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The Principal Components of Natural Images Revisited
May 2006 (vol. 28 no. 5)
pp. 822-826
This paper investigates the principal components (PCs) of natural gray and color images. A horizontal and vertical typology of PCs is found which leads to the identification of groups of basis functions for steerable bandpass filters. Using this system, the contribution of spatio-chromatic structure to the total variance can be quantified for selected spatial frequencies.

[1] H.B. Barlow, “Possible Principles Underlying the Transformations of Sensory Messages,” Sensory Comm., pp. 217-234, MIT Press, 1961.
[2] A.J. Bell and T.J. Sejnowski, “The Independent Components of Natural Images Are Edge Filters,” Vision Research, vol. 37, no. 27, pp. 3327-3338, 1997.
[3] G. Buchsbaum and A. Gottschalk, “Trichromacy, Opponent Colour Coding and Optimum Colour Information Transmission in the Retina,” Proc. Royal Soc. London B, vol. 220, pp. 89-113, 1983.
[4] R.L. de Valois, D.G. Albrecht, and L.G. Thorell, “Spatial Frequency Selectivity of Cells in Macaque Visual Cortex,” Vision Research, vol. 22, pp. 545-559, 1982.
[5] W.T. Freeman and E.H. Adelson, “The Design and Use of Steerable Filters,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 891-906, 1991.
[6] K. Gegenfurtner, “Color in the Cortex Revisited,” Nature Neuroscience, vol. 4, no. 4, pp. 339-340, 2001.
[7] D. Hall, J.L. Crowley, and V. Colin de Verdière, “View Invariant Object Recognition Using Coloured Receptive Fields,” Machine Graphics and Vision, vol. 9, no. 2, pp. 341-352, 2000.
[8] P.J.B. Hancock, R.J. Baddeley, and L.S. Smith, “The Principal Components of Natural Images,” Network, vol. 3, pp. 61-70, 1992.
[9] G. Heidemann, “Combining Spatial and Colour Information for Content Based Image Retrieval,” Computer Vision and Image Understanding, vol. 94, nos. 1-3, pp. 234-270, 2004.
[10] D.H. Hubel and T.N. Wiesel, “Receptive Fields, Binocular Interaction, and Functional Architecture in the Cat's Visual Cortex,” J. Physiology, vol. 160, pp. 106-154, 1962.
[11] E.N. Johnson, M.J. Hawken, and R. Shapley, “The Spatial Transformation of Color in the Primary Visual Cortex of the Macaque Monkey,” Nature Neuroscience, vol. 4, no. 4, pp. 409-416, 2001.
[12] J.P. Jones and L.A. Palmer, “An Evaluation of the Two-Dimensional Gabor Filter Model of Simple Receptive Fields in Cat Striate Cortex,” J. Neurophysiology, vol. 58, no. 6, pp. 1233-1258, 1987.
[13] D.J.C. MacKay and K.D. Miller, “Analysis of Linsker's Applications of Hebbian Rules to Linear Networks,” Network, vol. 1, pp. 257-297, 1990.
[14] D. Marr, Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. San Francisco: Freeman, 1982.
[15] Nova Development Corporation, Art Explosion Photo Gallery, 2002.
[16] E. Oja, “A Simplified Neuron Model as a Principal Component Analyzer,” J. Math. Biology, vol. 15, pp. 267-273, 1982.
[17] B.A. Olshausen and D.J. Field, “Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images,” Nature, vol. 381, pp. 607-609, 1996.
[18] P. Perona, “Deformable Kernels for Early Vision,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 5, pp. 488-499, May 1995.
[19] N. Petkov and P. Kruizinga, “Computational Models of Visual Neurons Specialised in the Detection of Periodic and Aperiodic Oriented Visual Stimuli: Bar and Grating Cells,” Biological Cybernetics, vol. 76, no. 2, pp. 83-96, 1997.
[20] D.L. Ruderman, T.W. Cronin, and C.-C. Chiao, “Statistics of Cone Responses to Natural Images: Implications for Visual Coding,” J. Optical Soc. Am. A, vol. 15, no. 8, pp. 2036-2045, 1998.
[21] T.D. Sanger, “Optimal Unsupervised Learning in a Single-Layer Linear Feedforward Neural Network,” Neural Networks, vol. 2, pp. 459-473, 1989.
[22] D.R. Tailor, L.H. Finkel, and G. Buchsbaum, “Color-Opponent Receptive Fields Derived from Independent Component Analysis of Natural Images,” Vision Research, vol. 40, no. 19, pp. 2671-2676, 2000.
[23] D.J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude Spectra of Natural Images,” Ophthalmic & Physiological Optics, vol. 12, no. 2, pp. 229-232, 1992.
[24] M. Turk and A. Pentland, “Eigenfaces for Recognition,” J. Cognitive Neuroscience, vol. 3, pp. 71-86, 1991.
[25] T. Wachtler, T.W. Lee, and T.J. Sejnowski, “Chromatic Structure of Natural Scenes,” J. Optical Soc. Am. A, vol. 18, no. 1, pp. 65-77, 2001.

Index Terms:
Statistical image representation, feature measurement, feature representation, texture, color scene analysis, shape, computer vision, computational models of vision, connectionism and neural nets.
Citation:
Gunther Heidemann, "The Principal Components of Natural Images Revisited," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 5, pp. 822-826, May 2006, doi:10.1109/TPAMI.2006.107
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