Reconstruction of Probability Density Functions from Channel Representations

  • Erik Jonsson
  • Michael Felsberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3540)

Abstract

The channel representation allows the construction of soft histograms, where peaks can be detected with a much higher accuracy than in regular hard-binned histograms. This is critical in e.g. reducing the number of bins of generalized Hough transform methods. When applying the maximum entropy method to the channel representation, a minimum-information reconstruction of the underlying continuous probability distribution is obtained.

The maximum entropy reconstruction is compared to simpler linear methods in some simulated situations. Experimental results show that mode estimation of the maximum entropy reconstruction outperforms the linear methods in terms of quantization error and discrimination threshold. Finding the maximum entropy reconstruction is however computationally more expensive.

Keywords

Probability Density Function Maximum Entropy Minimum Norm Quantization Error Maximum Entropy Method 
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.

References

  1. 1.
    Ballard, D.H.: Generalizing the Hough transform to detect arbitrary patterns. Pattern Recognition 2(13), 111–122 (1981)CrossRefGoogle Scholar
  2. 2.
    Berger, A., Della Pietra, S., Della Pietra, V.: A maximum entropy approach to natural language processing. Computational Linguistics 22(1), 790–799 (1996)Google Scholar
  3. 3.
    Debnath, L., Mikusiński, P.: Introduction to Hilbert Spaces with Applications. Academic Press, London (1999)MATHGoogle Scholar
  4. 4.
    Felsberg, M., Forssén, P.-E., Scharr, H.: Efficient robust smoothing of low-level signal features. Technical Report LiTH-ISY-R-2619, Dept. EE, Linköping University, SE-581 83 Linköping, Sweden (August 2004)Google Scholar
  5. 5.
    Felsberg, M., Granlund, G.: Anisotropic channel filtering. In: Bigun, J., Gustavsson, T. (eds.) SCIA 2003. LNCS, vol. 2749, pp. 755–762. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Forssén, P.-E.: Low and Medium Level Vision using Channel Representations. PhD thesis, Linköping University, Sweden, SE-581 83 Linköping, Sweden, Dissertation No. 858 (March 2004), ISBN 91-7373-876-XGoogle Scholar
  7. 7.
    Forssén, P.-E., Granlund, G.: Sparse feature maps in a scale hierarchy. In: AFPAC, Algebraic Frames for the Perception Action Cycle, Kiel, Germany (September 2000)Google Scholar
  8. 8.
    Granlund, G.H.: An associative perception-action structure using a localized space variant information representation. In: Proceedings of Algebraic Frames for the Perception-Action Cycle (AFPAC), Kiel, Germany (September 2000)Google Scholar
  9. 9.
    Haykin, S.: Neural Networks, A Comprehensive Foundation, 2nd edn. Prentice Hall, Englewood Cliffs (1999)MATHGoogle Scholar
  10. 10.
    Johansson, B.: Low Level Operations and Learning in Computer Vision. PhD thesis, Linköping University, Sweden, SE-581 83 Linköping, Sweden, Dissertation No. 912 (December 2004), ISBN 91-85295-93-0Google Scholar
  11. 11.
    Lowe, D.G.: Object recognition from local scale-invariant features. In: CVPR 2001 (2001)Google Scholar
  12. 12.
    Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, London (1998)MATHGoogle Scholar
  13. 13.
    Snippe, H.P., Koenderink, J.J.: Discrimination thresholds for channel-coded systems. Biological Cybernetics 66, 543–551 (1992)MATHCrossRefGoogle Scholar
  14. 14.
    Sonka, M., Hlavac, V., Boyle, R.: Image Processing, Analysis, and Machine Vision. Brooks / Cole (1999)Google Scholar
  15. 15.
    Unser, M.: Splines: A perfect fit for signal and image processing. IEEE Signal Processing Magazine 16(6), 22–38 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Erik Jonsson
    • 1
  • Michael Felsberg
    • 1
  1. 1.Computer Vision Laboratory, Dept. of Electrical EngineeringLinköping University 

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