Analysis of Two-Dimensional Non-Rigid Shapes
Analysis of Two-Dimensional Non-Rigid Shapes
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DOI：
10.1007/s11263-007-0078-4
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发表时间：
2008-06
影响因子：
19.5
通讯作者：
A. Bronstein;M. Bronstein;A. Bruckstein;R. Kimmel
中科院分区：
文献类型：
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作者：
A. Bronstein;M. Bronstein;A. Bruckstein;R. Kimmel
可变形二维形状的分析是许多模式识别、计算机视觉和计算机图形学应用中遇到的重要问题。在本文中，我们解决了三个主要问题，在非刚性形状的分析：相似性，部分相似性和对应关系。我们提出了一个公理化的构造变形不变的形状比较的相似性准则，基于固有的几何性质的形状，并表明，这样的标准是相关的Gromov-Hausdorff距离。接下来，我们扩展的相似性计算的问题，形状有相似的部分，但被认为是不同的整体时，并提出了一个建设的集值距离，帕累托最优的概念的基础上。最后，我们证明了非刚性形状之间的对应关系可以作为非刚性相似性问题的副产品。作为一个数值框架，我们使用的广义多维尺度（GMDS）方法，这是本文所讨论的三个问题的数值核心。
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.