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The aim of this paper is to derive and analyze a variational model for thejoint estimation of motion and reconstruction of image sequences, which isbased on a time-continuous Eulerian motion model. The model can be set up interms of the continuity equation or the brightness constancy equation. Theanalysis in this paper focuses on the latter for robust motion estimation onsequences of two-dimensional images. We rigorously prove the existence of aminimizer in a suitable function space setting. Moreover, we discuss thenumerical solution of the model based on primal-dual algorithms and investigateseveral examples. Finally, the benefits of our model compared to existingtechniques, such as sequential image reconstruction and motion estimation, areshown.

A Variational Model for Joint Motion Estimation and Image Reconstruction