Total-Variation Based Piecewise Affine Regularization

We introduce a novel second-order regularizer, the Affine Total-Variation term, to capture the geometry of piecewise affine functions. The approach is 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.