Non-rigid shape correspondence using pointwise surface descriptors and metric structures Anastasia Dubrovina, Dan Raviv and Ron Kimmel Abstract Finding a correspondence between two non-rigid shapes is one of the cor- nerstone problems in the field of three-dimensional shape processing. We describe a framework for marker-less non-rigid shape correspondence, based on matching intrinsic invariant surface descriptors, and the metric structures of the shapes. The matching task is formulated as a quadratic optimization problem that can be used with any type of descriptors and metric. We minimize it using a hierarchical match- ing algorithm, to obtain a set of accurate correspondences. Further, we present the correspondence ambiguity problem arising when matching intrinsically symmetric shapes using only intrinsic surface properties. We show that when using isometry invariant surface descriptors based on eigendecomposition of the Laplace-Beltrami operator, it is possible to construct distinctive sets of surface descriptors for differ- ent possible correspondences. When used in a proper minimization problem, those descriptors allow us to explore a number of possible correspondences between two given shapes. 1 Introduction Three-dimensional shape processing became increasingly popular in the last decade. One of its corner-stone tasks is detecting a correspondence between two given shapes. It is essential for shape comparison, retrieval, shape morphing and deforma- tion, or shape calculus [5], etc. The most interesting yet complex task is automatic Anastasia Dubrovina Technion, Israel Institute of Technology, e-mail: nastyad@cs.technion.ac.il Dan Raviv Technion, Israel Institute of Technology, e-mail: darav@cs.technion.ac.il Ron Kimmel Technion, Israel Institute of Technology e-mail: ron@cs.technion.ac.il 1