  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.
