Curvature prior for MRF-based segmentation and shape inpainting

Most image labeling problems such as segmentation and image reconstruction are fundamentally ill-posed and suffer from ambiguities and noise. Higher-order image priors encode high-level structural dependencies between pixels and are key to overcoming these problems. However, in general these priors lead to computationally intractable models. This paper addresses the problem of discovering compact representations of higher-order priors which allow efficient inference. We propose a framework for solving this problem that uses a recently proposed representation of higher-order functions which are encoded as lower envelopes of linear functions. Maximum a Posterior inference on our learned models reduces to minimizing a pairwise function of discrete variables. We show that our framework can learn a compact representation that approximates a low curvature shape prior and demonstrate its effectiveness in solving shape inpainting and image segmentation problems. © 2012 Springer-Verlag.