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

Abstract

Szeliski et al. published an influential study in 2006 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 phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically, the models today often include higher order interactions, flexible connectivity structures, large labelspaces of different cardinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of 32 state-ofthe-art optimization techniques on a corpus of 2,453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 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.

A class of valid inequalities for multilinear 0–1 optimization problems

“…Constraints (5) for y S , y T , and i ∈ S ∩ T are obtained by combining (22) and (24), and (22) and (27), respectively. Finally, the 2-links (13) and (14) are obtained from inequalities (24), (29) and (26), (27), respectively. So, we have established that P 2links S L = Pro j (x,y S ,y T ) (P).…”

“…The problem consists in taking a blurred image as an input and in reconstructing an original sharp base image based on this input. The interest of the vision instances, beside the practical importance of the underlying problem, is that they have a special structure for which linearization and related pseudo-Boolean optimization methods have proved to perform well (see, e.g., [28], [26], [17], [27]). It is out of the scope of the present paper to work with real-life images: we will rely on a simplified version of the problem and on relatively small scale instances in order to generate structured instances and to evaluate the impact of the 2-link inequalities in this setting.…”

Depth Estimation for Lytro Images by Adaptive Window Matching on EPI

“…Thus, the cost function can be solved with the MRF optimization method. For implementation, we follow the framework introduced by Kappes et al [21] which is a minimization method for Markov Random Fields. They have demonstrated different implementations for the MRF problem and have a good performance comparison among them.…”

Note Special Issue on Discrete Graphical Models in Biomedical Image Analysis

“…With the advances in efficient combinatorial optimization techniques such as graph cuts, linear programming and variants of belief propagation it is now feasible to perform inference in models with complex higher-order dependencies which often occur in biomedical settings. A recent comparative study (Kappes et al (2015)) investigates the performance of various optimization techniques for different models. The availability of open source implementations has added to their popularity.…”