Multi-scale gradient magnitude watershed segmentation

  • Ole Fogh Olsen
  • Mads Nielsen
Session 1: Segmentation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1310)


A partitioning of an nD image is defined as the watersheds of some locally computable inhomogeneity measure. Dependent on the scale of the inhomogeneity measure a coarse or fine partitioning is defined. By analysis of the structural changes (catastrophes) in the measure introduced when scale is increased, a multi-scale linking of segments can be defined. This paper describes the multi-scale linking based on recent results of the deep structure of the squared gradient field[1]. An interactive semi-automatic segmentation tool, and results on synthetic and real 3D medical images are presented.


Dissimilarity Measure Gradient Magnitude Catastrophe Theory Texture Segmentation Catchment Basin 
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.


  1. 1.
    O.F.Olsen and M.Nielsen, “Generic events for the gradient squared with application to multi-scale segmentation.” SS97, Utrecth, 1997.Google Scholar
  2. 2.
    J. J. Koenderink, Solid Shape. Cambridge, Mass.: MIT Press, 1990.Google Scholar
  3. 3.
    A. P. Witkin, “Scale space filtering,” in Proc. International Joint Conference on Artificial Intelligence, (Karlsruhe, Germany), pp. 1019–1023, 1983.Google Scholar
  4. 4.
    J. J. Koenderink, “The structure of images,” Biol. Cybern., vol. 50, pp. 363–370, 1984.Google Scholar
  5. 5.
    D. Mumford and J. Shah, “Boundary detection by minimizing functionals,” in Proc. IEEE Conf. on CVPR, (San Francisco), 1985.Google Scholar
  6. 6.
    Y. G. Leclerc, “Constructing simple stable descriptions for image partitioning,” IJCV, vol. 3, pp. 73–102, 1989.Google Scholar
  7. 7.
    U. Grenander, Y. Chow, and D. Keenan, Hands. A Pattern Theoretic Study of Biological Shapes. Springer Verlag, 1991.Google Scholar
  8. 8.
    T. Cootes, J. Taylor, D. Cooper, and J. Graham, “Active shape models-their training and application,” CVIU, vol. 61, pp. 38–59, January 1995.Google Scholar
  9. 9.
    R. C. Gonzales and R. E. Woods, Digital Image Processing. Addison Wesley, 1993.Google Scholar
  10. 10.
    K. L. Vincken, C. N. de Graaf, A. S. E. Koster, M. A. Viergever, F. J. R. Appelman, and G. R. Timmens, “Multiresolution segmentation of 3D images by the hyperstack,” in VBC, pp. 115–122, Los Alamitos, CA: IEEE CS Press, 1990.Google Scholar
  11. 11.
    L. M. Lifshitz and S. M. Pizer, “A multiresolution hierarchical approach to image segmentation based on intensity extrema,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 6, pp. 529–541, 1990.Google Scholar
  12. 12.
    J. M. Gauch, W. R. Oliver, and S. M. Pizer, “Multiresolution shape descriptions and their applications in medical imaging,” in IPMI 10, 1988.Google Scholar
  13. 13.
    D. Eberly and S. M. Pizer, “Ridge flow models for image segmentation,” Tech. Rep. TR93-056, University of North Carolina, Dept. of Computer Science, 1993.Google Scholar
  14. 14.
    J. Damon, “Local morse theory for solutions to the heat equation and gaussian blurring,” Journal of Differential Equations, vol. 115, January 1995.Google Scholar
  15. 15.
    J. N. Damon, “Properties of ridges and cores for two-dimensional images.” Unpub.Google Scholar
  16. 16.
    T. Lindeberg, Scale-Space Theory in Computer Vision. Kluwer Academic Publishers, 1994. ISBN 0-7923-9418-6.Google Scholar
  17. 17.
    J. H. Rieger, “Generic evolutions of edges on families of diffused greyvalue surfaces,” JMIV, vol. 5, pp. 207–217, 1995.Google Scholar
  18. 18.
    L. D. Griffin, A. C. F. Colchester, and G. P. Robinson, “Scale and segmentation of grey-level images using maximum gradient paths,” Image and Vision Computing, vol. 10, pp. 389–402, July/August 1992.Google Scholar
  19. 19.
    R. Gilmore, Catastrophe Theory for Scientists and Engineers. Dover, 1981. ISBN 0-486-67539-4.Google Scholar
  20. 20.
    L. Najman and M. Schmitt, “Watershed of a continuos function,” Signal Processing, vol. 38, pp. 99–112, July 1994.Google Scholar
  21. 21.
    F. Maes, D. Vandermeulen, P. Suetens, and G. Marchal, “Computer-aided interactive object delineation using an intelligent paintbrush technique,” in CVRMed95 (N. Ayache, ed.), pp. 77–83, Springer-Verlag, 1995. Lecture Notes 905.Google Scholar
  22. 22.
    F. Meyer, “Topographic distance and watershed lines,” Signal Processing, vol. 38, pp. 99–112, July 1994.Google Scholar
  23. 23.
    L. D. Griffin, Descriptions of Image Structure. PhD thesis, Uni. of London, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ole Fogh Olsen
    • 1
  • Mads Nielsen
    • 2
  1. 1.DIKUUniversity of CopenhagenCopenhagen EDenmark
  2. 2.3D-Lab, School of DentistryUniversity of CopenhagenDenmark

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