Discrete-continuous optimization for optical flow estimation

Accurate estimation of optical flow is a challenging task, which often requires addressing difficult energy optimization problems. To solve them, most top-performing methods rely on continuous optimization algorithms. The modeling accuracy of the energy in this case is often traded for its tractability. This is in contrast to the related problem of narrow-baseline stereo matching, where the top-performing methods employ powerful discrete optimization algorithms such as graph cuts and message-passing to optimize highly non-convex energies. In this paper, we demonstrate how similar non-convex energies can be formulated and optimized discretely in the context of optical flow estimation. Starting with a set of candidate solutions that are produced by fast continuous flow estimation algorithms, the proposed method iteratively fuses these candidate solutions by the computation of minimum cuts on graphs. The obtained continuous-valued fusion result is then further improved using local gradient descent. Experimentally, we demonstrate that the proposed energy is an accurate model and that the proposed discretecontinuous optimization scheme not only finds lower energy solutions than traditional discrete or continuous optimization techniques, but also leads to flow estimates that outperform the current state-of-the-art.