Motion Estimation under Location Uncertainty for Turbulent Fluid Flows*

We propose a novel optical flow formulation for estimating 2D velocity fields from images depicting the evolution of a passive scalar transported by a fluid flow. This motion estimator relies on a stochastic representation of the flow allowing to incorporate a notion of motion uncertainty. In this context, the Eulerian fluid flow velocity field is decomposed into two components: a large-scale motion field and a small-scale uncertainty component. We define the latter as a random field. Subsequently, the data term of the optical flow formulation is based on a stochastic transport equation derived from location uncertainty principle. In addition, a specific regularization term built from the assumption of constant kinetic energy involves the same diffusion tensor as the one appearing in the data term. Opposite to the classical estimators, this enables us to devise an optical flow method dedicated to fluid flows with a clear physical interpretation. Experimental evaluations are presented on both synthetic and real world image sequences. Results and comparisons indicate good performance of the proposed formulation for turbulent flow motion estimation.