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The paper presents a motion estimation method based on data assimilation in a dynamic model, named Image Model, expressing the physical evolution of a quantity observed on the images. The application concerns the retrieval of apparent surface velocity from a sequence of satellite data, acquired over the ocean. The Image Model includes a shallow-water approximation for the dynamics of the velocity field (the evolution of the two components of motion are linked by the water layer thickness) and a transport equation for the image field. For retrieving the surface velocity, a sequence of Sea Surface Temperature (SST) acquisitions is assimilated in the Image Model with a 4D-Var method. This is based on the minimization of a cost function including the discrepancy between model outputs and SST data and a regularization term. Several types of regularization norms have been studied. Results are discussed to analyze the impact of the different components of the assimilation system.