Minimum cut/maximum flow algorithms on graphs have emerged as an increasingly useful tool for exactor approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push -relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.

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An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision

After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for energy minimization in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-style "push-relabel" methods and algorithms based on Ford-Fulkerson style augmenting paths. We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and interactive segmentation. In many cases our new algorithm works several times faster than any of the other methods making near real-time performance possible.

/pdf/an-experimental-comparison-of-min-cut-max-flow-algorithms-22jytmna6l.pdf

An Experimental Comparison of Min-cut/Max-flow Algorithms for Energy Minimization in Vision

https://files.is.tue.mpg.de/chwang/papers/CVIU2013_MRFSurvey.pdf

Markov Random Field modeling, inference & learning in computer vision & image understanding: A survey

Combinatorial min-cut algorithms on graphs have emerged as an increaseingly useful tool for problems in vision. Typically, the use of graph-cuts is motivated by one of the following two reasons. Firstly, graph-cuts allow geometric interpretation; under certain conditions a cut on a graph can be seen as a hypersurface in N-D space embedding the corresponding graph. Thus, many applications in vision and graphics use min-cut algorithms as a tool for computing optimal hypersurfaces. Secondly, graph-cuts also work as a powerful energy minimization tool for a fairly wide class of binary and nonbinary energies that frequently occur in early vision. In some cases graph cuts produce globally optimal solutions. More generally, there are iterative techniques based on graph-cuts that produce provably good approximations which (were empirically shown to) correspond to high-quality solutions in practice. Thus, another large group of applications use graph-cuts as as an optimization technique for low-level vision problems based on global energy formulations.

/pdf/graph-cuts-in-vision-and-graphics-theories-and-applications-3zantcwhah.pdf

Graph Cuts in Vision and Graphics: Theories and Applications

Optimization with graph cuts became very popular in recent years. Progress in problems such as stereo correspondence, image segmentation, etc., can be attributed, in part, to the development of efficient graph cut based optimization. Recent evaluation of optimization techniques shows that the popular expansion and swap graph cut algorithms perform extremely well for energies where the underlying MRF has the Potts prior, which corresponds to the assumption that the true labeling is piecewise constant. For more general priors, however, such as corresponding to piece-wise smoothness assumption, both swap and expansion algorithms do not perform as well. We develop several optimization algorithms for truncated convex priors, which imply piecewise smoothness assumption. Both expansion and swap algorithms are based on moves that give each pixel a choice of only two labels. Our insight is that to obtain a good approximation under piecewise smoothness assumption, a pixel should have a choice among more than two labels. We develop new "range" moves which act on a larger set of labels than the expansion and swap algorithms. We evaluate our method on problems of image restoration, in-painting, and stereo correspondence. Our results show that we are able to get more accurate answers, both in terms of the energy, which is the direct goal, and in terms of accuracy, which is an indirect, but more important goal.

/pdf/graph-cut-based-optimization-for-mrfs-with-truncated-convex-3bsiu27yqj.pdf

Graph Cut Based Optimization for MRFs with Truncated Convex Priors

We propose an efficient, non-iterative method for estimating optical flow. We develop a probabilistic framework that is appropriate for describing the inherent uncertainty in the brightness constraint due to errors in image derivative computation. We separate the flow into two 1D representations and pose the problem of flow estimation as one of solving for the most probable configuration of 1D labels in an Markov random fields (MRF) with linear clique potentials. The global optimum for this problem can be efficiently solved for using the maximum flow computation in a graph. We develop this formulation and describe how the use of the probabilistic framework, the parametrisation and MRF formulation together enables one to capture the desirable properties for flow estimation, especially preserving motion discontinuities. We demonstrate the performance of our algorithm and compare our results with that of other algorithms described by Barron et. al. (1994).

S. Roy

Papers

MRF solutions for probabilistic optical flow formulations