Book Chapter10.1007/978-3-642-33715-4_2
Generic cuts: an efficient algorithm for optimal inference in higher order MRF-MAP
Chetan Arora,Subhashis Banerjee,Prem Kalra,S. N. Maheshwari +3 more
- 07 Oct 2012
- pp 17-30
TL;DR: It is shown experimentally that the implementation of the Generic Cuts algorithm is more than an order of magnitude faster than all algorithms including reduction based whose outputs on submodular potentials are near optimal.
read more
Abstract: We propose a new algorithm called Generic Cuts for computing optimal solutions to 2 label MRF-MAP problems with higher order clique potentials satisfying submodularity. The algorithm runs in time O(2kn3) in the worst case (k is clique order and n is the number of pixels). A special gadget is introduced to model flows in a high order clique and a technique for building a flow graph is specified. Based on the primal dual structure of the optimization problem the notions of capacity of an edge and cut are generalized to define a flow problem. We show that in this flow graph max flow is equal to min cut which also is the optimal solution to the problem when potentials are submodular. This is in contrast to all prevalent techniques of optimizing Boolean energy functions involving higher order potentials including those based on reductions to quadratic potential functions which provide only approximate solutions even for submodular functions. We show experimentally that our implementation of the Generic Cuts algorithm is more than an order of magnitude faster than all algorithms including reduction based whose outputs on submodular potentials are near optimal.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Playing with Duality: An overview of recent primal?dual approaches for solving large-scale optimization problems
TL;DR: In this article, the authors present the principles of primal?dual approaches while providing an overview of the numerical methods that have been proposed in different contexts, including convex analysis, discrete optimization, parallel processing, and nonsmooth optimization with an emphasis on sparsity issues.
405
•Posted Content
Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems
TL;DR: This article aims to present the principles of primal?dual approaches while providing an overview of the numerical methods that have been proposed in different contexts and lead to algorithms that are easily parallelizable.
119
Higher-Order Clique Reduction without Auxiliary Variables
Hiroshi Ishikawa
- 23 Jun 2014
TL;DR: A faster approximation that forego the guarantee of exact equivalence of minimizer in favor of speed and shows that the roof-dual algorithm after the reduction labels significantly more variables and the energy converges more rapidly.
A Primal-Dual Algorithm for Higher-Order Multilabel Markov Random Fields
Alexander Jobe Fix,Chen Wang,Ramin Zabih +2 more
- 23 Jun 2014
TL;DR: This paper proposes a new primal-dual energy minimization method that generalizes the PD3 technique for first-order MRFs, and relies on a variant of max-flow that can exactly optimize certain higher-order binary MRF's [14].
Complexity of Discrete Energy Minimization Problems
Mengtian Li,Alexander Shekhovtsov,Daniel Huber +2 more
- 08 Oct 2016
TL;DR: It is shown that general energy minimization, even in the 2-label pairwise case, and planarEnergy minimization with three or more labels are exp-APX-complete, which rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems.
28
References
•Book
Probabilistic graphical models : principles and techniques
Daniel L. Koller,Nir Friedman +1 more
- 31 Jul 2009
TL;DR: The framework of probabilistic graphical models, presented in this book, provides a general approach for causal reasoning and decision making under uncertainty, allowing interpretable models to be constructed and then manipulated by reasoning algorithms.
Fast approximate energy minimization via graph cuts
TL;DR: This work presents two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves, namely expansion moves and swap moves that allow important cases of discontinuity preserving energies.
On the statistical analysis of dirty pictures
TL;DR: In this paper, the authors proposed an iterative method for scene reconstruction based on a non-degenerate Markov Random Field (MRF) model, where the local characteristics of the original scene can be represented by a nondegenerate MRF and the reconstruction can be estimated according to standard criteria.
4.8K
What energy functions can be minimized via graph cuts
Vladimir Kolmogorov,R. Zabin +1 more
- 01 Jan 2004
TL;DR: This work gives a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables.
Fast approximate energy minimization via graph cuts
Yuri Boykov,Olga Veksler,Ramin Zabih +2 more
- 01 Jan 1999
TL;DR: This paper proposes two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed, and generates a labeling such that there is no expansion move that decreases the energy.