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.
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References
Socolinsky, D., Wolff, L.: Multispectral image visualization through first-order fusion. IEEE Trans. Image Processing 11(8), 923–931 (2002)
Alsam, A., Drew, M.: Fast colour2grey. In: IS&T/SID Color Imaging Conference, pp. 342–346 (2008)
Finlayson, G., Connah, D., Drew, M.: Lookup-table-based gradient field reconstruction. IEEE Trans Image Processing 20(10), 2827–2836 (2011)
Frieden, B.R., Gatenby, R.A.: Exploratory Data Analysis Using Fisher Information. Springer (2007)
Geusebroek, J.M., Smeulders, A.W.M.: Fragmentation in the vision of scenes. In: Proc. IEEE Int. Conf. Comp. Vision, pp. 130–135 (2003)
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)
Gijsenij, A., Gevers, T.: Color constancy using natural image statistics and scene semantics. IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 687–698 (2011)
Wichmann, F.A., Hill, N.J.: The psychometric function: I. fitting, sampling, and goodness of fit. Perception & Psychophysics 63(8), 1293–1313 (2001)
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)
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)
Rinne, H.: The Weibull Distribution: A Handbook. CRC Press (2008)
Amari, S., Nagaoka, H.: Methods of information geometry. Translations of mathematical monographs, vol. 191. American Mathematical Society (2000)
Murray, M., Rice, J.: Differential geometry and statistics. Monographs on Statistics and Applied Probability, vol. 48. Chapman and Hall (1993)
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)
Lenz, R.: Investigation of receptive fields using representations of dihedral groups. Journal of Visual Communication and Image Representation 6(3), 209–227 (1995)
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)
Lenz, R., Zografos, V., Solli, M.: Dihedral Color Filtering. In: Advanced Color Image Processing and Analysis. Springer (2012)
Sheskin, D.: Handbook of parametric and nonparametric statistical procedures. Chapman & Hall/CRC, Boca Raton (2004)
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)
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Lenz, R., Zografos, V. (2013). Fisher Information and the Combination of RGB Channels. In: Tominaga, S., Schettini, R., Trémeau, A. (eds) Computational Color Imaging. CCIW 2013. Lecture Notes in Computer Science, vol 7786. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36700-7_20
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DOI: https://doi.org/10.1007/978-3-642-36700-7_20
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