Stable Region Correspondences Between Non-Isometric Shapes

We consider the problem of finding meaningful correspondences between 3D models that are related but not necessarily very similar. When the shapes are quite different, a point‐to‐point map is not always appropriate, so our focus in this paper is a method to build a set of correspondences between sha...

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Veröffentlicht in:Computer graphics forum Jg. 35; H. 5; S. 121 - 133
Hauptverfasser: Ganapathi-Subramanian, V., Thibert, B., Ovsjanikov, M., Guibas, L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Blackwell Publishing Ltd 01.08.2016
Wiley
Schlagworte:
3-D graphics
Affinity
Algorithms
Analysis
Categories and Subject Descriptors (according to ACM CCS)
Eigenvalues
Geometric Modeling
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-3D Shape Matching
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—3D Shape Matching, Geometric Modeling, Shape Matching and Retrieval
Image processing systems
Matching
Mathematical analysis
Mathematical models
Mathematics
Shape Matching and Retrieval
Shape recognition
Similarity
Studies
Three dimensional models
ISSN:0167-7055, 1467-8659
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Beschreibung
Zusammenfassung:We consider the problem of finding meaningful correspondences between 3D models that are related but not necessarily very similar. When the shapes are quite different, a point‐to‐point map is not always appropriate, so our focus in this paper is a method to build a set of correspondences between shape regions or parts. The proposed approach exploits a variety of feature functions on the shapes and makes use of the key observation that points in matching parts have similar ranks in the sorting of the corresponding feature values. Our algorithm proceeds in two steps. We first build an affinity matrix between points on the two shapes, based on feature rank similarity over many feature functions. We then define a notion of stability of a pair of regions, with respect to this affinity matrix, obtained as a fixed point of a nonlinear operator. Our method yields a family of corresponding maximally stable regions between the two shapes that can be used to define shape parts. We observe that this is an instance of the biclustering problem and that it is related to solving a constrained maximal eigenvalue problem. We provide an algorithm to solve this problem that mimics the power method. We show the robustness of its output to noisy input features as well its convergence properties. The obtained part correspondences are shown to be almost perfect matches in the isometric case, and also semantically appropriate even in non‐isometric cases. We provide numerous examples and applications of this technique, for example to sharpening correspondences in traditional shape matching algorithms.
Bibliographie:istex:D3DF689CC3A53A6A472EE931E70EA2E89756C079
ArticleID:CGF12969
ark:/67375/WNG-CQLWSGS0-H
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12969