Shape Priors using Manifold Learning Techniques

We introduce a non-linear shape prior for the deformable 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 Nystr¨om 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...

• Type: Conference
• Year: 2007
• Where: ICCV
• Authors: Patrick Etyngier, Florent Ségonne, Renaud Keriven
• Keywords: Computer Vision, ICCV 2007, Manifold, Manifold Learning Techniques, finite Dimensional Manifold