Considerations Regarding the Minimum Spanning Tree Pyramid Segmentation Method

  • Adrian Ion
  • Walter G. Kropatsch
  • Yll Haxhimusa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4109)


The minimum spanning tree pyramid is a hierarchical image segmentation method. We study it’s properties and the regions it produces. We show the similarity with the watershed transform and present the method in a domain in which this is easy to understand. For this, a short overview of both methods is given. Catchment basins are contracted before their neighbouring local maximas. Smooth regions surrounded by borders with maximal local variation are selected. The maximum respectively minimum variation on the border of a region is larger than the maximum respectively minimum variation inside the region.


Edge Graph Catchment Basin Statistical Pattern Recognition Minimal Span Tree Problem Small Edge 
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.
    Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient graph-based image segmentation. International Journal of Computer Vision 59, 167–181 (2004)CrossRefGoogle Scholar
  2. 2.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 22, 888–905 (2000)CrossRefGoogle Scholar
  3. 3.
    Haxhimusa, Y., Kropatsch, W.G.: Segmentation graph hierarchies. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 343–351. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Keselman, Y., Dickinson, S.J.: Generic model abstraction from examples. IEEE Trans. Pattern Anal. Mach. Intell. 27, 1141–1156 (2005)CrossRefGoogle Scholar
  5. 5.
    Kropatsch, W.G., Haxhimusa, Y., Pizlo, Z., Langs, G.: Vision pyramids that do not grow too high. Pattern Recognition Letters 26, 319–337 (2005)CrossRefGoogle Scholar
  6. 6.
    Haxhimusa, Y., Ion, A., Kropatsch, W.G.: Evaluating graph-based segmentation algorithms. In: Proceedings of the 18th Internation Conference on Pattern Recognition, Hong Kong (2006)Google Scholar
  7. 7.
    Roerdink, J.B.T.M., Meijster, A.: The watershed transform: Definitions, algorithms and parallelization strategies. Fundamenta Informaticae 41, 187–228 (2000)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Brun, L., Kropatsch, W.G.: Irregular Pyramids with Combinatorial Maps. In: Amin, A., Pudil, P., Ferri, F.J., Iñesta, J.M. (eds.) SPR 2000 and SSPR 2000. LNCS, vol. 1876, pp. 256–265. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Neštřil, J., Miklovà, E., Neštřilova, H.: Otakar Boro̊vka on minimal spanning tree problem translation of both the 1926 papers, comments, history. Discrete Mathematics 233, 3–36 (2001)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Haxhimusa, Y.: Structurally Optimal Dual Graph Pyramid and its Application in Image Partitioning. PhD thesis, Vienna University of Technology, Faculty of Informatics, Institute of Computer Aided Automation, Pattern Recognition and Image Processing Group (2006)Google Scholar
  11. 11.
    Meyer, F.: Graph based morphological segmentation. In: Kropatsch, W.G., Jolion, J.-M. (eds.) 2nd IAPR-TC15 Workshop on Graph-based Representations in Pattern Recognition, Vienna, Austria, vol. 126, pp. 51–60. OCG (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Adrian Ion
    • 1
  • Walter G. Kropatsch
    • 1
  • Yll Haxhimusa
    • 1
  1. 1.Pattern Recognition and Image Processing GroupVienna University of TechnologyViennaAustria

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