Scale-Space Spectral Representation of Shape

We construct a scale space of shape of closed Riemannian manifolds, equipped with metrics derived from spectral representations and the Hausdorff distance. The representation depends only on the intrinsic geometry of the manifolds, making it robust to pose and articulation. The computation of shape distance involves an optimization problem over the 2^p-element group of all p-bit strings, which is approached with Markov chain Monte Carlo techniques. The methods are applied to cluster surfaces in 3D space.