Projecting onto a shape prior manifold

Incorporating shape priors in image segmentation has become a key problem in computer vision. Most existing work is limited to a linearized shape space with small deformation modes around a mean shape. These approaches are relevant only when the learning set is composed of very similar shapes. Also, there is no guarantee on the visual quality of the resulting shapes. In this paper, we introduce a new framework that can handle more general shape priors. We model a category of shapes as a finite dimensional manifold, the shape prior manifold, which we approximate from the shape samples using the Laplacian eigenmap technique. Our main contribution is to properly define a projection operator onto the manifold by interpolating between shape samples using local weighted means, thereby improving over the naive nearest neighbor approach. Our method is stated as a variational problem that is solved using an iterative numerical scheme. We obtain promising results with synthetic and real shapes which show the potential of our method for segmentation tasks.