Region-based Correspondence Between 3D Shapes via Spatially Smooth Biclustering

Region-based correspondence (RBC) is a highly relevant and non-trivial computer vision problem. Given two 3D shapes, RBC seeks segments/regions on these shapes that can be reliably put in correspondence. The problem thus consists both in finding the regions and determining the correspondences between them. This problem statement is similar to that of "biclustering", implying that RBC can be cast as a biclustering problem. Here, we exploit this implication by tackling RBC via a novel biclustering approach, called S4B (spatially smooth spike and slab biclustering), which: (i) casts the problem in a probabilistic low-rank matrix factorization perspective; (ii) uses a spike and slab prior to induce sparsity; (iii) is enriched with a spatial smoothness prior, based on geodesic distances, encouraging nearby vertices to belong to the same bicluster. This type of spatial prior cannot be used in classical biclustering techniques. We test the proposed approach on the FAUST dataset, outperforming both state-of-the-art RBC techniques and classical biclustering methods.