Analysis of two-dimensional non-rigid shapes

被引:77
作者
Bronstein, Alexander M. [1 ]
Bronstein, Michael M. [1 ]
Bruckstein, Alfred M. [1 ]
Kimmel, Ron [1 ]
机构
[1] Technion Israel Inst Technol, Dept Comp Sci, IL-32000 Haifa, Israel
关键词
non-rigid shapes; partial similarity; Pareto optimum; multidimensional scaling; GMDS; Gromov-Hausdorff distance; intrinsic geometry;
D O I
10.1007/s11263-007-0078-4
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
Analysis of deformable two-dimensional shapes is an important problem, encountered in numerous pattern recognition, computer vision and computer graphics applications. In this paper, we address three major problems in the analysis of non-rigid shapes: similarity, partial similarity, and correspondence. We present an axiomatic construction of similarity criteria for deformation-invariant shape comparison, based on intrinsic geometric properties of the shapes, and show that such criteria are related to the Gromov-Hausdorff distance. Next, we extend the problem of similarity computation to shapes which have similar parts but are dissimilar when considered as a whole, and present a construction of set-valued distances, based on the notion of Pareto optimality. Finally, we show that the correspondence between non-rigid shapes can be obtained as a byproduct of the non-rigid similarity problem. As a numerical framework, we use the generalized multidimensional scaling (GMDS) method, which is the numerical core of the three problems addressed in this paper.
引用
收藏
页码:67 / 88
页数:22
相关论文
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