Optimal Transport Model of Optical Flow Estimation: Constant and Varying Illumination Cases
Résumé
In this article, we consider a new modeling of optical flow estimation with constant or varying illumination based on mass optimal transport theory. While PDE classical approaches in motion analysis assume pixel-wise conservation of the intensity map along the flow of characteristics driven by the flow vector, the new formulation assumes a conservation of corresponding densities and yields a conservative transport equation encoding also the varying illumination. Namely, such variations are expressed as those of small volumes (of pixels) expressing compressibility constraint. When no variations of the illumination occur, we obtain an optimal transport generalized incompressible flow model more "rich" than classical ones. The model in this optimal transport approach offer a complete similarity to standard L² Monge-Kantorovich problem on mass transportation and generalized incompressible flows. We use the Benamou-Brenier algorithm for the optical flow computation. We present some numerical results and make some comparisons with more classical approaches to show the reliability of the optimal transport model, its perspectives and its limitations.
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