Topological analysis of shapes using Morse theory

被引：10
作者：
Allili, M. [1 ]
Corriveau, D.
机构：
[1] Bishops Univ, Dept Comp Sci, Lennoxville, PQ J1M 1Z7, Canada
[2] Univ Sherbrooke, Dept Comp Sci, Sherbrooke, PQ J1K 2R1, Canada
来源：
COMPUTER VISION AND IMAGE UNDERSTANDING | 2007年 / 105卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
shape representation; shape similarity; Morse theory; computational homology;
D O I：
10.1016/j.cviu.2006.10.004
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, we propose a novel method for shape analysis that is suitable for any multi-dimensional data set that can be modelled as a manifold. The descriptor is obtained for any pair (M, phi), where M is a closed smooth manifold and phi is a Morse function defined on M. More precisely, we characterize the topology of all pairs of sub-level sets (M-y, M-x) of phi, where M-a = phi(-1)((-infinity, a]), for all a is an element of R. Classical Morse theory is used to establish a link between the topology of a pair of sub-level sets of p and its critical points lying between the two levels. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：188 / 199
页数：12
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