Advertisement

Nonlocal Multiscale Hierarchical Decomposition on Graphs

  • Moncef Hidane
  • Olivier Lézoray
  • Vinh-Thong Ta
  • Abderrahim Elmoataz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6314)

Abstract

The decomposition of images into their meaningful components is one of the major tasks in computer vision. Tadmor, Nezzar and Vese [1] have proposed a general approach for multiscale hierarchical decomposition of images. On the basis of this work, we propose a multiscale hierarchical decomposition of functions on graphs. The decomposition is based on a discrete variational framework that makes it possible to process arbitrary discrete data sets with the natural introduction of nonlocal interactions. This leads to an approach that can be used for the decomposition of images, meshes, or arbitrary data sets by taking advantage of the graph structure. To have a fully automatic decomposition, the issue of parameter selection is fully addressed. We illustrate our approach with numerous decomposition results on images, meshes, and point clouds and show the benefits.

Keywords

Point Cloud Graph Structure Weighted Graph Image Denoising Exponential Weight 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Tadmor, E., Nezzar, S., Vese, L.: A multiscale image representation using hierarchical (BV, L2) decompositions. Multiscale Modeling and Simulation 2, 554–579 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Meyer, Y.: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. University Lecture Series. American Mathematical Society, Boston (2001)zbMATHGoogle Scholar
  3. 3.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)zbMATHCrossRefGoogle Scholar
  4. 4.
    Buades, A., Coll, B., Morel, J.M.: Nonlocal image and movie denoising. International Journal of Computer Vision 76, 123–139 (2008)CrossRefGoogle Scholar
  5. 5.
    Buades, A., Coll, B., Morel, J.M.: Image denoising methods. A new non-local principle 52, 113–147 (2010)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Elmoataz, A., Lézoray, O., Bougleux, S.: Nonlocal discrete regularization on weighted graphs: A framework for image and manifold processing. IEEE Transactions on Image Processing 17, 1047–1060 (2008)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Modeling and Simulation 7, 1005–1028 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Ohtake, Y., Belyaev, A., Seidel, H.-P.: A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions. In: Proceedings of the Shape Modeling International, p. 153 (2003)Google Scholar
  9. 9.
    Tadmor, E., Nezzar, S., Vese, L.: Multiscale hierarchical decomposition of images with applications to deblurring, denoising and segmentation. Communications in Mathematical Sciences 6, 281–307 (2008)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Chan, T.F., Osher, S., Shen, J.: The digital TV filter and nonlinear denoising. IEEE Transactions on Image Processing 10, 231–241 (2001)zbMATHCrossRefGoogle Scholar
  11. 11.
    Lezoray, O., Elmoataz, A., Bougleux, S.: Graph regularization for color image processing. Computer Vision and Image Understanding 107, 38–55 (2007)CrossRefGoogle Scholar
  12. 12.
    Kervrann, C.: An adaptive window approach for image smoothing and structures preserving. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3023, pp. 132–144. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Moncef Hidane
    • 1
  • Olivier Lézoray
    • 1
  • Vinh-Thong Ta
    • 1
  • Abderrahim Elmoataz
    • 1
  1. 1.ENSICAEN, CNRS, GREYC Image TeamUniversité de Caen Basse-NormandieCaen CedexFrance

Personalised recommendations