This paper studies image segmentation based on the minimum description length (MDL) functional combining spatial regularization with a penality for the number of distinct segments, a.k.a. label cost prior. Continuous MDL-based segmentation functionals were introduced in [39]. We propose a convex relaxation approach for optimizing MDL criterion that leads to a globally optimal solution.
As common in recent continuous convex formulations [30, 31], we use the totalvariation functional to encode spatial regularity of segmentation bondaries. To the best of our knowledge, we are the first to demostrate that the label cost prior can be also addressed within a continuous convex framework. The second-order cone programming algorithm is applied to tackle such nonsmooth convex energy functional. The experiments validate the proposed approach and theoretical results.