Non-Rigid Spectral Correspondence of Triangle Meshes

We present an algorithm for finding a meaningful vertex-to-vertex correspondence between two triangle meshes, which is designed to handle general non-rigid transformations. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform scaling and rigid-body transformation. Invariance to shape bending is achieved by relying on approximate geodesic point proximities on a mesh to capture its shape. To deal with moderate stretching, we first raise the issue of “eigenmode switching” and discuss heuristics to bring the eigenmodes to alignment. For additional non-rigid discrepancies in the spectral embeddings, we propose to use non-rigid alignment via thin-plate splines. This is combined with a refinement step based on geodesic proximities to improve dense correspondence. We show empirically that our algorithm outperforms previous spectral methods, as well as schemes that compute correspondence in the spatial domain via non-rigid iterative closest points or the use of local shape descriptors, e.g., 3D shape context. Finally, to speed up our algorithm, we examine the effect of using subsampling and Nyström method.