Non-linear observation equation for motion estimation

The paper addresses the estimation of motion on an image sequence by data assimilation methods. The core of the study concerns the definition of the data term, or observation equation, that links images to the underlying motion field. In the image processing literature, the optical flow equation is usually chosen to characterize these links. It expresses the Lagrangian constancy of grey level values in time. However, this optical flow equation is obtained by linearization and is no more valid in case of large displacements. The paper discusses the improvement obtained with the original non-linear transport equation of the image brightness by the velocity field. A 4D-Var data assimilation method is applied that solves the evolution equation of motion and the observation equation in its non-linear and linear forms. The comparison of results obtained with both observation equations is quantified on synthetic data and discussed on oceanographic Sea Surface Temperature images.