An ILP Solver for Multi-label MRFs with Connectivity Constraints

TL;DR

This paper introduces an exact ILP solver for multi-label MRFs with connectivity constraints, enabling globally optimal solutions and serving as a valuable tool for segmentation quality assessment and ground-truth generation.

Contribution

It develops a branch-and-cut ILP method that guarantees optimal solutions for multi-label MRFs with connectivity priors, surpassing previous LP relaxation approaches.

Findings

Provides globally optimal solutions for multi-label MRFs with connectivity constraints.

Demonstrates effectiveness on image datasets like BSDS500 and PASCAL.

Enables use as a post-processing tool for segmentation and ground-truth generation.

Abstract

Integer Linear Programming (ILP) formulations of Markov random fields (MRFs) models with global connectivity priors were investigated previously in computer vision, e.g., \cite{globalinter,globalconn}. In these works, only Linear Programing (LP) relaxations \cite{globalinter,globalconn} or simplified versions \cite{graphcutbase} of the problem were solved. This paper investigates the ILP of multi-label MRF with exact connectivity priors via a branch-and-cut method, which provably finds globally optimal solutions. The method enforces connectivity priors iteratively by a cutting plane method, and provides feasible solutions with a guarantee on sub-optimality even if we terminate it earlier. The proposed ILP can be applied as a post-processing method on top of any existing multi-label segmentation approach. As it provides globally optimal solution, it can be used off-line to generate ground-truth labeling, which serves as quality check for any fast on-line algorithm. Furthermore, it can be used to generate ground-truth proposals for weakly supervised segmentation. We demonstrate the power and usefulness of our model by several experiments on the BSDS500 and PASCAL image dataset, as well as on medical images with trained probability maps.