Stable Region Correspondences Between Non-Isometric Shapes

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dc.contributor.authorGanapathi-Subramanian, Vigneshen_US
dc.contributor.authorThibert, Borisen_US
dc.contributor.authorOvsjanikov, Maksen_US
dc.contributor.authorGuibas, Leonidasen_US
dc.contributor.editorMaks Ovsjanikov and Daniele Panozzoen_US
dc.date.accessioned2016-06-17T14:11:55Z
dc.date.available2016-06-17T14:11:55Z
dc.date.issued2016en_US
dc.description.abstractWe 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.en_US
dc.description.number5en_US
dc.description.sectionheadersFunctional Correspondenceen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume35en_US
dc.identifier.doi10.1111/cgf.12969en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages121-133en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12969en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subject3D Shape Matchingen_US
dc.subjectGeometric Modelingen_US
dc.subjectShape Matching and Retrievalen_US
dc.titleStable Region Correspondences Between Non-Isometric Shapesen_US
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35-Issue 5
SGP16: Eurographics Symposium on Geometry Processing (CGF 35-5)