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Issue No.01 - Jan. (2013 vol.35)
pp: 78-91
Iván Marín-Franch , Sch. of Optometry, Indiana Univ., Bloomington, IN, USA
D. H. Foster , Sch. of Electr. & Electron. Eng., Univ. of Manchester, Manchester, UK
The colors present in an image of a scene provide information about its constituent elements. But the amount of information depends on the imaging conditions and on how information is calculated. This work had two aims. The first was to derive explicitly estimators of the information available and the information retrieved from the color values at each point in images of a scene under different illuminations. The second was to apply these estimators to simulations of images obtained with five sets of sensors used in digital cameras and with the cone photoreceptors of the human eye. Estimates were obtained for 50 hyperspectral images of natural scenes under daylight illuminants with correlated color temperatures 4,000, 6,500, and 25,000 K. Depending on the sensor set, the mean estimated information available across images with the largest illumination difference varied from 15.5 to 18.0 bits and the mean estimated information retrieved after optimal linear processing varied from 13.2 to 15.5 bits (each about 85 percent of the corresponding information available). With the best sensor set, 390 percent more points could be identified per scene than with the worst. Capturing scene information from image colors depends crucially on the choice of camera sensors.
Image color analysis, Entropy, Mutual information, Sensors, Random variables, Lighting, Cameras,color constancy, Color vision, color information, digital color cameras, color processing, information theory, natural scenes, kth-nearest-neighbor statistics
Iván Marín-Franch, D. H. Foster, "Estimating Information from Image Colors: An Application to Digital Cameras and Natural Scenes", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.35, no. 1, pp. 78-91, Jan. 2013, doi:10.1109/TPAMI.2012.78
[1] J. von Kries, "Theoretische Studien über die Umstimmung des Sehorgans," Festschrift der Albrecht-Ludwigs-Universität in Freiburg zum Fünfzigjährigen Regierungs-Jubiläum Seiner Königlichen Hoheit des Grossherzogs Friedrich, C.A. Wagner's Universitäts-Buchdruckerei, Freiburg i. Br. [Translation: D.L. MacAdam, Sources of Color Science, MIT Press, 1970 ], pp. 145-158, 1902.
[2] J. von Kries, "Die Gesichtsempfindungen," Handbuch der Physiologie des Menschen, W. Nagel, Ed. Braunschweig: Vieweg und Sohn, vol. 3, Physiologie der Sinne, [Translation: D.L. MacAdam, Sources of Color Science, MIT Press, 1970], pp. 211-212, 1905.
[3] G. Wyszecki and W.S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, second ed. John Wiley, 1982.
[4] C.E. Shannon, "A Mathematical Theory of Communication," Bell System Technical J., vol. 27, pp. 379-423, 1948.
[5] C.E. Shannon, "A Mathematical Theory of Communication," Bell System Technical J., vol. 27, pp. 623-656, 1948.
[6] T.M. Cover and J.A. Thomas, Elements of Information Theory. John Wiley & Sons, 1991.
[7] P. Comon, "Independent Component Analysis, a New Concept?" Signal Processing, vol. 36, pp. 287-314, 1994.
[8] A. Hyvärinen, "Survey on Independent Component Analysis," Neural Computing Surveys, vol. 2, pp. 94-128, 1999.
[9] A. Hyvärinen and E. Oja, "Independent Component Analysis: Algorithms and Applications," Neural Networks, vol. 13, pp. 411-430, 2000.
[10] R. Steuer, J. Kurths, C.O. Daub, J. Weise, and J. Selbig, "The Mutual Information: Detecting and Evaluating Dependencies between Variables," Bioinformatics, vol. 18, pp. S231-S240, 2002.
[11] D.H. Foster, I. Marín-Franch, K. Amano, and S.M.C. Nascimento, "Approaching Ideal Observer Efficiency in Using Color to Retrieve Information from Natural Scenes," J. Optical Soc. Am. A, vol. 26, no. 11, pp. B14-B24, 2009.
[12] G. Buchsbaum and A. Gottschalk, "Trichromacy, Opponent Colours Coding and Optimum Colour Information Transmission in the Retina," Proc. Royal Soc. London. Series B, Biological Sciences, vol. 220, no. 1218, pp. 89-113, 1983.
[13] D.H. Foster, "Chromatic Function of the Cones," Encyclopedia of the Eye, D.A. Dartt, J.C. Besharse, R. Dana, and P. Bex, eds., Academic Press, pp. 266-274, 2010.
[14] I. Marín-Franch, "Information-Theoretic Analysis of Trichromatic Images of Natural Scenes under Different Phases of Daylight," PhD dissertation, School of Electrical and Electronic Eng., Univ. of Manchester, May 2009.
[15] D.H. Foster, K. Amano, S.M.C. Nascimento, and M.J. Foster, "Frequency of Metamerism in Natural Scenes," J. Optical Soc. Am. A, vol. 23, no. 10, pp. 2359-2372, 2006.
[16] D.B. Osteyee and I.J. Good, Information, Weight of Evidence, The Singularity between Probability Measures and Signal Detection, A. Dold and B. Eckmann, eds., Springer, 1974.
[17] G.A. Darbellay and I. Vajda, "Estimation of the Information by an Adaptive Partitioning of the Observation Space," IEEE Trans. Information Theory, vol. 45, no. 4, pp. 1315-1321, May 1999.
[18] B. Silverman, Density Estimation for Statistics and Data Analysis. Chapman & Hall, 1986.
[19] P. Grassberger, "Entropy Estimates from Insufficient Samplings," arXiv:physics/0307138v2, 2008.
[20] L.F. Kozachenko and N.N. Leonenko, "Sample Estimate of the Entropy of a Random Vector," Problems of Information Transmission, vol. 23, no. 2, pp. 95-101, 1987. [translated from Problemy Peredachi Informatsii, vol. 23, no. 2,pp. 9-16, 1987]
[21] A. Kraskov, H. Stögbauer, and P. Grassberger, "Estimating Mutual Information," Physical Rev. E, vol. 69, pt. 066138, 2004.
[22] J.D. Victor, "Binless Strategies for Estimation of Information from Neural Data," Physical Rev. E, vol. 66, p. 051903, 2002.
[23] H. Stögbauer, A. Kraskov, S.A. Astakhov, and P. Grassberger, "Least-Dependent-Component Analysis Based on Mutual Information," Physical Rev. E, vol. 70, p. 066123, 2004.
[24] M.N. Goria, N.N. Leonenko, V.V. Mergel, and P.L. Novi Inverardi, "A New Class of Random Vector Entropy Estimators and Its Applications in Testing Statistical Hypotheses," J. Nonparametic Statistics, vol. 17, no. 3, pp. 277-297, 2005.
[25] I. Csiszár and P. Narayan, "Channel Capacity for a Given Decoding Metric," IEEE Trans. Information Theory, vol. 41, no. 1, pp. 35-43, Jan. 1995.
[26] N. Merhav, G. Kaplan, A. Lapidoth, and S. Shamai, "On Information Rates for Mismatched Decoders," IEEE Trans. Information Theory, vol. 40, no. 6, pp. 1953-1967, Nov. 1994.
[27] A. Lapidoth, "Nearest Neighbor Decoding for Additive Non-Gaussian Noise Channels," IEEE Trans. Information Theory, vol. 42, no. 5, pp. 1520-1529, Sept. 1996.
[28] D.H. Foster, S.M.C. Nascimento, and K. Amano, "Information Limits on Neural Identification of Colored Surfaces in Natural Scenes," Visual Neuroscience, vol. 21, pp. 331-336, 2004.
[29] D.H. Foster, S.M.C. Nascimento, and K. Amano, "Information Limits on Identification of Natural Surfaces by Apparent Colour," Perception, vol. 34, pp. 1001-1006, 2005.
[30] S.M.C. Nascimento, F.P. Ferreira, and D.H. Foster, "Statistics of Spatial Cone-Excitation Ratios in Natural Scenes," J. Optical Soc. Am. A, vol. 19, no. 8, pp. 1484-1490, 2002.
[31] R.F. Lyon and P.M. Hubel, "Eyeing the Camera: Into the Next Century," Proc. 10th Color Imaging Conf. Color Science and Eng. Systems, Technologies, Applications, pp. 349-355, 2002.
[32] J.M. DiCarlo, E. Montgomery, and S.W. Trovinger, "Emissive Chart for Imager Calibration," Proc. 12th Color Imaging Conf.: Color Science and Eng. Systems, Technologies, Applications, pp. 295-301, 2004.
[33] A. Stockman and L.T. Sharpe, "The Spectral Sensitivities of the Middle- and Long-Wavelength-Sensitive Cones Derived from Measurements in Observers of Known Genotype," Vision Research, vol. 40, pp. 1711-1737, 2000.
[34] S.M.C. Nascimento, D.H. Foster, and K. Amano, "Psychophysical Estimates of the Number of Spectral-Reflectance Basis Functions Needed to Reproduce Natural Scenes," J. Optical Soc. Am. A, vol. 22, no. 6, pp. 1017-1022, 2005.
[35] E.K. Oxtoby and D.H. Foster, "Perceptual Limits on Low-Dimensional Models of Munsell Reflectance Spectra," Perception, vol. 34, pp. 961-966, 2005.
[36] D.B. Judd, D.L. MacAdam, and G. Wyszecki, "Spectral Distribution of Typical Daylight as a Function of Correlated Color Temperature," J. Optical Soc. Am., vol. 54, no. 8, pp. 1031-1040, 1964.
[37] S. Arya, D.M. Mount, N.S. Netanyahu, R. Silverman, and A.Y. Wu, "An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions," J. ACM, vol. 45, no. 6, pp. 891-923, 1998.
[38] J.A. Worthey, "Limitations of Color Constancy," J. Optical Soc. Am. A, vol. 2, no. 7, pp. 1014-1026, 1985.
[39] J.M. Troost, L. Wei, and C.M.M. de Weert, "Binocular Measurements of Chromatic Adaptation," Vision Research, vol. 32, no. 10, pp. 1987-1997, 1992.
[40] E.H. Land and J.J. McCann, "Lightness and Retinex Theory," J. Optical Soc. Am., vol. 61, no. 1, pp. 1-11, 1971.
[41] E.H. Land, "Recent Advances in Retinex Theory," Vision Research, vol. 26, no. 1, pp. 7-21, 1986.
[42] D.H. Foster and S.M.C. Nascimento, "Relational Colour Constancy from Invariant Cone-Excitation Ratios," Proc. Royal Soc. B, vol. 257, pp. 115-121, 1994.
[43] B.V. Funt and G.D. Finlayson, "Color Constant Color Indexing," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 5, pp. 522-529, May 1995.
[44] G.D. Finlayson, M.S. Drew, and B.V. Funt, "Spectral Sharpening: Sensor Transformations for Improved Color Constancy," J. Optical Soc. Am. A, vol. 11, no. 5, pp. 1553-1563, 1994.
[45] G.D. Finlayson, M.S. Drew, and B.V. Funt, "Color Constancy: Generalized Diagonal Transforms Suffice," J. Optical Soc. Am. A, vol. 11, no. 11, pp. 3011-3019, 1994.
[46] B. Funt and H. Jiang, "Non-Von-Kries 3-Parameter Color Prediction," Proc. Human Vision and Electronic Imaging VIII, pp. 182-189. 2003.
[47] D.H. Foster and K. Żychaluk, "Is There a Better Non-Parametric Alternative to Von Kries Scaling?" Proc. Fourth European Conf. Colour in Graphics, Imaging and Vision, pp. 41-44, 2008.
[48] H. Terstiege, "Chromatic Adaptation: A State-of-the-Art Report," J. Color Appearance, vol. 1, no. 4, pp. 19-23, cont. p. 40, 1972.
[49] G. Buchsbaum, "A Spatial Processor Model for Object Color Perception," J. Franklin Inst., vol. 310, no. 1, pp. 1-26, 1980.
[50] M. D'Zmura and G. Iverson, "Color Constancy III General Linear Recovery of Spectral Descriptions for Lights and Surfaces," J. Optical Soc. Am. A, vol. 11, no. 9, pp. 2389-2400, 1994.
[51] G.D. Finlayson, S.D. Hordley, and P.M. Hubel, "Color by Correlation: A Simple, Unifying Framework for Color Constancy," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 11, pp. 1209-1221, Nov. 2001.
[52] D.H. Foster, "Does Colour Constancy Exist?" Trends in Cognitive Sciences, vol. 7, no. 10, pp. 439-443, 2003.
[53] H.G. Sperling and R.S. Harwerth, "Red-Green Cone Interactions in the Increment-Threshold Spectral Sensitivity of Primates," Science, vol. 172, no. 3979, pp. 180-184, 1971.
[54] R.L. De Valois, N.P. Cottaris, S.D. Elfar, L.E. Mahon, and J.A. Wilson, "Some Transformations of Color Information from Lateral Geniculate Nucleus to Striate Cortex," Proc. Nat'l Academy of Sciences USA, vol. 97, no. 9, pp. 4997-5002, 2000.
[55] J.C. Lagarias, J.A. Reeds, M.H. Wright, and P.E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optimization, vol. 9, no. 1, pp. 112-147, 1998.
[56] I. Marín-Franch and D.H. Foster, "Number of Perceptually Distinct Surface Colors in Natural Scenes," J. Vision, vol. 10, no. 9, p. 9, 2010.
[57] D.W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization. J. Wiley, 1992.
[58] R.P.W. Duin, "On the Choice of the Smoothing Parameters for Parzen Estimators of Probability Density Functions," IEEE Trans. Computers, vol. 25, no. 11, pp. 1175-1179, Nov. 1976.
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