Submodularization for Quadratic Pseudo-Boolean Optimization

TL;DR

This paper introduces a novel local submodular approximation framework for optimizing binary non-submodular energies in computer vision, outperforming existing methods and extending to higher-order problems.

Contribution

It proposes a new local submodular approximation approach for quadratic pseudo-Boolean optimization, with algorithms that outperform standard techniques.

Findings

State-of-the-art results on various applications

Outperforms methods like LBP, QPBO, TRWS

Applicable to higher-order problems

Abstract

Many computer vision problems require optimization of binary non-submodular energies. We propose a general optimization framework based on local submodular approximations (LSA). Unlike standard LP relaxation methods that linearize the whole energy globally, our approach iteratively approximates the energies locally. On the other hand, unlike standard local optimization methods (e.g. gradient descent or projection techniques) we use non-linear submodular approximations and optimize them without leaving the domain of integer solutions. We discuss two specific LSA algorithms based on "trust region" and "auxiliary function" principles, LSA-TR and LSA-AUX. These methods obtain state-of-the-art results on a wide range of applications outperforming many standard techniques such as LBP, QPBO, and TRWS. While our paper is focused on pairwise energies, our ideas extend to higher-order problems. The code is available online (http://vision.csd.uwo.ca/code/).