Bayesian Real-time Optical Flow

Optical flow can be used to compute motion detection, time to collision, structure, focus of expansion as well as object segmentation. Unfortunately, most optical flow techniques do not provide accurate and dense measures that are useful for these types of computations. In addition, most techniques are also slow computationally. Albeit, one method proposed by Camus is able to perform optical flow computations in real-time capitalizing on redundancies in the computation and spatial-temporal sampling trade-offs. It is a simple technique based on simulating various motions and computing the SD (sum-difference) of patches. Its problem is that the produced field is not accurate and arbitrary in aperture and blank wall situations. We show that the simulating of various futures can be used as the factored samples that produce the likelihood probabilities that can be used in a particle filtering framework. Maximization/minimization or computing the expectations of the likelihood at a particular location does not necessarily produce the proper flow. We suggest that likelihoods are well behaved when their variance is small and these can be propagated firstly to address aperture problems and secondly to address the extended blank wall problem. We show this propagation with thresholded likelihood values and speculate on how the likelihood distributions can be integrated into an algorithm that has its basis in particle filtering.