MAP Estimation of Semi-Metric MRFs via Hierarchical Graph Cuts

TL;DR

This paper introduces a hierarchical graph cut method for MAP estimation in semi-metric MRFs, offering faster solutions with guarantees comparable to LP relaxations, and demonstrating superior performance on synthetic and real data.

Contribution

The authors propose a novel hierarchical move making algorithm for semi-metric MRFs that is faster than existing LP relaxation methods while maintaining theoretical guarantees.

Findings

Outperforms existing algorithms on synthetic data

Outperforms existing algorithms on real data

Provides faster MAP estimation with LP guarantees

Abstract

We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making strategy where each move is computed efficiently by solving an st-MINCUT problem. Unlike previous move making approaches, e.g. the widely used a-expansion algorithm, our method obtains the guarantees of the standard linear programming (LP) relaxation for the important special case of metric labeling. Unlike the existing LP relaxation solvers, e.g. interior-point algorithms or tree-reweighted message passing, our method is significantly faster as it uses only the efficient st-MINCUT algorithm in its design. Using both synthetic and real data experiments, we show that our technique outperforms several commonly used algorithms.