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A competitive study of the pseudoflow algorithm for the minimum s–t cut problem in vision applications

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Abstract

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 s–t 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 s–t 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 s–t cut problem.

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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.

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Authors and Affiliations

  1. Technion-Israel Institute of Technology, 32000, Haifa, Israel

    B. Fishbain

  2. University of California, Berkeley, CA, USA

    Dorit S. Hochbaum

  3. Technische Universitaet Berlin, Berlin, Germany

    Stefan Mueller

Authors
  1. B. Fishbain
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  2. Dorit S. Hochbaum
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  3. Stefan Mueller
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Corresponding author

Correspondence to B. Fishbain.

Appendices

Appendix1: Problem sizes

See Tables 6, 7, 8, 9

Table 7 Problems’ sizes—multi-view problems
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Table 8 Problems’ sizes: surface fitting problems
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Table 9 Segmentation problems’ sizes
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Appendix2: Run-times

See Tables 10, 11, 12, 13, 14, 15, 16, 17

Table 10 Initialization stage run-times: Stereo Vision problems
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Table 11 Initialization stage run-times: Multi-View problems
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Table 12 Initialization stage run-times: Surface Fitting problems
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Table 13 Initialization stage run-times: Segmentation problems
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Table 14 Total run-times of the initialization and  min-cut and max-flow stages: Stereo Vision problems
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Table 15 Total run-times of the initialization and  min-cut and  max-flow stages: Multi-View problems
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Table 16 Total run-times of the initialization and  min-cut and  max-flow stages: Surface Fitting problems
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Table 17 Total run-times of the initialization and  min-cut and max-flow stages: Segmentation problems
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Appendix3: Memory utilization

See Tables 18, 19, 20, 21

Table 18 Memory utilization in (MBytes) for Stereo problems
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Table 19 Memory utilization in (MBytes) for multi-view problems
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Table 20 Memory utilization in (MBytes) for Surface Fitting problems
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Table 21 Memory utilization in (MBytes) for Segmentation problems
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Fishbain, B., Hochbaum, D.S. & Mueller, S. A competitive study of the pseudoflow algorithm for the minimum s–t cut problem in vision applications. J Real-Time Image Proc 11, 589–609 (2016). https://doi.org/10.1007/s11554-013-0344-3

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