Approximately Isometric Shape Correspondence by Matching Pointwise Spectral Features and Global Geodesic Structures

A practical method for finding correspondences between nonrigid isometric shapes is presented. It utilizes both pointwise surface descriptors, and metric structures defined on the shapes to perform the matching task, which is formulated as a quadratic minimization problem. Further, the paper explores the correspondence ambiguity problem arising when matching intrinsically symmetric shapes using only intrinsic surface properties. It is shown 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 different possible correspondences. When used in a proper minimization problem, those descriptors allow us to explore number of possible correspondences between two given shapes.