Skip to main content

Multi-label MRF Optimization via a Least Squares s − t Cut

  • Conference paper
Advances in Visual Computing (ISVC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5875))

Included in the following conference series:

Abstract

We approximate the k-label Markov random field optimization by a single binary (s − t) graph cut. Each vertex in the original graph is replaced by only ceil(log 2(k)) new vertices and the new edge weights are obtained via a novel least squares solution approximating the original data and label interaction penalties. The s − t cut produces a binary “Gray” encoding that is unambiguously decoded into any of the original k labels. We analyze the properties of the approximation and present quantitative and qualitative image segmentation results, one of the several computer vision applications of multi label-MRF optimization.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE PAMI 23, 1222–1239 (2001)

    Google Scholar 

  2. Grady, L.: Random walks for image segmentation. IEEE PAMI 28, 1768–1783 (2006)

    Google Scholar 

  3. Boykov, Y., Funka-Lea, G.: Graph cuts and efficient N-D image segmentation. International Journal of Computer Vision 70, 109–131 (2006)

    Article  Google Scholar 

  4. Ishikawa, H.: Exact optimization for markov random fields with convex priors. IEEE PAMI 25, 1333–1336 (2003)

    Google Scholar 

  5. Schlesinger, D., Flach, B.: Transforming an arbitrary min-sum problem into a binary one. Tech. Report TUD-FI06-01, Dresden University (2006)

    Google Scholar 

  6. Veksler, O.: Graph cut based optimization for MRFs with truncated convex priors. In: IEEE CVPR, pp. 1–8 (2007)

    Google Scholar 

  7. Lempitsky, V., Rother, C., Blake, A.: Logcut - efficient graph cut optimization for markov random fields. In: IEEE ICCV, pp. 1–8 (2007)

    Google Scholar 

  8. Komodakis, N., Tziritas, G., Paragios, N.: Performance vs computational efficiency for optimizing single and dynamic MRFs: Setting the state of the art with primal-dual strategies. Comput. Vis. Image Underst. 112, 14–29 (2008)

    Article  Google Scholar 

  9. Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. IEEE PAMI 28, 1568–1583 (2006)

    Google Scholar 

  10. Kohli, P., Shekhovtsov, A., Rother, C., Kolmogorov, V., Torr, P.: On partial optimality in multi-label MRFs. In: International Conference on Machine learning (ICML), pp. 480–487. ACM, New York (2008)

    Chapter  Google Scholar 

  11. Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., Rother, C.: A comparative study of energy minimization methods for markov random fields with smoothness-based priors. IEEE PAMI 30, 1068–1080 (2008)

    Google Scholar 

  12. Ramalingam, S., Kohli, P., Alahari, K., Torr, P.: Exact inference in multi-label CRFs with higher order cliques. In: IEEE Conference on Computer Vision and Pattern Recognition, 2008. CVPR 2008, pp. 1–8 (2008)

    Google Scholar 

  13. Björk, A.: Numerical Methods for Least Squares Problem. SIAM, Philadelphia (1996)

    Google Scholar 

  14. Dice, L.R.: Measures of the amount of ecologic association between species. Ecology 26, 279–302 (1945)

    Article  Google Scholar 

  15. Cocosco, C.A., Kollokian, V., Kwan, R.K.-s., Pike, G.B., Evans, A.C.: Brainweb: Online interface to a 3D MRI simulated brain database. NeuroImage 5, 425 (1997)

    Google Scholar 

  16. Lawson, C., Hanson, R.: Solving Least Squares Problems. Society for Industrial Mathematics (1974)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hamarneh, G. (2009). Multi-label MRF Optimization via a Least Squares s − t Cut. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2009. Lecture Notes in Computer Science, vol 5875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10331-5_98

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-10331-5_98

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10330-8

  • Online ISBN: 978-3-642-10331-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics