Sparse Modeling of Intrinsic Correspondences

Pokrass et al. [PBBS12] present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. They show that such scarce information as two sets of regions in two shapes is sufficient to establish very accurate correspondences between shapes. The paper presents methods from the field of sparse modeling and show how they can be aplied to simultaneously solve for an unknown permutation ordering of the regions on two shapes and for an unknown correspondence in functional representation. It further presents numerical solutions to the resulting optimization problems. The paper also presents results and compare them to state-of-the-art methods. In this seminar paper, we give an overview on their work. Figure 1: In their work on the Sparse Modeling of Intrinsic Correspondences, Pokrass et al. present a novel and first of its kind approach to shape matching. They show how to use tools from the field of sparse modeling to simultaneously search for an approximately diagonal C and permutation Π, bringing a set of regions into correspondence. The latter are given in functional representation by coefficients A and B. These indicator functions can represent any intrinsic property of two near-isometric shapes, e.g. repeatable regions like MSER. Such scarce information is sufficient to achieve high quality matchings with the presented robust permuted sparse coding algorithm, which outperforms state-of-the-art methods.