Advertisement

Combinatorial Pyramids and Discrete Geometry for Energy-Minimizing Segmentation

  • Martin Braure de Calignon
  • Luc Brun
  • Jacques-Olivier Lachaud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4292)

Abstract

This paper defines the basis of a new hierarchical segmentation framework based on an energy minimization scheme. This new framework is based on two formal tools. First, a combinatorial pyramid encodes efficiently a hierarchy of partitions. Secondly, discrete geometric estimators measure precisely some important geometric parameters of the regions. These measures combined with photometrical and topological features of the partition allow to design energy terms based on discrete measures. Our segmentation framework exploits these energies to build a pyramid of image partitions with a minimization scheme. Some experiments illustrating our framework are shown and discussed.

Keywords

Image Energy Initial Partition Maximal Segment Hierarchical Segmentation Digital Curve 
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.
    Chan, T.F.: Active contours without edges. IEEE Transactions on image Processing 10(2), 266–277 (2001)MATHCrossRefGoogle Scholar
  2. 2.
    Leclerc, Y.G.: Constructing simple stable descriptions for image partitioning. International Journal of Computer Vision 3(1), 73–102 (1989)CrossRefGoogle Scholar
  3. 3.
    Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Transactions on PAMI 26(19), 1124–1137 (2004)Google Scholar
  4. 4.
    Koepfler, G., Lopez, C., Morel, J.M.: A multiscale algorithm for image segmentation by variational method. SIAM J. Numerical Analysis 31(1), 282–299 (1994)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Morel, J.M., Solimini, S.: Variational methods in image segmentation. In: Progress in Nonlinear Differentiel Equations and Their Applications, vol. 14. Birkhäuser, Boston (1995)Google Scholar
  6. 6.
    Reddings, N.J., Crisp, D.J., Tang, D.H., Newsam, G.N.: An efficient algorithm for mumford-shah segmentation and its application to sar imagery. In: Proc. Conf. Digital Image Computing Techniques and applications (DICTA), pp. 35–41 (1999)Google Scholar
  7. 7.
    Guigues, L., Cocquerez, J., Le Men, H.: Scale-sets image analysis. International Journal of Computer Vision 68(1), 289–317 (2006)CrossRefGoogle Scholar
  8. 8.
    Jolion, J.M.: Data driven decimation of graphs. In: Jolion, J.M., Kropatsch, W., Vento, M. (eds.) Proceedings of 3rd IAPR-TC15 Workshop on Graph based Representation in Pattern Recognition, Ischia-Italy, pp. 105–114 (2001)Google Scholar
  9. 9.
    Kropatsch, W.G., Haxhimusa, Y., Lienhardt, P.: Hierarchies relating topology and geometry. In: Christensen, H., Nagel, H.H. (eds.) Proceedings of Cognitive Vision Systems (Seminar Nº 03441 Dagstuhl) (2003)Google Scholar
  10. 10.
    Brun, L., Kropatsch, W.: Contains and inside relationships within combinatorial pyramids. Pattern Recognition 39(4), 515–526 (2006)MATHCrossRefGoogle Scholar
  11. 11.
    Lienhardt, P.: Topological models for boundary representations: a comparison with n-dimensional generalized maps. Computer-Aided Design 23(1), 59–82 (1991)MATHCrossRefGoogle Scholar
  12. 12.
    Klette, R., Rosenfeld, A.: Digital Geometry - Geometric Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco (2004)MATHGoogle Scholar
  13. 13.
    Debled-Renesson, I., Réveillès, J.P.: A linear algorithm for segmentation of discrete curves. International Journal of Pattern Recognition and Artificial Intelligence 9, 635–662 (1995)CrossRefGoogle Scholar
  14. 14.
    Feschet, F., Tougne, L.: Optimal time computation of the tangent of a discrete curve: Application to the curvature. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 31–40. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  15. 15.
    Lachaud, J.-O., Vialard, A., de Vieilleville, F.: Analysis and comparative evaluation of discrete tangent estimators. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 240–251. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Coeurjolly, D., Klette, R.: A comparative evaluation of length estimators of digital curves. IEEE Trans. on Pattern Anal. and Machine Intell. 26(2), 252–257 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Braure de Calignon
    • 1
  • Luc Brun
    • 2
  • Jacques-Olivier Lachaud
    • 1
  1. 1.LaBRI CNRS UMR 5800Université Bordeaux 1
  2. 2.GreyC CNRS UMR 6072Équipe Image – ENSICAEN

Personalised recommendations