Conference Proceedings, P415, DOI 10.1145/280814.280947
[3]  
[Anonymous], 2003, PROC 19 ANN S COMPUT, DOI DOI 10.1145/777792.777839
[4]  
[Anonymous], 1960, NUMER MATH, DOI 10.1007/bf01386217
[5]  
Bhatia R., 1997, MATRIX ANAL, V169
[6]  
Bobenko A. I., 2008, Discrete Differential Geometry. Integrable Structure (Graduate Studies in Mathematics, V98
[7]   Fast and Robust Normal Estimation for Point Clouds with Sharp Features [J].
Boulch, Alexandre ;
Marlet, Renaud .
COMPUTER GRAPHICS FORUM, 2012, 31 (05) :1765-1774
[8]   NUMERICAL-METHODS FOR COMPUTING INTERFACIAL MEAN-CURVATURE [J].
BULLARD, JW ;
GARBOCZI, EJ ;
CARTER, WC ;
FULLER, ER .
COMPUTATIONAL MATERIALS SCIENCE, 1995, 4 (02) :103-116
[9]   Estimating differential quantities using polynomial fitting of osculating jets [J].
Cazals, F ;
Pouget, M .
COMPUTER AIDED GEOMETRIC DESIGN, 2005, 22 (02) :121-146
[10]   A comparative evaluation of length estimators of digital curves [J].
Coeurjolly, D ;
Klette, R .
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 2004, 26 (02) :252-258