Total-Variation Based Piecewise Affine Regularization

Authors:
Jing Yuan;Christoph Schnörr;Gabriele Steidl
Affiliations:
Image and Pattern Analysis Group Dept. Mathematics and Computer Science, University of Heidelberg, Germany;Image and Pattern Analysis Group Dept. Mathematics and Computer Science, University of Heidelberg, Germany;Appl. Math. Comp. Sci. Group Dept. Mathematics and Computer Science, University of Mannheim,
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

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Abstract

In this paper, we introduce a novel second-order regularizer, the Affine Total-Variation term, to capture the geometry of piecewise affine functions. The approach can be characterized by two convex decompositions of a given image into piecewise affine structure and texture and noise, respectively. A convergent multiplier-based method is presented for computing a global optimum by computationally cheap iterative steps. Experiments with images and vector fields validate our approach and illustrate the difference to classical TV denoising and decomposition.