Journal of Real-Time Image Processing

, Volume 11, Issue 3, pp 589–609 | Cite as

A competitive study of the pseudoflow algorithm for the minimum st cut problem in vision applications

  • B. FishbainEmail author
  • Dorit S. Hochbaum
  • Stefan Mueller
Original Research Paper


Rapid advances in image acquisition and storage technology underline the need for real-time algorithms that are capable of solving large-scale image processing and computer-vision problems. The minimum st cut problem, which is a classical combinatorial optimization problem, is a prominent building block in many vision and imaging algorithms such as video segmentation, co-segmentation, stereo vision, multi-view reconstruction, and surface fitting to name a few. That is why finding a real-time algorithm which optimally solves this problem is of great importance. In this paper, we introduce to computer vision the Hochbaum’s pseudoflow (HPF) algorithm, which optimally solves the minimum st cut problem. We compare the performance of HPF, in terms of execution times and memory utilization, with three leading published algorithms: (1) Goldberg’s and Tarjan’s Push-Relabel; (2) Boykov’s and Kolmogorov’s augmenting paths; and (3) Goldberg’s partial augment-relabel. While the common practice in computer-vision is to use either BK or PRF algorithms for solving the problem, our results demonstrate that, in general, HPF algorithm is more efficient and utilizes less memory than these three algorithms. This strongly suggests that HPF is a great option for many real-time computer-vision problems that require solving the minimum st cut problem.


Network flow algorithms Maximum-flow Minimum-cut Segmentation Stereo vision Multi-view reconstruction Surface fitting 


The first author was partially funded by the New York Metropolitan and the Technion’s Security Science and Technology research funds, The German-Israeli Foundation for Scientific Research and Development (GIF) Young Scientist Program, the Technion Center of Excellence in Exposure Science and Environmental Health and the CITI-SENSE project of the 7th European Framework Program (FP7), ENV.2012.6.5-1. The second author was supported in part by NSF awards No. CMMI-1200592 and CBET-0736232.


  1. 1.
    Ahuja, R.K., Kodialam, M., Mishra, A.K., Orlin, J.B.: Computational investigations of maximum flow algorithms. Eur. J. Oper. Res. 97(3), 509–542 (1997)CrossRefzbMATHGoogle Scholar
  2. 2.
    Ahuja, R.K., Magnanti T.L., Orlin J.B.: Network flows: theory, algorithms, and applications. Prentice-Hall, Englewood Cliffs (1993)Google Scholar
  3. 3.
    Ali, S., Shah, M.: Human action recognition in videos using kinematic features and multiple instance learning. IEEE Trans Pattern Anal. Mach. Intell. 32(2), 288–303 (2010)CrossRefGoogle Scholar
  4. 4.
    Anderson, R.J., Setubal, J.C: Goldberg’s algorithm for maximum flow in perspective: a computational study. In: Network flows and matching: First DIMACS Implementation Challenge. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 12, pp. 123–133 (1991)Google Scholar
  5. 5.
    Arora, C., Banerjee, S., Kalra, P., Maheshwari, S.: An efficient graph cut algorithm for computer vision problems. In: Kostas, D., Petros, M., Nikos P., (eds.) Computer Vision ECCV 2010. Lecture Notes in Computer Science, vol 6313, pp. 552–565. Springer, Heidelberg (2010)Google Scholar
  6. 6.
    Azar, Y., Madry, A., Moscibroda, T., Panigrahi, D., Srinivasan, A.: Maximum bipartite flow in networks with adaptive channel width. Theor. Comput. Sci. 412(24), 2577–2587 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bai, X., Wang, J., Simons, D., Sapiro, G.: Video snapcut: robust video object cutout using localized classifiers. ACM Trans. Graph. 28(3), 70:1–70:11 (2009)Google Scholar
  8. 8.
    Borradaile, G., Klein, P.: An o(n log n) algorithm for maximum st-flow in a directed planar graph. J. ACM 56(2), 9:1–9:30 (2009)Google Scholar
  9. 9.
    Boykov, Y., Funka-Lea, G.: Graph cuts and efficient n-d image segmentation. Int. J. Comput. Vis. 70(2), 109131 (2006)CrossRefGoogle Scholar
  10. 10.
    Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans. Pattern Anal. Mach. Intell. 26(9), 1124–1137 (2004)CrossRefzbMATHGoogle Scholar
  11. 11.
    Boykov, Y., Lempitsky, V.: From photohulls to photoflux optimization. In: British Machine Vision Conference (BMVC), vol. III, pp. 1149–1158 (2006)Google Scholar
  12. 12.
    Chandran, B.G., Hochbaum, D.S.: A computational study of the pseudoflow and push-relabel algorithms for the maximum flow problem. Oper. Res. 57(2), 358–376 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Cherkassky, B.V., Goldberg A.V.: On implementing the push—relabel method for the maximum flow problem. Algorithmica 19(4), 390–410 (1997)Google Scholar
  14. 14.
    Computer Vision Research Group. Max-flow problem instances in vision. Technical report, University of Western Ontario. (2009). Accessed Oct 2009.
  15. 15.
    Delong, A., Boykov, Y.: A scalable graph-cut algorithm for n-d grids. In: IEEE computer society conference on computer vision and pattern recognition, pp. 1–8 (2008)Google Scholar
  16. 16.
    Derigs, U., Meier, W.: Implementing Goldberg’s max-flow-algorithm a computational investigation. Math. Methods Oper. Res. 33(6), 383–403 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Fishbain, B., Hochbaum, D.S., Yang, Y.T.: Graph-cuts target tracking in videos through joint utilization of color and coarse motion data. UC Berkeley Manuscript (2012)Google Scholar
  18. 18.
    Ford, L.R., Fulkerson, D.R.: Maximal flow through a network. Can. J. Math. 8(3), 339–404 (1956)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Goldberg, A.V.: The partial augment–relabel algorithm for the maximum flow problem. Algorithms-ESA 2008, pp. 466–477 (2008)Google Scholar
  20. 20.
    Goldberg, A.V.: Hi-level variant of the push-relabel (ver. 3.5) (2010). Accessed Jan 2010Google Scholar
  21. 21.
    Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. J. ACM 35(4), 921–940 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Gracias, N., Mahoor, M., Negahdaripour, S., Gleason, A.: Fast image blending using watersheds and graph cuts. Image Vis. Comput. 27(5), 597–607 (2009) [The 17th British Machine Vision Conference (BMVC 2006)]Google Scholar
  23. 23.
    Grundmann, M., Kwatra, V., Mei Han, and Essa, I.: Efficient hierarchical graph-based video segmentation. In: 2010 IEEE conference on computer vision and pattern recognition (CVPR), pp. 2141–2148 (2010)Google Scholar
  24. 24.
    Hochbaum D.S.: An efficient algorithm for image segmentation, markov random fields and related problems. J. ACM 48(4), 686–701 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Hochbaum, D.S.: The pseudoflow algorithm: a new algorithm for the maximum-flow problem. Oper. Res. 56(4), 992–1009 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Hochbaum, D.S.: Efficient and effective image segmentation interactive tool. In: BIOSIGNALS 2009-international conference on bio-inspired systems and signal processing, pp. 459–461 (2009)Google Scholar
  27. 27.
    Hochbaum, D.S.: Polynomial time algorithms for ratio regions and a variant of normalized cut. IEEE Trans. Pattern Recognit. Mach. Intell. 32(5), 889–898 (2009)CrossRefGoogle Scholar
  28. 28.
    Hochbaum, D.S.: HPF Implementation Ver. 3.3. (2010). Accessed Jan 2010Google Scholar
  29. 29.
    Hochbaum, D.S., Orlin J.B.: Simplifications and speedups of the pseudoflow algorithm. Networks (2012, to appear)Google Scholar
  30. 30.
    Hochbaum, D.S., Singh, V.: An efficient algorithm for co-segmentation. In: International conference on computer vision (ICCV) (2009)Google Scholar
  31. 31.
    Ideses, I., Yaroslavsky, L., Fishbain, B.: Real-time 2d to 3d video conversion. J. Real Time Image Process. 2(1), 3–9 (2007)CrossRefGoogle Scholar
  32. 32.
    Italiano, G.F., Nussbaum, Y., Sankowski, P., and Wulff-Nilsen, C.: Improved algorithms for min cut and max flow in undirected planar graphs. In: Proceedings of the 43rd annual ACM symposium on theory of computing, STOC ’11, pp. 313–322. ACM, New York (2011)Google Scholar
  33. 33.
    Kalarot, R., Morris J.: Comparison of fpga and gpu implementations of real-time stereo vision. In: 2010 IEEE computer society conference on computer vision and pattern recognition workshops (CVPRW), pp. 9 –15 (2010)Google Scholar
  34. 34.
    Kolmogorov, V.: An implementation of the maxflow algorithm. (2010). Accessed Jan 2010
  35. 35.
    Lempitsky, V., Boykov, Y.: Global optimization for shape fitting. In: Proceedings of IEEE conference on computer vision and pattern recognition CVPR ’07, pp. 1–8 (2007)Google Scholar
  36. 36.
    Lempitsky, V., Boykov, Y., Ivanov, D.: Oriented visibility for multiview reconstruction. In: Leonardis, A, Bischof, H., Pinz, A. (eds.) Computer Vision ECCV 2006. Lecture Notes in Computer Science, vol. 3953, pp. 226–238. Springer, Heidelberg (2006)Google Scholar
  37. 37.
    Liu, J., Sun, J.: Parallel graph-cuts by adaptive bottom-up merging. In: 2010 IEEE conference on computer vision and pattern recognition (CVPR), pp. 2181–2188 (2010)Google Scholar
  38. 38.
    Mu, Y., Zhang, H., Wang, H., Zuo, W.: Automatic video object segmentation using graph cut. In: IEEE international conference on image processing, 2007 (ICIP 2007), vol. 3, pp. III–377–III–380 (2007)Google Scholar
  39. 39.
    Nakamura Y., Matsuura T., Satoh K., and Ohta Y. (1996) Occlusion detectable stereo—occlusion patterns in camera matrix. In: IEEE computer society conference on computer vision and pattern recognition 0:371Google Scholar
  40. 40.
    Ngo, C.-W., Ma, Y.-F., Zhang, H.-J.: Video summarization and scene detection by graph modeling. IEEE Trans. Circuits Syst. Video Technol. 15(2),. 296–305 (2005)Google Scholar
  41. 41.
    Qranfal, J., Hochbaum, D.S., Tanoh, G.: Experimental analysis of the mrf algorithm for segmentation of noisy medical images. Algorithmic Oper. Res. 6(2) (2012)Google Scholar
  42. 42.
    Scharstein, D., Szeliski, R., Zabih, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. In: Proc. IEEE workshop on stereo and multi-baseline vision (SMBV 2001), pp. 131–140 (2001)Google Scholar
  43. 43.
    Sharon, E., Galun, M., Sharon, D., Basri, R., Brandt, A.: Hierarchy and adaptivity in segmenting visual scenes. Nature 442(7104), 810–813 (2006)CrossRefGoogle Scholar
  44. 44.
    Shekhovtsov, A., Hlavac V.: A distributed mincut/maxflow algorithm combining path augmentation and push-relabel. In: Boykov, Y., Kahl, F., Lempitsky, V., Schmidt, F., (eds.) Energy Minimization Methods in Computer Vision and Pattern Recognition. Lecture Notes in Computer Science, vol. 6819, pp. 1–16. Springer, Heidelberg (2011)Google Scholar
  45. 45.
    Sinha, S.N., Steedly, D., Szeliski, R., Agrawala, M., Pollefeys, M.: Interactive 3d architectural modeling from unordered photo collections. In: SIGGRAPH Asia ’08: ACM SIGGRAPH Asia 2008 papers, pp. 1–10. ACM, New York (2008)Google Scholar
  46. 46.
    Sleator, D.D., Tarjan R.E.: A data structure for dynamic trees. In: Proceedings of the thirteenth annual ACM symposium on Theory of computing (STOC ’81) pp. 114–122. ACM, New York (1981)Google Scholar
  47. 47.
    Snavely, N., Seitz, S.M., Szeliski, R.: Photo tourism: exploring photo collections in 3d. ACM Trans. Graphics 25(3) (2006)Google Scholar
  48. 48.
    Snow, D., Viola, P., Zabih, R.: Exact voxel occupancy with graph cuts. In: Proceedings of IEEE conference on computer vision and pattern recognition, vol. 1, pp. 345–352 (2000)Google Scholar
  49. 49.
    Stanford Computer Graphics Laboratory. “the stanford 3d scanning repository”. Technical report, Stanford, Palo-Alto, CA, USA, (2009). Accessed Oct 2009
  50. 50.
    Starck, J., Hilton, A.: Surface capture for performance-based animation. IEEE Comput. Graphics Appl. 27(3), 21–31 (2007)CrossRefGoogle Scholar
  51. 51.
    Strandmark, P., Kahl, F.: Parallel and distributed graph cuts by dual decomposition. In: 2010 IEEE conference on computer vision and pattern recognition (CVPR), pp. 2085–2092 (2010)Google Scholar
  52. 52.
    Vineet, V., Narayanan, P.J.: Cuda cuts: Fast graph cuts on the gpu. In: IEEE computer society conference on computer vision and pattern recognition workshops, 2008. CVPRW ’08. pp. 1–8 (2008)Google Scholar
  53. 53.
    Vogiatzis, G., Torr, P.H.S., Cipolla, R.: Multi-view stereo via volumetric graph-cuts. In: Computer Vision and Pattern Recognition (CVPR), vol. 2, pp. 391–398 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • B. Fishbain
    • 1
    Email author
  • Dorit S. Hochbaum
    • 2
  • Stefan Mueller
    • 3
  1. 1.Technion-Israel Institute of TechnologyHaifaIsrael
  2. 2.University of CaliforniaBerkeleyUSA
  3. 3.Technische Universitaet BerlinBerlinGermany

Personalised recommendations