Hierarchical Tree of Image Derived by Diffusion Filtering

  • Haruhiko Nishiguchi
  • Atsushi Imiya
  • Tomoya Sakai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4040)


This paper aims to introduce a class of non-linear diffusion filterings based on deep structure analysis in scale space. In linear scale space, the trajectory of extrema is called stationary curves. This curves provides deep structure analysis and hierarchical expression of signals. The motion of extrema in linear scale space is controlled by a function of the higher derivatives of the signals. We introduce a non-linear diffusion filterings based on the absolute values of second derivative of signals.


Singular Point Stationary Point Structure Tree Hessian Matrix Deep Structure 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Iijima, T.: Pattern Recognition, Corona-sha, Tokyo (1974) (in Japanese)Google Scholar
  2. 2.
    Zhao, N.-Y., Iijima, T.: Theory on the method of determination of view-point and field of vision during observation and measurement of figure. IEICE Japan, Trans. D. J68-D, 508–514 (1985) (in Japanese)Google Scholar
  3. 3.
    Zhao, N.-Y., Iijima, T.: A theory of feature extraction by the tree of stable view-point. IEICE Japan, Trans. D J68-D, 1125–1132 (1985) (in Japanese)Google Scholar
  4. 4.
    Imiya, A., Sugiura, T., Sakai, T., Kato, Y.: Temporal structure tree in digital linear scale space. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, pp. 356–371. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Kuijper, A.: The Deep Structure of Gaussian Scale Space Images, Ph.D. thesis, Utrecht University (2002)Google Scholar
  6. 6.
    Sakai, T., Imiya, A.: Hierarchical analysis of low-contrast temporal images with linear scale space. In: Sonka, M., Kakadiaris, I.A., Kybic, J. (eds.) CVAMIA/MMBIA 2004. LNCS, vol. 3117, pp. 145–156. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Transaction on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)CrossRefGoogle Scholar
  8. 8.
    Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998)MATHGoogle Scholar
  9. 9.
    Weickert, J.: Applications of nonlinear diffusion in image processing and computer vision. Acta Mathematica Universitatis Comenianae 70(1), 33–50 (2001)MATHMathSciNetGoogle Scholar
  10. 10.
    Bracewell, R.N.: Two-Dimensional Imaging. Prentice-Hall, New Jersey (1995)MATHGoogle Scholar
  11. 11.
    Kimmel, R.: Numerical Geometry of Images. Springer, New York (2004)MATHGoogle Scholar
  12. 12.
    Barash, D., Kimmel, R.: An accurate operator splitting scheme for nonlinear diffusion filtering. In: Kerckhove, M. (ed.) Scale-Space 2001. LNCS, vol. 2106, pp. 281–289. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Schroeder, M.R.: Number Theory in Science and Communication, 3rd edn. Springer, Heidelberg (1997)MATHGoogle Scholar
  14. 14.
    Neelin, P.: McConnell Brain Imaging Centre,

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Haruhiko Nishiguchi
    • 1
  • Atsushi Imiya
    • 2
  • Tomoya Sakai
    • 2
  1. 1.School of Science and TechnologyChiba UniversityJapan
  2. 2.Institute of Media and Information TechnologyChiba UniversityChibaJapan

Personalised recommendations