Parallel and deterministic algorithms from MRFs (Markov Random Fields): Surface reconstruction and integration. Memorandum report

TLDR: In this paper, the authors derived deterministic approximations to Markov Random Fields (MRFs) models, which can be applied in the output of the visual processes to reconstruct surfaces from sparse and noisy depth data, or to integrate early vision processes to label physical discontinuities.

Abstract: In recent years many researchers have investigated the use of Markov random fields (MRFs) for computer vision. They can be applied for example in the output of the visual processes to reconstruct surfaces from sparse and noisy depth data, or to integrate early vision processes to label physical discontinuities. Drawbacks of MRFs models have been the computational complexity of the implementation and the difficulty in estimating the parameters of the model. This paper derives deterministic approximations to MRFs models. One of the considered models is shown to give in a natural way the graduate non convexity (GNC) algorithm. This model can be applied to smooth a field preserving its discontinuities. A new model is then proposed: it allows the gradient of the field to be enhanced at the discontinuities and smoothed elsewhere. All the theoretical results are obtained in the framework of the mean field theory, that is a well known statistical mechanics technique. A fast, parallel, and iterative algorithm to solve the deterministic equations of the two models is presented, together with experiments on synthetic and real images. The algorithm is applied to the problem of surface reconstruction is in the case of sparse data. A fast algorithm ismore » also described that solves the problem of aligning the discontinuities of different visual models with intensity edges via integration.« less