MRF solutions for probabilistic optical flow formulations

We propose an efficient, non-iterative method for estimating optical flow. We develop a probabilistic framework that is appropriate for describing the inherent uncertainty in the brightness constraint due to errors in image derivative computation. We separate the flow into two 1D representations and pose the problem of flow estimation as one of solving for the most probable configuration of 1D labels in an Markov random fields (MRF) with linear clique potentials. The global optimum for this problem can be efficiently solved for using the maximum flow computation in a graph. We develop this formulation and describe how the use of the probabilistic framework, the parametrisation and MRF formulation together enables one to capture the desirable properties for flow estimation, especially preserving motion discontinuities. We demonstrate the performance of our algorithm and compare our results with that of other algorithms described by Barron et. al. (1994)