A Comparative Study of Energy Minimization Methods for Markov Random Fields with Smoothness-Based Priors

TLDR

Energy minimization for pixel‑labeling tasks such as depth or texture computation is a key early‑vision problem expressed as Markov random fields, yet its algorithms are often viewed as intractable and their trade‑offs remain poorly understood. The paper introduces benchmarks to compare solution quality and runtime of common energy‑minimization algorithms. The study evaluates graph cuts, LBP, tree‑reweighted message passing, and ICM on benchmark problems from stereo, image stitching, interactive segmentation, and denoising, and supplies a software interface for easy method switching. Graph cuts and LBP are powerful, forming the basis of most top‑performing stereo methods, and the benchmark results, code, and images are publicly available at the Middlebury MRF website.

Abstract

Among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel-labeling tasks such as depth or texture computation. It has been known for decades that such problems can be elegantly expressed as Markov random fields, yet the resulting energy minimization problems have been widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the top-performing stereo methods. However, the tradeoffs among different energy minimization algorithms are still not well understood. In this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods graph cuts, LBP, and tree-reweighted message passing in addition to the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching, interactive segmentation, and denoising. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods. Benchmarks, code, images, and results are available at http://vision.middlebury.edu/MRF/.