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

arXiv: https://arxiv.org/abs/1404.0533 · HTML: https://mlsanity.com/paper/1404.0533/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2014.

## Built on by (most cited first, 16 of 16)

- [Fusion Moves for Graph Matching](https://mlsanity.com/paper/2101.12085/) (2021)
- [A Comparative Study of Graph Matching Algorithms in Computer Vision](https://mlsanity.com/paper/2207.00291/) (2022)
- [FastDOG: Fast Discrete Optimization on GPU](https://mlsanity.com/paper/2111.10270/) (2021)
- [PGMax: Factor Graphs for Discrete Probabilistic Graphical Models and Loopy Belief Propagation in JAX](https://mlsanity.com/paper/2202.04110/) (2022)
- [Learning to solve Minimum Cost Multicuts efficiently using Edge-Weighted Graph Convolutional Neural Networks](https://mlsanity.com/paper/2204.01366/) (2022)
- [Structured Prediction Problem Archive](https://mlsanity.com/paper/2202.03574/) (2022)
- [Review of Serial and Parallel Min-Cut/Max-Flow Algorithms for Computer Vision](https://mlsanity.com/paper/2202.00418/) (2022)
- [Quantum Annealing for Computer Vision Minimization Problems](https://mlsanity.com/paper/2312.12848/) (2023)
- [Tikhonov Regularization of Circle-Valued Signals](https://mlsanity.com/paper/2108.02602/) (2021)
- [Efficient semidefinite bounds for multi-label discrete graphical models](https://mlsanity.com/paper/2111.12491/) (2021)
- [Super-Reparametrizations of Weighted CSPs: Properties and Optimization Perspective](https://mlsanity.com/paper/2201.02018/) (2022)
- [A Nonlocal Graph-PDE and Higher-Order Geometric Integration for Image Labeling](https://mlsanity.com/paper/2205.03991/) (2022)
- [Convergence of Some Convex Message Passing Algorithms to a Fixed Point](https://mlsanity.com/paper/2403.07004/) (2024)
- [An Optimization Framework to Enforce Multi-View Consistency for Texturing 3D Meshes](https://mlsanity.com/paper/2403.15559/) (2024)
- [In-Context Graphical Inference](https://mlsanity.com/paper/2606.05042/) (2026)
- [Avoiding Exponential Blow-Up in Distributive Lattice Submodular Minimization](https://mlsanity.com/paper/2606.14764/) (2026)

## Abstract (arXiv)

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 la-bel-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 32 state-of-the-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.