Compact Part-Based Shape Spaces for Dense Correspondences

We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble optimization method that improves given coarse correspondences to obtain dense correspondences. Following ideas from minimum description length approaches, it maximizes the compactness of the induced shape space to obtain high-quality correspondences. We make a number of improvements that are important for computer graphics applications: Our approach handles meshes of general topology and handles partial matching between input of varying topology. To this end we introduce a novel part-based generative statistical shape model. We develop a novel analysis algorithm that learns such models from training shapes of varying topology. We also provide a novel synthesis method that can generate new instances with varying part layouts and subject to generic variational constraints. In practical experiments, we obtain a substantial improvement in correspondence quality over state-of-the-art methods. As example application, we demonstrate a system that learns shape families as assemblies of deformable parts and permits real-time editing with continuous and discrete variability.