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<p>The estimation of dense velocity fields from image sequences is basically an ill-posed problem, primarily because the data only partially constrain the solution. It is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches. In this paper, the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints. It is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances. The theoretical framework relies on Bayesian estimation associated with global statistical models, namely, Markov random fields. The constraints introduced here aim to address the following issues: optical flow estimation while preserving motion boundaries, processing of occlusion regions, fusion between gradient and feature-based motion constraint equations. Deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field. The algorithm is well suited to a multiresolution implementation which brings an appreciable speed-up as well as a significant improvement of estimation when large displacements are present in the scene. Experiments on synthetic and real world image sequences are reported.</p>
multimodal estimation; discontinuous optical flow; Markov random fields; dense velocity fields; ill-posed problem; motion boundaries; occlusion regions; motion estimation; visual motion; flow estimation; Bayesian estimation; global statistical models; gradient-based motion constraint equations; feature-based motion constraint equations; deterministic relaxation algorithms; real world image sequences; synthetic image sequences; Bayes methods; image sequences; Markov processes; motion estimation; statistics

F. Heitz and P. Bouthemy, "Multimodal Estimation of Discontinuous Optical Flow using Markov Random Fields," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 15, no. , pp. 1217-1232, 1993.
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