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Generalized Spatio-Chromatic Diffusion
October 2002 (vol. 24 no. 10)
pp. 1298-1309

Abstract—In this paper, a framework for diffusion of color images is presented. The method is based on the theory of thermodynamics of irreversible transformations which provides a suitable basis for designing correlations between the different color channels. More precisely, we derive an equation for color evolution which comprises a purely spatial diffusive term and a nonlinear term that depends on the interactions among color channels over space. We apply the proposed equation to images represented in several color spaces, such as RGB, CIELAB, Opponent colors, and IHS.

[1] B. Dresp and S. Grossberg, “Spatial Facilitation by Colour and Luminance Edges: Boundary, Surface, and Attentional Factors,” Vision Research, vol. 39, pp. 3431-3443, 1999.
[2] S. Konishi, A.L. Yuille, J. Coughlan, and S.C. Zhu, Fundamental Bounds on Edge Detection: An Information Theoretic Evaluation of Different Edge Cues Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 573-579, 1999.
[3] A. Witkin, “Scale Space Filtering,” Proc. Int'l Joint Conf. Artificial Intelligence, pp. 1019-1023, 1983.
[4] J. Koenderink, “The Structure of Images,” Biological Cybernetics, no. 50, pp. 363-370, 1984.
[5] T. Lindeberg, Scale-Space Theory in Computer Vision. Kluwer Academic, 1994.
[6] Geometry-Driven Diffusion in Computer Vision, B.M. ter Haar Romeny, ed. Kluwer, 1994.
[7] L. Florack, Image Structure. Dordrecht, The Netherlands: Kluwer Academic, 1997.
[8] R. Whitaker and G. Gerig, “Vector-Valued Diffusion,” Geometry-Driven Diffusion in Computer Vision, B. ter Haar Romeny, ed., Dordrecht, The Netherlands, Kluwer Academic, 1994.
[9] J. Weickert, “Coherence-Enhancing Diffusion of Colour Images,” Proc. Seventh Nat'l Symp. Pattern Recognition and Image Analysis, vol. 1, pp. 239-244, 1997.
[10] N. Sochen, R. Kimmel, and R. Malladi, “A Geometrical Framework for Low Level Vision,” IEEE Trans. Image Processing, vol. 7, no. 3, pp. 310-318, 1998.
[11] G. Sapiro and D. Ringach, “Anisotropic Diffusion of Multivalued Images with Applications to Color Filtering,” IEEE Trans. Image Processing, vol. 5, pp. 1582-1586, 1996.
[12] J. Weickert, Anisotropic Diffusion in Image Processing. Stuttgart, Germany: Teubner Verlag, 1998.
[13] M. Proesmans, E. Pauwels, and L. van Gool, “Coupled Geometry-Driven Diffusion Equations for Low-Level Vision,” Geometry-Driven Diffusion in Computer Vision, B. ter Haar Romeny, ed., Dordrecht, The Netherlands: Kluwer Academic, 1994.
[14] B. Tang, G. Sapiro, and V. Caselles, “Color Image-Enhancement via Chromaticity Diffusion,” IEEE Trans. Image Processing, vol. 10, pp. 701-707, May 2001.
[15] L. Florack, “Non-Linear Scale-Spaces Isomorphic to the Linear Case with Application to Scalar, Vector, and Multispectral Images,” J. Math. Imaging and Vision, vol. 15, pp. 39-53, 2001.
[16] T. Caelli and D. Reye, “On the Classification of Image Regions by Colour, Texture and Shape,” Pattern Recognition, vol. 26, no. 4, pp. 461-470, 1993.
[17] B. Wandell, Foundations of Vision. Sunderland, Mass.: Sinauer, 1995.
[18] S. de Groot and P. Mazur, Non-Equilibrium Thermodinamics. Amsterdam: North-Holland, 1962.
[19] M. Ferraro, G. Boccignone, and T. Caelli, “On the Representation of Image Structures via Scale-Space Entropy Condition,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 11, pp. 1199-1203, Nov. 1999.
[20] M. Nitzberg and T. Shiota, “Nonlinear Image Filtering with Edge and Corner Enhancement,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, pp. 826-833, 1992.
[21] T. Lindeberg and J. Garding, “Shape-Adapted Smoothing in Estimation of 3-D Depth Cues from Affine Distorsions of Local 2-D Brightness Structure,” Proc. Third European Conf. Computer Vision, vol. 800, pp. 389-400, 1994.
[22] P. Grindrod, Patterns and Waves. Oxford, U.K.: Clarendon Press, 1991.
[23] S.C. Zhu and D. Mumford, “Prior Learning and Gibbs Reaction-Diffusion,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 11, Nov. 1997.
[24] P. Perona and J. Malik, "Scale-Space and Edge Detection Using Anisotropic Diffusion," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629639, July 1990.
[25] D.H. Ballard and C.M. Brown, Computer Vision, Prentice Hall, Upper Saddle River, N.J., 1982.
[26] G. Wyszecki and W. Stiles, Color Science-Concepts and Methods, Quantitative Data and Formulas. New York: Wiley, 1982.
[27] I. Pitas, Digital Image Processing Algorithms, Prentice Hall, New York, 1993.
[28] T. Carron and P. Lambert, “Color Edge Detector Using Jointly Hue, Saturation and Intensity,” Proc. Int'l Conf. Image Processing '94, vol. 3, pp. 977-981, Nov. 1994.
[29] P. Perona, “Orientation Diffusion,” IEEE Trans. Image Processing, vol. 7, no. 3, pp. 457-467, 1998.
[30] P. Trahanias and A. Venetsanopoulos, “Vector Directional Filters—A New Class of Multichannel Image Processing Filters,” IEEE Trans. Image Processing, vol. 2, pp. 528-534, Oct. 1993.
[31] J. Canny, “A Computational Approach to Edge Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, June 1986.
[32] G. Boccignone, M. Ferraro, and T. Caelli, “Encoding Visual Information Using Anisotropic Transformations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 2, pp. 207-211, Feb. 2001.
[33] P.K. Sahoo, S. Soltani, A.K.C. Wong, and Y.C. Chen, “A Survey of Thresholding Techniques,” Computer Vision, Graphics, and Image Processing, vol. 41, pp. 233-260, 1988.

Index Terms:
Color images, scale-space, vector-valued diffusion.
Citation:
Giuseppe Boccignone, Mario Ferraro, Terry Caelli, "Generalized Spatio-Chromatic Diffusion," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 10, pp. 1298-1309, Oct. 2002, doi:10.1109/TPAMI.2002.1039202
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