Skip to main content

Image Smoothing and Segmentation by Graph Regularization

  • Conference paper
Advances in Visual Computing (ISVC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3804))

Included in the following conference series:

Abstract

We propose a discrete regularization framework on weighted graphs of arbitrary topology, which leads to a family of nonlinear filters, such as the bilateral filter or the TV digital filter. This framework, which minimizes a loss function plus a regularization term, is parameterized by a weight function defined as a similarity measure. It is applicable to several problems in image processing, data analysis and classification. We apply this framework to the image smoothing and segmentation problems.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Morel, J.M., Solimini, S.: Variational methods in image segmentation. Birkhauser Boston Inc., Cambridge (1995)

    Google Scholar 

  2. Tsai, Y.H.R., Osher, S.: Total variation and level set methods in image science. Acta Numerica 14, 509–573 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Osher, S., Shen, J.: Digitized PDE method for data restoration. In: Anastassiou, E.G.A. (ed.) Analytical-Computational methods in Applied Mathematics, pp. 751–771. Chapman & Hall/CRC (2000)

    Google Scholar 

  4. Chan, T., Osher, S., Shen, J.: The digital TV filter and nonlinear denoising. IEEE Trans. Image Processing 10, 231–241 (2001)

    Article  MATH  Google Scholar 

  5. Zhou, D., Schölkopf, B.: A regularization framework for learning from graph data. In: ICML Workshop on Statistical Relational Learning and Its Connections to Other Fields, pp. 132–137 (2004)

    Google Scholar 

  6. Zhou, D., Schölkopf, B.: Regularization on discrete spaces. In: Kropatsch, W.G., Sablatnig, R., Hanbury, A. (eds.) DAGM 2005. LNCS, vol. 3663, pp. 361–368. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Belkin, M., Matveeva, I., Niyogi, P.: Regularization and semi-supervised learning on large graphs. In: Shawe-Taylor, J., Singer, Y. (eds.) COLT 2004. LNCS (LNAI), vol. 3120, pp. 624–638. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Mumford, D., Shah, J.: Optimal approximation of piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–685 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  9. Arbeláez, P.A., Cohen, L.D.: Energy partitions and image segmentation. Journal of Mathematical Imaging and Vision 20, 43–57 (2004)

    Article  MathSciNet  Google Scholar 

  10. Barash, D.: A fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation. IEEE Trans. Pattern Analysis and Machine Intelligence 24, 844–847 (2002)

    Article  Google Scholar 

  11. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: ICCV 1998: Proceedings of the Sixth International Conference on Computer Vision, Washington, DC, USA, pp. 839–846. IEEE Computer Society, Los Alamitos (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bougleux, S., Elmoataz, A. (2005). Image Smoothing and Segmentation by Graph Regularization. In: Bebis, G., Boyle, R., Koracin, D., Parvin, B. (eds) Advances in Visual Computing. ISVC 2005. Lecture Notes in Computer Science, vol 3804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11595755_95

Download citation

  • DOI: https://doi.org/10.1007/11595755_95

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30750-1

  • Online ISBN: 978-3-540-32284-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics