BAYESIAN-ESTIMATION OF MOTION VECTOR-FIELDS

This paper presents a new approach to the estimation of 2-D motion vector fields from time-varying images. The approach is stochastic both in its formulation and in the solution method. The formulation involves the specification of a deterministic structural model along with stochastic observation and motion field models. Two motion models are proposed: a globally smooth model based on vector Markov random fields and a piecewise smooth model derived from coupled vector-binary Markov random fields. Two estimation criteria are studied. In the maximum a posteriori probability (MAP) estimation, the a posteriori probability of motion given data is maximized, whereas in the minimum expected cost (MEC) estimation, the expectation of a certain cost function is minimized. The MAP estimation is performed via simulated annealing, whereas the MEC algorithm performs iteration-wise averaging. Both algorithms generate sample fields by means of stochastic relaxation implemented via the Gibbs sampler. Two versions are developed: one for a discrete state space and the other for a continuous state space. The MAP estimation is incorporated into a hierarchical environment to deal efficiently with large displacements. Numerous experimental results of application of these algorithms to natural and computer-generated images with natural and synthetic motion are shown.