Spatial-awareness spectral embedding (SASE) for robust shape matching

Shape matching in the spectral domain has gained great popularity in recent years. Most algorithms, however, rely on invariant global spectral embeddings of the shapes to find correspondence, where spatial neighborhood information is not explicitly incorporated into the matching procedure. Misalignments of global as well as local structures are often resulted due to the lack of spatial guidance. In this paper, we identify a number of ambiguities existing in spectral embedding and matching, and subsequently propose a general framework to improve the matching coherence. At the center of the framework is a hybrid spatial-awareness spectral embedding (SASE), which allows various neighborhood and topological information, such as pair-wise distance, relative angles w.r.t. object centers, to be integrated into commute-time (CT) embeddings. A probabilistic expectation maximization (EM) algorithm with imposed regularity is employed to seek an optimal matching of the SASE embeddings. Experimental evaluations of the algorithm on 2D and 3D data demonstrate both the effectiveness and robustness of our approach.