Abstract

Abstract. We propose an algorithmic framework to compute global solutions of variational models with convex regularity terms that permit quite arbitrary data terms. While the minimization of variational problems with convex data and regularity terms is straight forward (using for example gradient descent), this is no longer trivial for functionals with non-convex data terms. Using the theoretical framework of calibrations the original variational problem can be written as the maximum flux of a particular vector field going through the boundary of the subgraph of the unknown function. Upon relaxation this formulation turns the problem into a convex problem, however, in higher dimension. In order to solve this problem, we propose a fast primal dual algorithm which significantly outperforms existing algorithms. In experimental results we show the application of our method to outlier filtering of range images and disparity estimation in stereo images using a variety of convex regularity terms. Key words. Variational methods, calibrations, total variation, convex optimization. AMS subject classifications. 49M20, 49M29, 65K15, 68U10. 1. Introduction. Energy

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