Section: New Results

Segmentation and registration of 3D shapes

One of the fundamental problems in 2D and 3D shape analysis is their segmentation and registration. We address both these issues within the framework of spectral graph theory. Namely, we started by developing a shape registration method based on Spectral graph matching and we applied this method for registering shapes described by meshes [53] . The method is based on the Laplacian embedding of meshes into an Euclidean space. Hence, the problem of matching two meshes is equivalent to the problem of registering two clouds of points. We thoroughly addressed the problem of point registration and we devised a probabilistic registration method based on Gaussian mixtures and convex optimization [54] .

In parallel, we started to investigate the problem of shape segmentation using a combination of non-parametric and parametric clustering techniques, namely we combined spectral clustering with Gaussian mixture models [44] , [22] . The ongoing work investigates constrained clustering methods and their use to the problem of learning shape segmentation. This completes our work on articulated object tracking [14] .