In this paper we explore the use of ranking as a mean of guiding unsupervised image segmentation. Starting by the well known Pagerank algorithm we introduce an extension based on quantum walks. Pagerank (rank) can be used to prioritize the merging of segments embedded in uniform regions (parts of the image with roughly similar appearance statistics). Quantum Pagerank, on the other hand, gives high priority to boundary segments. This latter effect is due to the higher order interactions captured by quantum fluctuations. However we found that qrank does not always outperform its classical version. We analyze the Pascal VOC database and give Intersection over Union (IoU) performances.


random walks quantum walks ranking segment grouping 


  1. 1.
    Grady, L.: Random walks for image segmentation. TPAMI 28(11), 1768–1783 (2006)CrossRefGoogle Scholar
  2. 2.
    Burges, C.J.C., Platt, J.C.: Semi-supervised learning with conditional harmonic mixing. In: Chapelle, O., Schölkopf, B., Zien, A. (eds.) Semi-Supervised Learning. MIT Press, Cambridge (2006)Google Scholar
  3. 3.
    Zhou, D., Huang, J., Schšlkopf, B.: Learning from labeled and unlabeled data on a directed graph. In: ICML, pp. 1041–1048 (2005)Google Scholar
  4. 4.
    Achanta, R., Shaji, A., Smith, K., Lucchi, A., Fua, P., Süsstrunk, S.: Slic superpixels compared to state-of-the-art superpixel methods. TPAMI 34(11), 2274–2282 (2012)CrossRefGoogle Scholar
  5. 5.
    Nock, R., Nielsen, F.: Statistical region merging. TPAMI 26(11), 1452–1458 (2004)CrossRefGoogle Scholar
  6. 6.
    Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: Bringing order to the web (1999)Google Scholar
  7. 7.
    Johns, J., Mahadevan, S.: Constructing basis functions from directed graphs for value function approximation. In: ICML, pp. 385–392 (2007)Google Scholar
  8. 8.
    Langville, A.N., Meyer, C.D.: Deeper inside pagerank. Internet Mathematics 1, 335–400 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48, 1687–1690 (1993)CrossRefGoogle Scholar
  10. 10.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: ACM Symposium on Theory of Computing, pp. 212–219 (1996)Google Scholar
  11. 11.
    Szegedy, M.: Quantum speed-up of markov chain based algorithms. In: FOCS, pp. 32–41. IEEE Computer Society (2004)Google Scholar
  12. 12.
    Paparo, G.D., Martin-Delgado, M.A.: Google in a quantum network. CoRR abs/1112.2079 (2011)Google Scholar
  13. 13.
    Paparo, G.D., M’́uller, M., Comellas, F., Martin-Delgado, M.A.: Quantum google in a complex network. Scientific Reports 3, 2773 (2013)CrossRefGoogle Scholar
  14. 14.
    Carreira, J., Sminchisescu, C.: Cpmc: Automatic object segmentation using constrained parametric min-cuts. TPAMI 34(7), 1312–1328 (2012)CrossRefGoogle Scholar
  15. 15.
    Maire, M., Arbelaez, P., Fowlkes, C.C., Malik, J.: Using contours to detect and localize junctions in natural images. In: CVPR (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Francisco Escolano
    • 1
    • 2
    • 3
  • Boyan Bonev
    • 1
    • 2
    • 3
  • Edwin R. Hancock
    • 1
    • 2
    • 3
  1. 1.Department of Computer Science and AIUniversity of AlicanteSpain
  2. 2.Department of StatisticsUCLAUSA
  3. 3.Department of Computer ScienceUniversity of YorkUK

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