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Image Smoothing and Segmentation by Graph Regularization

  • Sébastien Bougleux
  • Abderrahim Elmoataz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3804)

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.

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References

  1. 1.
    Morel, J.M., Solimini, S.: Variational methods in image segmentation. Birkhauser Boston Inc., Cambridge (1995)Google Scholar
  2. 2.
    Tsai, Y.H.R., Osher, S.: Total variation and level set methods in image science. Acta Numerica 14, 509–573 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 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. 4.
    Chan, T., Osher, S., Shen, J.: The digital TV filter and nonlinear denoising. IEEE Trans. Image Processing 10, 231–241 (2001)zbMATHCrossRefGoogle Scholar
  5. 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. 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)CrossRefGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 8.
    Mumford, D., Shah, J.: Optimal approximation of piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–685 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Arbeláez, P.A., Cohen, L.D.: Energy partitions and image segmentation. Journal of Mathematical Imaging and Vision 20, 43–57 (2004)CrossRefMathSciNetGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sébastien Bougleux
    • 1
  • Abderrahim Elmoataz
    • 2
  1. 1.GREYC CNRS UMR 6072, ENSICAENCaenFrance
  2. 2.LUSAC, Site UniversitaireCherbourg-OctevilleFrance

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