Efficient MRF Energy Minimization via Adaptive Diminishing Smoothing

TL;DR

This paper introduces an adaptive smoothing algorithm for Markov Random Field energy minimization that guarantees convergence and improves efficiency by dynamically adjusting smoothing based on the duality gap.

Contribution

It proposes a theoretically grounded adaptive smoothing diminishing algorithm for LP relaxation in MRF energy minimization, enhancing existing methods.

Findings

Demonstrates efficiency with a smoothed TRW-S algorithm

Provides convergence guarantees for the adaptive smoothing approach

Avoids ad hoc smoothing parameter tuning

Abstract

We consider the linear programming relaxation of an energy minimization problem for Markov Random Fields. The dual objective of this problem can be treated as a concave and unconstrained, but non-smooth function. The idea of smoothing the objective prior to optimization was recently proposed in a series of papers. Some of them suggested the idea to decrease the amount of smoothing (so called temperature) while getting closer to the optimum. However, no theoretical substantiation was provided. We propose an adaptive smoothing diminishing algorithm based on the duality gap between relaxed primal and dual objectives and demonstrate the efficiency of our approach with a smoothed version of Sequential Tree-Reweighted Message Passing (TRW-S) algorithm. The strategy is applicable to other algorithms as well, avoids adhoc tuning of the smoothing during iterations, and provably guarantees convergence to the optimum.