A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problems

Abstract

Seven years ago, Szeliski et al. published an influential study on energy minimization methods for Markov random fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems.While these insights remain generally useful today, the phenominal success of random field models means that the kinds of inference problems we solve have changed significantly. Specifically, the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different cardinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of 24 state-of-art techniques on a corpus of 2,300 energy minimization instances from 20 diverse computer vision applications. To ensure reproducibility, we evaluate all methods in the OpenGM2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types.

Pseudo-bound Optimization for Binary Energies

“…parameter. This practical consideration is important when selecting parametric pseudo-bound families for specific applications, e.g (12), (16), or (19). Note that parametric maxflow can be easily parallelized to further accelerate our algorithm.…”

“…Recently high-order [2,3,12,13,15,26,29,38] and non-submodular pairwise [11,16,21,19] energy minimization have drawn tremendous research interests. Those energy functions arise naturally in many computer vision and image processing applications.…”

“…Examples of high-order functions include but are not limited to constraints on segment volume [12,38], clique labeling consistency [13,18,35] and matching target distributions [2,3,12,29]. Pairwise non-submodular energies occur in deconvolution [11], curvature regularization [8,11,28], inpainting [16] and surface registration [16].…”

“…Existing approximation methods make optimization tractable either by global or local linearization. Well established LP relaxation methods such as QPBO [4,30] and TRWS [19] are examples of global linearization techniques for solving non-submodular energies in vision [16]. By relaxing the integrality constraints, they globally transform the original function into a linear function with extra variables and linear constraints.…”

(Hyper)-graphical models in biomedical image analysis

“…Graph-based representations were introduced in computer vision at mid-eighties [2] through Markov Random Fields as a novel mathematical modeling framework constrained though from the lack of efficient inference methods as well as processing power -and became again popular during the past two decades thanks to the development of efficient optimization algorithms [3,4].…”