Shape Matching via Quotient Spaces

• Published in: Computer graphics forum Vol. 32; no. 5; pp. 1 - 11
• Main Authors: Ovsjanikov, Maks, Mérigot, Quentin, Pătrăucean, Viorica, Guibas, Leonidas
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.08.2013; Wiley
• Subjects: Ambiguity; Combinatorial analysis; Computational Geometry; Computer graphics; Computer Science; I.3.3 [Computer Graphics]:-Shape Analysis; Information management; Landmarks; Matching; Quotients; Sampling; Studies; Symmetry; Symmetry detection; United States > US; shape maps; symmetry; Shape matching
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12167

We introduce a novel method for non‐rigid shape matching, designed to address the symmetric ambiguity problem present when matching shapes with intrinsic symmetries. Unlike the majority of existing methods which try to overcome this ambiguity by sampling a set of landmark correspondences, we address this problem directly by performing shape matching in an appropriate quotient space, where the symmetry has been identified and factored out. This allows us to both simplify the shape matching problem by matching between subspaces, and to return multiple solutions with equally good dense correspondences. Remarkably, both symmetry detection and shape matching are done without establishing any landmark correspondences between either points or parts of the shapes. This allows us to avoid an expensive combinatorial search present in most intrinsic symmetry detection and shape matching methods. We compare our technique with state‐of‐the‐art methods and show that superior performance can be achieved both when the symmetry on each shape is known and when it needs to be estimated.