Fisher Information and the Combination of RGB Channels

  • Reiner Lenz
  • Vasileios Zografos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7786)

Abstract

We introduce a method to combine the color channels of an image to a scalar valued image. Linear combinations of the RGB channels are constructed using the Fisher-Trace-Information (FTI), defined as the trace of the Fisher information matrix of the Weibull distribution, as a cost function. The FTI characterizes the local geometry of the Weibull manifold independent of the parametrization of the distribution. We show that minimizing the FTI leads to contrast enhanced images, suitable for segmentation processes. The Riemann structure of the manifold of Weibull distributions is used to design optimization methods for finding optimal weight RGB vectors. Using a threshold procedure we find good solutions even for images with limited content variation. Experiments show how the method adapts to images with widely varying visual content. Using these image dependent de-colorizations one can obtain substantially improved segmentation results compared to a mapping with pre-defined coefficients.

Keywords

Fisher information Weibull distribution information geometry RGB2Gray mapping 

References

  1. 1.
    Socolinsky, D., Wolff, L.: Multispectral image visualization through first-order fusion. IEEE Trans. Image Processing 11(8), 923–931 (2002)CrossRefGoogle Scholar
  2. 2.
    Alsam, A., Drew, M.: Fast colour2grey. In: IS&T/SID Color Imaging Conference, pp. 342–346 (2008)Google Scholar
  3. 3.
    Finlayson, G., Connah, D., Drew, M.: Lookup-table-based gradient field reconstruction. IEEE Trans Image Processing 20(10), 2827–2836 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Frieden, B.R., Gatenby, R.A.: Exploratory Data Analysis Using Fisher Information. Springer (2007)Google Scholar
  5. 5.
    Geusebroek, J.M., Smeulders, A.W.M.: Fragmentation in the vision of scenes. In: Proc. IEEE Int. Conf. Comp. Vision, pp. 130–135 (2003)Google Scholar
  6. 6.
    Geusebroek, J.-M.: The Stochastic Structure of Images. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 327–338. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Gijsenij, A., Gevers, T.: Color constancy using natural image statistics and scene semantics. IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 687–698 (2011)CrossRefGoogle Scholar
  8. 8.
    Wichmann, F.A., Hill, N.J.: The psychometric function: I. fitting, sampling, and goodness of fit. Perception & Psychophysics 63(8), 1293–1313 (2001)CrossRefGoogle Scholar
  9. 9.
    Oller, J.M.: Information metric for extreme value and logistic probability distributions. Sankhya: The Indian J. of Stat., Series A (1961-2002) 49(1), 17–23 (1987)MATHMathSciNetGoogle Scholar
  10. 10.
    Zografos, V., Lenz, R.: Spatio-chromatic Image Content Descriptors and Their Analysis Using Extreme Value Theory. In: Heyden, A., Kahl, F. (eds.) SCIA 2011. LNCS, vol. 6688, pp. 579–591. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Rinne, H.: The Weibull Distribution: A Handbook. CRC Press (2008)Google Scholar
  12. 12.
    Amari, S., Nagaoka, H.: Methods of information geometry. Translations of mathematical monographs, vol. 191. American Mathematical Society (2000)Google Scholar
  13. 13.
    Murray, M., Rice, J.: Differential geometry and statistics. Monographs on Statistics and Applied Probability, vol. 48. Chapman and Hall (1993)Google Scholar
  14. 14.
    Cao, L., Sun, H., Wang, X.: The geometric structures of the Weibull distribution manifold and the generalized exponential distribution manifold. Tamkang Journal of Mathematics 39(1), 45–52 (2008)MATHMathSciNetGoogle Scholar
  15. 15.
    Lenz, R.: Investigation of receptive fields using representations of dihedral groups. Journal of Visual Communication and Image Representation 6(3), 209–227 (1995)CrossRefGoogle Scholar
  16. 16.
    Lenz, R., Bui, T.H., Takase, K.: A group theoretical toolbox for color image operators. In: Proc. ICIP 2005, pp. III–557–560. IEEE (2005)Google Scholar
  17. 17.
    Lenz, R., Zografos, V., Solli, M.: Dihedral Color Filtering. In: Advanced Color Image Processing and Analysis. Springer (2012)Google Scholar
  18. 18.
    Sheskin, D.: Handbook of parametric and nonparametric statistical procedures. Chapman & Hall/CRC, Boca Raton (2004)MATHGoogle Scholar
  19. 19.
    Mester, R., Conrad, C., Guevara, A.: Multichannel Segmentation Using Contour Relaxation: Fast Super-Pixels and Temporal Propagation. In: Heyden, A., Kahl, F. (eds.) SCIA 2011. LNCS, vol. 6688, pp. 250–261. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Reiner Lenz
    • 1
  • Vasileios Zografos
    • 2
  1. 1.Department of Science and Technology and Department of Electrical EngineeringLinköping UniversityNorrköpingSweden
  2. 2.Department of Electrical EngineeringLinköping UniversityLinköpingSweden

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