This paper presents a new approach for the estimation of motion trajectories from image sequences. This approach is seen to be similar to both "token tracking" feature-based methods, and "block based" region-matching approaches. Initially, a parametric motion trajectory model is formulated, and the motion trajectory estimation problem is conveniently cast into a Markov Random Field (MRF) framework which allows a priori motion constraints to be expressed. A three-stage optimization algorithm is presented, and a recursive estimation approach is developed. A method for the robust detection of areas of occlusion is presented, as are comparative results to show the relative success of this motion estimation approach. Although robustly computed motion trajectories show great promise in many motion-related areas of computer vision, this paper illustrates their use in the context of motion compensated prediction as part of a video compression algorithm.