Fast Segmentation Methods Based on Partial Differential Equations and the Watershed Transformation

  • Joachim Weickert
Conference paper
Part of the Informatik aktuell book series (INFORMAT)


Segmentation algorithms are presented which combine regularization by nonlinear partial differential equations (PDEs) with a watershed transformation with region merging. We develop efficient algorithms for two well-founded PDE methods. They use an additive operator splitting (AOS) leading to recursive and separable filters. Further speed-up can be obtained by embedding AOS schemes into a pyramid framework. Examples demonstrate that the preprocessing by these PDE techniques eases and stabilizes the segmentation. The typical CPU time for segmenting a 2562 image on a workstation is less than 2 seconds.


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  1. 1.
    S. Beucher, Segmentation tools in mathematical morphology, C.H. Chen, L.F. Pau, P.S.P. Wang (Eds.), Handbook of pattern recognition and computer vision, World Scientific, Singapore, 443–456, 1992.Google Scholar
  2. 2.
    P.J. Burt, E.H. Adelson, The Laplacian pyramid as a compact image code, IEEE Trans. Comm., Vol. 31, 532–540, 1983.CrossRefGoogle Scholar
  3. 3.
    F. Catte, P.-L. Lions, J.-M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., Vol. 29, 182–193, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    J. Fairfield, Toboggan contrast enhancement for contrast segmentation, Proc. ICPR 10 (Atlantic City, June 16–21, 1990), Vol. 1, 712–716, 1990.Google Scholar
  5. 5.
    L.D. Griffin, A.C.F. Colchester, G.P. Robinson, Scale and segmentation of grey- level images using maximum gradient paths, Image Vision Comput., Vol. 10, 389–402, 1992.CrossRefGoogle Scholar
  6. 6.
    N. Nordstrom, Biased anisotropic diffusion - a unified regularization and diffusion approach to edge detection, Image Vision Comput., Vol. 8, 318–327, 1990.CrossRefGoogle Scholar
  7. 7.
    O.F. Olsen, Multiscale watershed segmentation, J. Sporring, M. Nielsen, L. Florack, P. Johansen (Eds.), Gaussian scale-space theory, Kluwer, Dordrecht, 191–200, 1997.Google Scholar
  8. 8.
    P. Perona, J. Malik, Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 12, 629–639, 1990.CrossRefGoogle Scholar
  9. 9.
    C. Schnorr, Unique reconstruction of piecewise smooth images by minimizing strictly convex non-quadratic functionals, J. Math. Imag. Vision, Vol. 4, 189–198, 1994.MathSciNetCrossRefGoogle Scholar
  10. 10.
    J. Weickert, Anisotropic diffusion in image processing, Teubner-Verlag, Stuttgart, 1998.zbMATHGoogle Scholar
  11. 11.
    J. Weickert, B.M. ter Haar Romeny, M.A. Viergever, Efficient and reliable schemes for nonlinear diffusion filtering, IEEE Trans. Image Proc., Vol. 7, 398–410, 1998.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Joachim Weickert
    • 1
  1. 1.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark

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