Partial Shape Matching Without Point-Wise Correspondence

作     者：Jonathan Pokrass Alexander M.Bronstein Michael M.Bronstein 

作者机构：School of Electrical EngineeringTel Aviv UniversityIsrael Institute of Computational ScienceFaculty of InformaticsUniversitàdella Svizzera Italiana(USI)LuganoSwitzerland 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2013年第6卷第1期

页      面：223-244页

核心收录：

学科分类：0820[工学-石油与天然气工程] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：The author would like to thank the referees for the helpful suggestions This work has been supported in part by the Israeli Science Foundation grant 615/11 the German-Israeli Foundation grant 2269/2010 and the Swiss High Performance and High Productivity Computing(HP2C)grant 

主　　题：Deformable shapes partial matching partial correspondence partial similarity diffusion geometry Laplace-Beltrami operator shape descriptors heat kernel signature Mumford-Shah regularization 

摘      要：Partial similarity of shapes is a challenging problem arising in many important applications in computer vision,shape analysis,and graphics,*** one has to deal with partial information and acquisition *** problem is especially hard when the underlying shapes are non-rigid and are given up to a *** matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two,taking into account possibly different *** this paper,we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid *** use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts *** problem is regularized using the Mumford-Shah *** show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes,and present experiments demonstrating the success of the proposed method.