Shape Matching via Quotient Spaces

Figure 1: The proposed framework for isometric shape matching allows establishing dense correspondences between symmet-ric shapes in a principled way. Here, we first estimate a single map in an appropriate quotient space and then use it to generate 8 different point-to-point maps between two octopus models. Each correspondence is shown by transferring the XYZ functions from the target onto the source and rendering them as RGB channels on the mesh. Note, e.g. the location of the orange arm. 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. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: — Shape Analysis. 1