Shape Priors Using Manifold Learning Techniques

Abstract

We introduce a non-linear shape prior for the de- formable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps, that we call the shape prior manifold. Our method computes a Delaunay triangulation of the reduced space, considered as Euclidean, and uses the resulting space partition to identify the closest neighbors of any given shape based on its Nystrom extension. Our contribution lies in three aspects. First, we propose a solution to the pre-image problem and define the projection of a shape onto the manifold. Based on closest neighbors for the Diffusion distance, we then describe a variational framework for manifold denoising. Finally, we introduce a shape prior term for the deformable framework through a non-linear energy term designed to attract a shape towards the manifold at given constant embedding. Results on shapes of cars and ventricule nuclei are presented and demonstrate the potentials of our method.