Minimum cut/maximum flow (min-cut/max-flow) algorithms solve a variety of problems in computer vision and thus significant effort has been put into developing fast min-cut/max-flow algorithms. As a result, it is difficult to choose an ideal algorithm for a given problem. Furthermore, parallel algorithms have not been thoroughly compared. In this paper, we evaluate the state-of-the-art serial and parallel min-cut/max-flow algorithms on the largest set of computer vision problems yet. We focus on generic algorithms, i.e., for unstructured graphs, but also compare with the specialized GridCut implementation. When applicable, GridCut performs best. Otherwise, the two pseudoflow algorithms, Hochbaum pseudoflow and excesses incremental breadth first search, achieves the overall best performance. The most memory efficient implementation tested is the Boykov-Kolmogorov algorithm. Amongst generic parallel algorithms, we find the bottom-up merging approach by Liu and Sun to be best, but no method is dominant. Of the generic parallel methods, only the parallel preflow push-relabel algorithm is able to efficiently scale with many processors across problem sizes, and no generic parallel method consistently outperforms serial algorithms. Finally, we provide and evaluate strategies for algorithm selection to obtain good expected performance. We make our dataset and implementations publicly available for further research.

We introduce a parallel version of the Quadratic Pseudo-Boolean Optimization (QPBO) algorithm for solving binary optimization tasks, such as image segmentation. The original QPBO implementation by Kolmogorov and Rother relies on the Boykov-Kolmogorov (BK) maxflow/mincut algorithm and performs well for many image analysis tasks. However, the serial nature of their QPBO algorithm results in poor utilization of modern hardware. By redesigning the QPBO algorithm to work with parallel maxflow/mincut algorithms, we significantly reduce solve time of large optimization tasks. We compare our parallel QPBO implementation to other state-of-the-art solvers and benchmark them on two large segmentation tasks and a substantial set of small segmentation tasks. The results show that our parallel QPBO algorithm is over 20 times faster than the serial QPBO algorithm on the large tasks and over three times faster for the majority of the small tasks. Although we focus on image segmentation, our algorithm is generic and can be used for any QPBO problem. Our implementation and experimental results are available at DOI: 10.5281/zenodo.5201620