Abstract Classical approaches to shape correspondence base their computation purely on the properties, in particular geometric similarity, of the shapes in question. Their performance still falls far short of that of humans in challenging cases where corresponding shape parts may differ significantly in geometry or even topology. We stipulate that in these cases, shape correspondence by humans involves recognition of the shape parts where prior knowledge on the parts would play a more dominant role than geometric similarity. We introduce an approach to part correspondence which incorporates prior knowledge imparted by a training set of pre‐segmented, labeled models and combines the knowledge with content‐driven analysis based on geometric similarity between the matched shapes. First, the prior knowledge is learned from the training set in the form of per‐label classifiers. Next, given two query shapes to be matched, we apply the classifiers to assign a probabilistic label to each shape face. Finally, by means of a joint labeling scheme, the probabilistic labels are used synergistically with pairwise assignments derived from geometric similarity to provide the resulting part correspondence. We show that the incorporation of knowledge is especially effective in dealing with shapes exhibiting large intra‐class variations. We also show that combining knowledge and content analyses outperforms approaches guided by either attribute alone.
We introduce an algorithm for unsupervised co-segmentation of a set of shapes so as to reveal the semantic shape parts and establish their correspondence across the set. The input set may exhibit significant shape variability where the shapes do not admit proper spatial alignment and the corresponding parts in any pair of shapes may be geometrically dissimilar. Our algorithm can handle such challenging input sets since, first, we perform co-analysis in a descriptor space, where a combination of shape descriptors relates the parts independently of their pose, location, and cardinality. Secondly, we exploit a key enabling feature of the input set, namely, dissimilar parts may be "linked" through third-parties present in the set. The links are derived from the pairwise similarities between the parts' descriptors. To reveal such linkages, which may manifest themselves as anisotropic and non-linear structures in the descriptor space, we perform spectral clustering with the aid of diffusion maps. We show that with our approach, we are able to co-segment sets of shapes that possess significant variability, achieving results that are close to those of a supervised approach.
We introduce an algorithm for unsupervised co-segmentation of a set of shapes so as to reveal the semantic shape parts and establish their correspondence across the set. The input set may exhibit significant shape variability where the shapes do not admit proper spatial alignment and the corresponding parts in any pair of shapes may be geometrically dissimilar. Our algorithm can handle such challenging input sets since, first, we perform co-analysis in a descriptor space , where a combination of shape descriptors relates the parts independently of their pose, location, and cardinality. Secondly, we exploit a key enabling feature of the input set, namely, dissimilar parts may be "linked" through third-parties present in the set. The links are derived from the pairwise similarities between the parts' descriptors. To reveal such linkages, which may manifest themselves as anisotropic and non-linear structures in the descriptor space, we perform spectral clustering with the aid of diffusion maps. We show that with our approach, we are able to co-segment sets of shapes that possess significant variability, achieving results that are close to those of a supervised approach.
We introduce an algorithm for unsupervised co-segmentation of a set of shapes so as to reveal the semantic shape parts and establish their correspondence across the set. The input set may exhibit significant shape variability where the shapes do not admit proper spatial alignment and the corresponding parts in any pair of shapes may be geometrically dissimilar. Our algorithm can handle such challenging input sets since, first, we perform co-analysis in a descriptor space, where a combination of shape descriptors relates the parts independently of their pose, location, and cardinality. Secondly, we exploit a key enabling feature of the input set, namely, dissimilar parts may be "linked" through third-parties present in the set. The links are derived from the pairwise similarities between the parts' descriptors. To reveal such linkages, which may manifest themselves as anisotropic and non-linear structures in the descriptor space, we perform spectral clustering with the aid of diffusion maps. We show that with our approach, we are able to co-segment sets of shapes that possess significant variability, achieving results that are close to those of a supervised approach.
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