Optical Flow and Image Registration: A New Local Rigidity Approach for Global Minimization

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We address the theoretical problems of optical flow estimation and image registration in a multi-scale framework in any dimension. Much work has been done based on the minimization of a distance between a first image and a second image after applying deformation or motion field. We discuss the classical multiscale approach and point out the problem of validity of the motion constraint equation (MCE) at lower resolutions. We introduce a new local rigidity hypothesis allowing to write proof of such a validity. This allows us to derive sufficient conditions for convergence of a new multi-scale and iterative motion estimation/ registration scheme towards a global minimum of the usual nonlinear energy instead of a local minimum as did all previous methods. Although some of the sufficient conditions cannot always be fulfilled because of the absence of the necessary a priori knowledge on the motion, we use an implicit approach. We illustrate our method by showing results on synthetic and real examples (Motion, Registration, Morphing), including large deformation experiments.