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An Anisotropic Diffusion Algorithm with Optimized Rotation Invariance

  • Hanno Scharr
  • Joachim Weickert
Part of the Informatik aktuell book series (INFORMAT)

Abstract

For strongly directed anisotropic diffusion filtering it is crucial to use numerical schemes with highly accurate directional behaviour. To this end, we introduce a novel algorithm for coherence-enhancing anisotropic diffusion. It applies recently discovered differentiation filters with optimal rotation invariance [10], and comes down to an explicit scheme on a 5 × 5 stencil. By comparing it with several common algorithms we demonstrate its superior behaviour regarding rotation invariance and avoidance of blurring artifacts (dissipativity). We also show that the new scheme is more than three times more efficient than common explicit schemes on 3 x 3 stencils. It does not require to solve linear systems of equations, and it can be easily implemented in any dimension.

Keywords

Low-level vision diffusion filtering scale-spaces rotation invariance fast algorithms 

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References

  1. 1.
    G.-H. Cottet, M. El Ayyadi, A Volterra type model for image processing, IEEE Trans. Image Proc., Vol. 7, 292–303, 1998.CrossRefGoogle Scholar
  2. 2.
    G.-H. Cottet, L. Germain, Image processing through reaction combined with nonlinear diffusion,Math. Comp., Vol. 61, 659–673, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    W. Förstner, E. Gülch, A fast operator for detection and precise location of distinct points, corners and centres of circular features, Proc. ISPRS Intercommission Conf. on Fast Processing of Photogrammetric Data (Interlaken, June 2-4, 1987), 281-305, 1987.Google Scholar
  4. 4.
    B. ter Haar Romeny, L. Florack, J. Koenderink, M. Viergever (Eds.), Scale-Space Theory in Computer Vision, Lecture Notes in Computer Science, Vol. 1252, Springer, Berlin, 1997.Google Scholar
  5. 5.
    B. Jawerth, P. Lin, E. Sinzinger, Lattice Boltzmann models for anisotropic diffusion of images, J. Math. Imag. Vision, Vol. 11, 231–237, 1999.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    B. Jähne, Performance characteristics of low-level motion estimators in spatiotemporal images, W. Förstner(Ed.), DAGM-Workshop Performance Characteristics and Quality of Computer Vision Algorithms, Braunschweig, September 18, 1997.Google Scholar
  7. 7.
    B. Jähne, H. Scharr, S. Körkel, Principles of Filter Design, B. Jähne, H. Haußecker, P. Geißler (Eds.), Handbook on Computer Vision and Applications, Vol. 2: Signal Processing and Pattern Recognition, Academic Press, San Diego, 125–152, 1999.Google Scholar
  8. 8.
    M. Nielsen, P. Johansen, O.F. Olsen, J. Weickert (Eds.), Scale-Space Theories in Computer Vision, Lecture Notes in Computer Science, Springer, Berlin, Vol. 1682, 1999.Google Scholar
  9. 9.
    T. Preußer, M. Rumpf, An adaptive finite element method for large scale image processing, J. Visual Comm. Image Repr., Vol. 11, 183–195, 2000.CrossRefGoogle Scholar
  10. 10.
    H. Scharr, S. Körkel, B. Jähne, Numerische Isotropieoptimierung von FIR-Filtern mittels Querglättung, E. Paulus, F.M. Wahl (Eds.), Mustererkennung 1997, 367-374, Braunschweig, Springer, 1997.Google Scholar
  11. 11.
    H. Scharr, Optimal Operators in Digital Image Processing, PhD thesis, Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany, 2000.Google Scholar
  12. 12.
    J. Weickert, Anisotropic Diffusion in Image Processing, Teubner, Stuttgart, 1998.Google Scholar
  13. 13.
    J. Weickert, Nonlinear diffusion filtering, B. Jähne, H. Haußecker, P. Geißler (Eds.),Handbook on Computer Vision and Applications,Vol. 2: Signal Processing and Pattern Recognition, Academic Press, San Diego, 423–450, 1999.Google Scholar
  14. 14.
    J. Weickert, Coherence-enhancing diffusion filtering, Int. J. Comput. Vision, Vol. 31, 111–127, 1999.CrossRefGoogle Scholar
  15. 15.
    J. Weickert, H. Scharr, A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance, Report 4/2000, Computer Science Series, Dept. of Mathematics and Computer Science, University of Mannheim, Germany, 2000. To appear in J. Visual Comm. Image Repr.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hanno Scharr
    • 1
  • Joachim Weickert
    • 2
  1. 1.Interdisciplinary Center for Scientific ComputingRuprecht Karls UniversityHeidelbergGermany
  2. 2.Computer Vision, Graphics, and Pattern Recognition Group, Dept. of Mathematics and Computer ScienceUniversity of MannheimMannheimGermany

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