Multi-class labeling is one of the core problems in image analysis. We show how this combinatorial problem can be approximately solved using tools from convex optimization. We suggest a novel functional based on a multidimensional total variation formulation, allowing for a broad range of data terms. Optimization is carried out in the operator splitting framework using Douglas-Rachford Splitting. In this connection, we compare two methods to solve the Rudin-Osher-Fatemi type subproblems and demonstrate the performance of our approach on single- and multichannel images.
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