An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision

Yuri Boykov, Vladimir Kolmogorov

In IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1124-1137, Sept. 2004.


After ...(references) 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 new algorithm (see IMPLEMENTATION below) 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.

WHOLE PAPER: pdf file (615Kb)
IMPLEMENTATION: Note that all experimental results reported in the paper are based on original implementation of our max-flow algorithm that we developed while at Siemens Corp. Research (Princeton, NJ). We are not allowed to distribute that version. However, we can provide a comparable version that was later independently re-implemented by Vladimir based on published materials. Download a local copy maxflow-v3.01.src.tar.gz (13Kb) or go to Vladimir's site. For a commercial license please contact Marina Santilli m.santilli {at}
EARLIER VERSION: EMMCVPR'01. Note that the PAMI paper above describes an improved version of our max-flow algorithm. The PAMI version also includes significantly more experiments on a larger set of applications in vision.