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On generalized entropies and scale-space

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Book cover Scale-Space Theory in Computer Vision (Scale-Space 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1252))

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Part of this work was performed during a Joint-Study visit at IBM, Almaden Research Center, 650 Harry Road, San Jose, CA 95120-6099, USA.

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References

  1. J. Aczél. On mean values. Bulletin of the American Mathematic Society, 54:392–400, 1948.

    Google Scholar 

  2. J. Aczél and Z. Daróczy. On information measures and their characterizations. Academic Press, 1973.

    Google Scholar 

  3. A. D. Brink. Using spatial information as an aid to maximum entropy image threshold selection. Pattern Recognition Letters, 17(1):29–36, January 1996.

    Google Scholar 

  4. A. D. Brink and N. E. Pendock. Minimum cross-entropy threshold selection. Pattern Recognition, 29(1):179–188, January 1996.

    Google Scholar 

  5. James Damon. Local morse theory for gaussian blurred functions. In Jon Sporring, Mads Nielsen, Luc Florack, and Peter Johansen, editors, Gaussian Scale-Space Theory. Kluwer Academic Publishers, The Netherlands, 1997. (in print).

    Google Scholar 

  6. L. M. J. Florack, B. M. ter Haar Romeny, J. J. Koenderink, and M. A. Viergever. Linear scale-space. Journal of Mathematical Imaging and Vision, 4(4):325–351, 1994.

    Google Scholar 

  7. P. Grassberger and I. Procaccia. Dimensions and entropies of strange attractors from a fluctuating dynamics approach. Physica D, 13:34–54, 1984.

    Google Scholar 

  8. G. H. Hardy, J. E. Littlewood, and G. Pólya. Inequalities. Cambridge University Press, 1934.

    Google Scholar 

  9. R. V. Hartley. Transmission of information. Bell System Technical Journal, 7:535–563, 1928.

    Google Scholar 

  10. Thomas C. Hasley, Mogens H. Jensen, Leo P. Kadanoff, Itamar Procaccia, and Boris I. Shraiman. Fractal measures and their singularities: The characterization of strange sets. Physical Review A, 33:1141–1151, 1986.

    Google Scholar 

  11. H. G. E. Hentschel and Itamar Procaccia. The infinite number of generated dimensions of fractals and strange attractors. Physica D, 8:435–444, 1983.

    Google Scholar 

  12. Martin Jägersand. Saliency maps and attention selection in scale and spatial coordinates: An information theoretic approach. In Fifth International Conference on Computer Vision, pages 195–202. IEEE Computer Society Press, June 1995.

    Google Scholar 

  13. Peter Johansen. On the classification of toppoints in scale space. Journal of Mathematical Imaging and Vision, 4:57–67, 1994.

    Google Scholar 

  14. J. J. Koenderink. The structure of images. Biological Cybernetics, 50:363–370, 1984.

    Google Scholar 

  15. L. M. Lifshitz and S. M. Pizer. A multiresolution hierarchical approach to image segmentation based on intensity extrema. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(6):529–541, 1990.

    Google Scholar 

  16. A. Oomes and P. R. Snoeren. Structural information in scale-space. In Peter Johansen, editor, Proceedings of the Copenhagen Workshop on Gaussian Scale-Space Theory, pages 48–57, Universitetsparken 1, DK-2100 Copenhagen, Denmark, May 10–13 1996. Technical Report DIKU-96/19 ISSN 01078283.

    Google Scholar 

  17. A. H. J. Oomes and E. L. J. Leeuwenberg. A scale-space measure of image complexity. Perception, 23:20–21, 1994. supplement.

    Google Scholar 

  18. Edward Ott. Chaos in dynamical systems. Cambridge University Press, 1994.

    Google Scholar 

  19. Alfréd Rényi. On the foundations of information theory. In Pál Turán, editor, Selected Papers of Alfréd Rényi, volume 2, pages 304–318. Akadémiai Kiadó, Budapest, 1976. (Originally: Rev. Inst. Internat. Stat., 33, 1965, p. 1–14).

    Google Scholar 

  20. Alfréd Rényi. Some fundamental questions of information theory. In Pál Turán, editor, Selected Papers of Alfréd Rényi, volume 3, pages 526–552. Akadémiai Kiadó, Budapest, 1976. (Originally: MTA III. Oszt. Közl., 10, 1960, p. 251–282).

    Google Scholar 

  21. Manfred Schroeder. Fractals, Chaos, Power Laws — Minutes from an infinite paradise. W. H. Freeman and Company, 1991.

    Google Scholar 

  22. Heinz Georg Schuster. Deterministic Chaos. VCH Verlagsgesellschaft mbH, 1989.

    Google Scholar 

  23. C. E. Shannon and W. Weaver. The Mathematical Theory of Communication. The University of Illinois Press, Urbana, Chicago, London, 1949.

    Google Scholar 

  24. Jeffrey S. Simonoff. Smoothing Methods in Statistics. Springer Series in Statistics. Springer-Verlag, 1996.

    Google Scholar 

  25. Jon Sporring. The entropy of scale-space. In Proceedings of 13'th International Conference on Pattern Recognition (ICPR'96), Vienna, Austria, August 1996.

    Google Scholar 

  26. Jacques Levy Vehel and Pascal Mignot. Multifractal segmentation of images. Fractals, 2(3):379–382, June 1994.

    Google Scholar 

  27. J. Weickert. Anisotropic Diffusion in Image Processing. PhD thesis. University of Kaiserslautern, Department of Mathematics, Kaiserslautern, Germany, January 29 1996.

    Google Scholar 

  28. J. Weickert, S. Ishikawa, and A. Imiya. On the history of gaussian scale-space axiomatics. In Jon Sporring, Mads Nielsen, Luc Florack, and Peter Johansen, editors, Gaussian Scale-Space Theory. Kluwer Academic Publishers, The Netherlands, 1997. (in print).

    Google Scholar 

  29. N. Wiener. Cybernetics. Wiley, New York, 1948.

    Google Scholar 

  30. A. P. Witkin. Scale-space filtering. In Proc. 8th Int. Joint Conf. on Artificial Intelligence (IJCAI '83), volume 2, pages 1019–1022, Karlsruhe, Germany, August 1983.

    Google Scholar 

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Author information

Author notes

  1. Joachim Weickert

    Present address: Dept. of Computer Science, University of Copenhagen, 2100, Copenhagen East, Denmark

Authors and Affiliations

  1. Image Group Dept. of Computer Science, University of Copenhagen, Universitetsparken 1, DK-2100, Copenhagen, Denmark

    Jon Sporring

  2. Image Sciences Institute, Utrecht University Hospital, Heidelberglaan 100 E 01.334, NL-3584, CX Utrecht, The Netherlands

    Joachim Weickert

Authors
  1. Jon Sporring
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  2. Joachim Weickert
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Editor information

Bart ter Haar Romeny Luc Florack Jan Koenderink Max Viergever

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© 1997 Springer-Verlag Berlin Heidelberg

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Sporring, J., Weickert, J. (1997). On generalized entropies and scale-space. In: ter Haar Romeny, B., Florack, L., Koenderink, J., Viergever, M. (eds) Scale-Space Theory in Computer Vision. Scale-Space 1997. Lecture Notes in Computer Science, vol 1252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63167-4_39

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  • DOI: https://doi.org/10.1007/3-540-63167-4_39

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  • Print ISBN: 978-3-540-63167-5

  • Online ISBN: 978-3-540-69196-9

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