Symmetry aware embedding for shape correspondence

Abstract In this paper, we present symmetry-aware embedding for shape correspondence, which is robust against symmetric (left–right) flips and rotational (front–back) flips. Unlike previous embedding approaches that embed surfaces into a high-dimensional space, our technique is based on a low dimensional (3D) embedding. Our method can solve left–right flips by finding a 3D rigid transformation between two embedding surfaces without reflections. Using the global reflectional symmetry plane to align two surfaces, we can further reduce the problem to that of finding the rotation that corrects the signs of the front–back and up–down directions (there are four possible solutions). We exploit this simple problem formulation and alleviate the front–back flips, by explicitly comparing the front and back of embedding surfaces based on the global and local extrinsic shape characteristics. Consequently, reasonably accurate point-to-point correspondences can be established simply by performing the nearest neighbor search in our embedding space. Experimental results based on a shape correspondence benchmark showed that our method produces stable matching results.