​A Space-Time Parallel Method for the Optic Flow Estimation in Large Displacements and Varying Illumination Case

Abstract

We consider a unified variational PDEs model to solve the optic flow problem for large displacements and varying illumination. Although, the energy functional is nonconvex and severely nonlinear, we show that the model offers a well suited framework to extend the efficient methods we used for small displacements. In particular, we resort to an adaptive control of the diffusion and the illumination coefficients which allows us to preserve the edges and to obtain a sparse vector field. We develop a combined space-time parallel programming strategy based on a Schwarz domain decomposition method to speed up the computations and to handle high resolution images, and the parareal algorithm, to enhance the speedup and to achieve a lowest-energy local minimum. This full parallel method gives raise to several iterative schemes and allows us to obtain a good balance between several objectives, e.g. accuracy, cost reduction, time saving and achieving the "best" local minimum. We present several numerical simulations to validate the different algorithms and to compare their performances.