Submodular relaxation for inference in Markov random fields

TL;DR

This paper introduces a submodular relaxation method for approximate inference in Markov random fields, which is applicable to both pairwise and high-order models and considers global potentials.

Contribution

The paper proposes a novel submodular relaxation approach that differs from dual decomposition, enabling efficient approximate inference in complex MRFs.

Findings

Method effectively handles high-order MRFs.

Approach incorporates global potentials.

Experimental results demonstrate competitive performance.

Abstract

In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.