  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.
