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.