Projection onto a Shape Manifold for Image Segmentation with Prior

Image segmentation with shape priors has received a lot of attention over the past years. Most existing work focuses on a linearized shape space with small deformation modes around a mean shape, which is relevant only when considering similar 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 dimensionality reduction techniques suchlike Laplacian eigenmaps. Unfortunately, this model does not provide an explicit projection operator onto the manifold. Our contribution is twofold. First, we calculate the low dimensional representation of any point not in the training set. Second, we properly define a projection operator onto the manifold by interpolating between shape samples using local weighted means. We show results both on synthetic and real shapes and demonstrate the potential of our method for segmentation tasks.