A First Derivative Potts Model for Segmentation and Denoising Using ILP

TL;DR

This paper introduces a novel integer linear programming formulation of the first derivative Potts model that simultaneously addresses image segmentation and denoising, solved efficiently with standard MIP solvers.

Contribution

It presents the first ILP formulation for the derivative Potts model with an $ ext{L}_1$ data term, enabling joint segmentation and denoising in a unified framework.

Findings

Outperforms multicut-based methods in experiments

Efficiently solves the joint segmentation and denoising problem

Demonstrates competitive results on benchmark images

Abstract

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.