Skip to main content

Diverse M-Best Solutions by Dynamic Programming

  • Conference paper
  • First Online:
Pattern Recognition (GCPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10496))

Included in the following conference series:

Abstract

Many computer vision pipelines involve dynamic programming primitives such as finding a shortest path or the minimum energy solution in a tree-shaped probabilistic graphical model. In such cases, extracting not merely the best, but the set of M-best solutions is useful to generate a rich collection of candidate proposals that can be used in downstream processing. In this work, we show how M-best solutions of tree-shaped graphical models can be obtained by dynamic programming on a special graph with M layers. The proposed multi-layer concept is optimal for searching M-best solutions, and so flexible that it can also approximate M-best diverse solutions. We illustrate the usefulness with applications to object detection, panorama stitching and centerline extraction.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    See the Supplementary for an application to depth estimation from stereo.

  2. 2.

    http://www.mitocheck.org/.

References

  1. Arteta, C., Lempitsky, V., Noble, J.A., Zisserman, A.: Learning to detect partially overlapping instances. In: Proceedings of the IEEE Conference on Computer Vision And Pattern Recognition (CVPR 2013), Portland, OR, USA, 25–27 June 2013, pp. 3230–3237 (2013)

    Google Scholar 

  2. Batra, D., Yadollahpour, P., Guzman-Rivera, A., Shakhnarovich, G.: Diverse M-best solutions in Markov random fields. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012. LNCS, vol. 7576, pp. 1–16. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33715-4_1

    Chapter  Google Scholar 

  3. Batra, D.: An efficient message-passing algorithm for the M-best map problem. In: Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence (UAI 2012) (2012)

    Google Scholar 

  4. Bellman, R.: On the theory of dynamic programming. Proc. Nat. Acad. Sci. 38(8), 716–719 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, C., Liu, H., Metaxas, D., Zhao, T.: Mode estimation for high dimensional discrete tree graphical models. In: Advances in Neural Information Processing Systems (NIPS 2014), Montréal, Canada, 8–13 December 2014, pp. 1323–1331 (2014)

    Google Scholar 

  6. Chen, C., Kolmogorov, V., Zhu, Y., Metaxas, D.N., Lampert, C.H.: Computing the M most probable modes of a graphical model. In: AISTATS, pp. 161–169 (2013)

    Google Scholar 

  7. Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  8. Eppstein, D.: Finding the k shortest paths. SIAM J. Comput. 28(2), 652–673 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Flerova, N., Rollon, E., Dechter, R.: Bucket and mini-bucket schemes for M Best solutions over graphical models. In: Croitoru, M., Rudolph, S., Wilson, N., Howse, J., Corby, O. (eds.) GKR 2011. LNCS, vol. 7205, pp. 91–118. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29449-5_4

    Chapter  Google Scholar 

  10. Fromer, M., Globerson, A.: An LP view of the M-best MAP problem. In: Advances in Neural Information Processing Systems, pp. 567–575 (2009)

    Google Scholar 

  11. Fujita, Y., Nakamura, Y., Shiller, Z.: Dual Dijkstra search for paths with different topologies. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 2003), vol. 3, Taipei, Taiwan, 14–19 September 2003, pp. 3359–3364 (2003)

    Google Scholar 

  12. Held, M., Schmitz, M., Fischer, B., Walter, T., Neumann, B., Olma, M., Peter, M., Ellenberg, J., Gerlich, D.: Cellcognition: time-resolved phenotype annotation in high-throughput live cell imaging. Nat. Methods 7(9), 747–754 (2010)

    Article  Google Scholar 

  13. Jug, F., Pietzsch, T., Kainmüller, D., Funke, J., Kaiser, M., van Nimwegen, E., Rother, C., Myers, G.: Optimal joint segmentation and tracking of Escherichia coli in the mother machine. In: Proceedings of the First International Workshop on Bayesian and grAphical Models for Biomedical Imaging (BAMBI 2014), Cambridge, MA, USA, 18 September 2014, pp. 25–36 (2014)

    Google Scholar 

  14. Kirillov, A., Savchynskyy, B., Schlesinger, D., Vetrov, D., Rother, C.: Inferring M-best diverse labelings in a single one. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV 2015), Santiago, Chile, 13–16 December 2015, pp. 1814–1822 (2015)

    Google Scholar 

  15. Koller, D., Friedman, N.: Probabilistic Graphical Models: Principles and Techniques. MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  16. Lampert, C.H.: Maximum margin multi-label structured prediction. In: Advances in Neural Information Processing Systems, pp. 289–297 (2011)

    Google Scholar 

  17. Lawler, E.: A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem. Manag. Sci. 18(7), 401–405 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  18. Milan, A., Schindler, K., Roth, S.: Detection-and trajectory-level exclusion in multiple object tracking. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3682–3689 (2013)

    Google Scholar 

  19. Nilsson, D.: An efficient algorithm for finding the m most probable configurationsin probabilistic expert systems. Stat. Comput. 8(2), 159–173 (1998)

    Article  MathSciNet  Google Scholar 

  20. Papandreou, G., Yuille, A.L.: Perturb-and-map random fields: using discrete optimization to learn and sample from energy models. In: 2011 International Conference on Computer Vision, pp. 193–200. IEEE (2011)

    Google Scholar 

  21. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, Burlington (1988)

    MATH  Google Scholar 

  22. Prasad, A., Jegelka, S., Batra, D.: Submodular meets structured: finding diverse subsets in exponentially-large structured item sets. In: Advances in Neural Information Processing Systems (NIPS 2014), Montréal, Canada, 8–13 December 2014, pp. 2645–2653 (2014)

    Google Scholar 

  23. Rollon, E., Flerova, N., Dechter, R.: Inference schemes for M best solutions for soft CSPs. In: Proceedings of the Seventh International Workshop on Preferences and Soft Constraints, vol. 2. Sitges, Spain, 1 October 2011

    Google Scholar 

  24. Schiegg, M., Hanslovsky, P., Haubold, C., Koethe, U., Hufnagel, L., Hamprecht, F.: Graphical model for joint segmentation and tracking of multiple dividing cells. Bioinformatics 31(6), 948–956 (2015)

    Article  Google Scholar 

  25. Schlesinger, M.I., Hlavác, V.: Ten Lectures on Statistical and Structural Pattern Recognition, vol. 24. Springer Science & Business Media, New York (2013)

    MATH  Google Scholar 

  26. Seroussi, B., Golmard, J.L.: An algorithm directly finding the k most probable configurations in Bayesian networks. Int. J. Approx. Reason. 11(3), 205–233 (1994)

    Article  Google Scholar 

  27. Summa, B., Tierny, J., Pascucci, V.: Panorama weaving: fast and flexible seam processing. ACM Trans. Graph. 31(4), 83:1–83:11 (2012)

    Article  Google Scholar 

  28. Yadollahpour, P., Batra, D., Shakhnarovich, G.: Discriminative re-ranking of diverse segmentations. In: The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2013

    Google Scholar 

  29. Yanover, C., Weiss, Y.: Finding the m most probable configurations using loopy belief propagation. In: Advances in Neural Information Processing Systems, vol. 16, p. 289 (2004)

    Google Scholar 

Download references

Acknowledgements

This work was partially supported by the HGS MathComp Graduate School, DFG grant HA 4364/9-1, SFB 1129 for integrative analysis of pathogen replication and spread, and the Swiss National Science Foundation under Grant 200020_162343/1.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fred A. Hamprecht .

Editor information

Editors and Affiliations

1 Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 2778 KB)

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Haubold, C., Uhlmann, V., Unser, M., Hamprecht, F.A. (2017). Diverse M-Best Solutions by Dynamic Programming. In: Roth, V., Vetter, T. (eds) Pattern Recognition. GCPR 2017. Lecture Notes in Computer Science(), vol 10496. Springer, Cham. https://doi.org/10.1007/978-3-319-66709-6_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66709-6_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66708-9

  • Online ISBN: 978-3-319-66709-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics