Parallel and Deterministic Algorithms from MRF’s: Surface Reconstruction

In recent years many researchers have investigated the use of Bayesian and the special case of Markov random fields (MRF’s) for computer vision. They can be applied for example to reconstruct surfaces from sparse and noisy depth data coming from the output of a visual process, or to integrate early vision processes to label physical discontinuities. Drawbacks of MRF models are the computational complexity of the implementation and the difficulty in estimating the parameters of the model. In this paper we derive deterministic approximations to MRI models. One of the models is shown to give in a natural way the graduated nonconvexity (GNC) algorithm proposed by Blake and Zisserman. This model can be applied to smooth a field preserving its discontinuities. A class of more complex models is then proposed in order to deal with a variety of vision problems. All the theoretical results are obtained in the framework of sta-tistical mechanics and mean field techniques. A parallel, iterative algorithm to solve the deterministic equations of the two models is presented, together with some experiments on synthetic and real images.