A First Derivative Potts Model for Segmentation and Denoising Using MILP.

Unsupervised image segmentation and denoising are two fundamental tasks in image processing. Usually, graph based models such as multicut are used for segmentation and variational models are employed for denoising. Our approach addresses both problems at the same time. We propose a novel ILP formulation of the first derivative Potts model with the (ell _1) data term, where binary variables are introduced to deal with the (ell _0) norm of the regularization term. The ILP is then solved by a standard off-the-shelf MIP solver. Numerical experiments are compared with the multicut problem.