Advertisement

Constructing Stochastic Pyramids by MIDES — Maximal Independent Directed Edge Set

  • Yll Haxhimusa
  • Roland Glantz
  • Walter G. Kropatsch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2726)

Abstract

We present a new method (MIDES) to determine contraction kernels for the construction of graph pyramids. Experimentally the new method has a reduction factor higher than 2.0. Thus, the new method yields a higher reduction factor than the stochastic decimation algorithm (MIS) and maximal independent edge set (MIES), in all tests. This means the number of vertices in the subgraph induced by any set of contractible edges is reduced to half or less by a single parallel contraction. The lower bound of the reduction factor becomes crucial with large images.

Keywords

irregular graph pyramids maximal independent set maximal independent directed edge set topology preserving contraction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Bister, J. Cornelis, and A. Rosenfeld. A critical view of pyramid segmentation algorithms. Pattern Recognition Letters, Vol. 11(No. 9):pp. 605–617, September 1990.zbMATHCrossRefGoogle Scholar
  2. 2.
    M. Borowy and J. Jolion. A pyramidal framework for fast feature detection. In Proc. of 4th Int. Workshop on Parellel Image Analysis, pages 193–202, 1995.Google Scholar
  3. 3.
    M. Burge and W. G. Kropatsch. Run Graphs and MLPP Graphs in Line Image Encoding. In W. G. Kropatsch and J.-M. Jolion, editors, 2nd IAPR-TC-15 Workshop on Graph-based Representation, pages 11–19. OCG-Schriftenreihe, Österreichische Computer Gesellschaft, 1999. Band 126.Google Scholar
  4. 4.
    K. Cho and P. Meer. Image Segmentation from Consensus Information. CVGIP: Image Understanding, 68(1):72–89, 1997.Google Scholar
  5. 5.
    N. Christofides. Graph Theory-An Algorithmic Approach. Academic Press, New York, London, San Francisco, 1975.zbMATHGoogle Scholar
  6. 6.
    R. Glantz, R. Englert, and W. G. Kropatsch. Representation of Image Structure by a Pair of Dual Graphs. In W. G. Kropatsch and J.-M. Jolion, editors, 2nd IAPR-TC-15 Workshop on Graph-based Representation, pages 155–163. OCG-Schriftenreihe, Österreichische Computer Gesellschaft, 1999. Band 126.Google Scholar
  7. 7.
    Y. Haxhimusa, R. Glantz, M. Saib, Langs, and W. G. Kropatsch. Logarithmic Tapering Graph Pyramid. In L. van Gool, editor, Proceedings of 24th DAGM Symposium, pages 117–124, Swiss, 2002. Springer Verlag LNCS 2449.Google Scholar
  8. 8.
    Y. Haxhimusa and W. G. Kropatsch. Experimental Results of MIS, MIES, MIDES and D3P. Technical Report No.78, PRIP, Vienna University of Technology. http://www.prip.tuwien.ac.at/ftp/pub/publications/trs, 2003.Google Scholar
  9. 9.
    J.-M. Jolion. Stochastic pyramid revisited. Pattern Recognition Letters, 24(8):pp. 1035–1042, 2003.zbMATHCrossRefGoogle Scholar
  10. 10.
    J.-M. Jolion and A. Montanvert. The adaptive pyramid, a framework for 2D image analysis. Computer Vision, Graphics, and Image Processing: Image Understanding, 55(3):pp.339–348, May 1992.zbMATHGoogle Scholar
  11. 11.
    J.-M. Jolion and A. Rosenfeld. A Pyramid Framework for Early Vision. Kluwer Academic Publishers, 1994.Google Scholar
  12. 12.
    P. Kammerer and R. Glantz. Using Graphs for Segmenting Crosshatched Brush Strokes. In J.-M. Jolion, W. G. Kropatsch, and M. Vento, editors, 3nd IAPR-TC-15 Workshop on Graph-based Representation, pages 74–83. CUEN, 2001.Google Scholar
  13. 13.
    W. G. Kropatsch. Building Irregular Pyramids by Dual Graph Contraction. IEEProc. Vision, Image and Signal Processing, Vol. 142(No. 6):pp. 366–374, December 1995.CrossRefGoogle Scholar
  14. 14.
    W. G. Kropatsch and M. Burge. Minimizing the Topological Structure of Line Images. In A. Amin, D. Dori, P. Pudil, and H. Freeman, editors, Advances in Pattern Recognition, Joint IAPR International Workshops SSPR’98 and SPR’98, volume Vol. 1451 of Lecture Notes in Computer Science, pages 149–158, Sydney, Australia, August 1998. Springer, Berlin Heidelberg, New York.CrossRefGoogle Scholar
  15. 15.
    W. G. Kropatsch and H. Macho. Finding the structure of connected components using dual irregular pyramids. In Cinquième Colloque DGCI, pages 147–158. LLAIC1, Université d’Auvergne, ISBN 2-87663-040-0, September 1995.Google Scholar
  16. 16.
    C. Mathieu, I. E. Magnin, and C. Baldy-Porcher. Optimal stochastic pyramid: segmentation of MRI data. Proc. Med. Imaging VI: Image Processing, SPIE Vol.1652:pp.14–22, Feb. 1992.Google Scholar
  17. 17.
    P. Meer. Stochastic image pyramids. Computer Vision, Graphics, and Image Processing, Vol. 45(No. 3):pp.269–294, March 1989.CrossRefGoogle Scholar
  18. 18.
    P. Meer, D. Mintz, A. Montanvert, and A. Rosenfeld. Consensus vision. In AAAI-90 Workshop on Qualitative Vision, Boston, Massachusetts, USA, July 29 1990.Google Scholar
  19. 19.
    A. Montanvert, P. Meer, and A. Rosenfeld. Hierarchical image analysis using irregular tesselations. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(No.4):pp.307–316, April 1991.CrossRefGoogle Scholar
  20. 20.
    A. Rosenfeld, editor. Multiresolution Image Processing and Analysis. Springer, Berlin, 1984.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Yll Haxhimusa
    • 1
  • Roland Glantz
    • 2
  • Walter G. Kropatsch
    • 1
  1. 1.Pattern Recognition and Image Processing Group 183/2 Institute for Computer Aided AutomationVienna University of TechnologyViennaAustria
  2. 2.Dipartimento di InformaticaUniversità di Ca’ Foscari di VeneziaMestre (VE)Italy

Personalised recommendations