Persistent homology and partial similarity of shapes

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• 作者：Barbara Di Fabio^a ; ^{barbara.difabio@unibo.it} ; Claudia Landi^b ; ^a ; ^{clandi@unimore.it}
• 关键词：Mayer&ndash ; Vietoris formula ; Extended persistence ; Hausdorff distance
• 刊名：Pattern Recognition Letters
• 出版年：2012
• 期刊代码：101_01678655
• 类别：cp
• 出版时间：1 August, 2012
• 卷：33
• 期：11
• 页码：1445-1450
• 文件大小：876 K

摘要

Persistent homology provides shapes descriptors called persistence diagrams. We use persistence diagrams to address the problem of shape comparison based on partial similarity. We show that two shapes having a common sub-part in general present a common persistence sub-diagram. Hence, the partial Hausdorff distance between persistence diagrams measures partial similarity between shapes. The approach is supported by experiments on 2D and 3D data sets.