This work studied the possibilities for implementing a computer retina and cortex model. Although the details of the retina, cortex, and even the whole of the human vision system remain unknown, based on some results of previous researches on both biology and digital image processing, the fovea model can be roughly realized, and consequently some possible applications can be fulfilled.
However, some issues remain open to question. For example, this experiment examines 2 or 3 types of ganglions. In fact, over 20 different structures of ganglions have already been identified. Thus, it is interesting to consider the relationships among these different types of implementations, particularly in cases where the response of a ganglion is related to the time domain. Studying the relationship between the structure of the retina and possible applications for image processing offers one of the most interesting topics for future research.
This study also proposed a simulation of human visual cortex is proposed. It mimics the mechanism of the early stage of the human vision, and experimental results are generally consistent to the human visual sensation. After post processing, the detected boundaries also have adequate accuracy for the other image processing applications such as stereo, and pattern recognition. By implementing the proposed algorithm on the Cellular Neural Networks (CNN), the computational time will greatly decrease. The real-time processing capability is critical in some applications, such as the object tracking.
Although the proposed algorithm is widely tested to detect boundaries of synthetic textures successfully, there are still some problems demanding to be overcome:
1. As same as the other algorithms for textures analysis which is also based on the Gabor filters, there are too many parameters need to be determined. Determining the parameters will much more complex when the synthesized texture patterns increased. Currently, we
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are still looking for the solutions for those kinds of problems.
2. For the sake of keeping the structure simple and combining the hybrid-order features easily without the clustering methods, we use same resolution for all of the Gabor filters in the approach.
3. In this approach, we only consider the first and the second order features. According to some research results, there are still some higher-order features that can be utilized. For example, color is one of them. We do believe proposed approach can be extended to color textures by integrating color information.
132 REFERENCES
[1] D. H. Hubel, Eye, brain, and vision. Yew York: Scienceific American, 1988.
[2] D. H. Hubel and T. N. Wiesel, "Receptive fields, binocular interaction,and functional architecture in the cat's visual cortex," J. Physiol. (Lond.), vol. 160, pp. 106-154, 1962.
[3] J. I. Yellot, "Spectral consequences of photoreceptor sampling in the rhesus retina," Science, vol. 221, pp. 382-385, 1983.
[4] S. Shah and M. D. Levine, "Visual information processing in primate cone pathways - part ii:
experiments," IEEE Transactions on Systems, Man, and Sybernetics - Part B: Cybernetics, vol. 26, pp. 275-289, April 1996.
[5] J. Thiem and G. Hartmann, "Biology-inspired design of digital Gabor filters upon a hexagonal sampling scheme," in International Conference on Pattern Recognition, 2000.
(ICPR'00) Barcelona, Spain, 2000, pp. 445-448.
[6] D. Bálya, B. Roska, T. Roska, and F. S.Werblin, "A CNN framwork for modeling parallel processing in a mammalian retina," International Journal of Circuit Theory and Applications (CTA), vol. 30, pp. 363-393, 2002.
[7] I. Chen, "Visual and visuomotor processes," in Vision and cognition Taipei: Yuan-Liou, 1999, pp. 128-158.
[8] D. H. Hubel and T. N. Wiesel, "Sequence regularity and geometry of orientation columns in themonkey striate cortex," J. Comput. Neurol., vol. 158, pp. 267-293, 1974.
[9] L. O. Chua and L. Yang, "Cellular neural networks: applications," IEEE Transactions on Circuits and Systems, vol. 35, pp. 1273-1290, Oct. 1988.
[10] L. O. Chua and L. Yang, "Cellular neural networks: theory," IEEE Transactions on Circuits and Systems, vol. 35, pp. 1257-1272, Oct. 1988.
[11] K. R. Crounse and L. O. Chua, "Methods for image processing and pattern formation in cellular neural networks," IEEE Transactions on Circuits and Systems - I, vol. 42, pp.
583-601, Oct. 1995.
[12] C. H. Huang and C. T. Lin, "Cellular neural networks for hexagonal image processing," in Cellular Neural Networks and their Applications, 2005. CNNA2005. The 9th International Workshop on, Hsinchu, Taiwan, 2005, pp. 81-84.
[13] L. Middleton, J. Sivaswamy, and G. Coghill, "The FFT in a hexagonal-image processing framework," in Image and Vision Computing 2001. IVCNZ 2001. New Zealand Conference on, Dunedin, New Zealand, 2001, pp. 231-236.
[14] B. E. Shi, "Gabor-type filtering in space and time with cellular neural networks," IEEE Transactions on Circuits and Systems - I, vol. 45, pp. 121-132, Feb. 1998.
[15] H. Kobayashi, J. L. White, and A. A. Abidi, "An active resister network for Gaussian filtering of images," IEEE Journals on Solid-state Circuits, vol. 26, pp. 738-748, May 1991.
[16] D. Gabor, "Theory of communication," J. Inst. Elect. Eng., vol. 93, pp. 429-457, 1946.
[17] D. P. Peterson and D. Middleton, "Sampling and reconstruction of wave-number-limited
133
function in N-dimensional Euclidean spaces," Information and Control, vol. 5, pp. 279-323, 1962.
[18] A. Rosenfeld and J. L. Pfaltz, "Distance function on digital pictures," Pattern Recognition, vol. 1, pp. 33-61, 1968.
[19] M. J. E. Golay, "Hexagonal parallel pattern transformations," IEEE Transactions on Computing, vol. C-8, pp. 733-740, Aug. 1969.
[20] I. Her, "A symmetrical coordinate frame on the hexagonal grid for computer graphics and vision," ASME Journals of Mechanical Design, vol. 115, pp. 447-449, Sept. 1993.
[21] I. Her and C. T. Yuan, "Re-sampling on a psudo-hexagonal grid," in Graphics Models Image Processing Computer Vision, Graphics, and Image Processing, International Conference on, 1994 (CVGIP'94), 1994, pp. 336-347.
[22] E. Luczak and A. Rosenfeld, "Distance on a hexagonal grid," IEEE Transactions on Computing, vol. C-25, pp. 532-533, 1976.
[23] J. Serra, Image analysis and mathematical morphology. London: Acadmic, 1982.
[24] R. C. Staunton, "The design of hexagonal sampling structures for image digitization and their use with local operators," Image and Vision Computing, vol. 7, pp. 162-166, Aug.
1989.
[25] R. Ulichney, Digital halftoning vol. 1: The MIT Press, 1987.
[26] C. A. Wuthrich and P. Stuck, "An algorithmic comparison between square-and hexagonal-based grids," in Graphical Models and Image Processing Computer Vision, Graphics, and Image Processing, International Conference on, 1991 (CVGIP'91), 1991, pp.
324-329.
[27] S. B. M. Bell, F. C. Holroyd, and D. C. Mason, "A digital grometry for hexagonal pixels,"
Image and Vision Computing, vol. 7, pp. 194-204, Aug 1989.
[28] E. S. Deutsh, "On parallel operations on hexagonal arrays," IEEE Transactions on Computing, vol. C-19, pp. 982-983, Oct 1970.
[29] R. M. Mersereau, "The processing of hexagonally sampled two-dimensional signals,"
Proceedings of IEEE, vol. PROC-67, pp. 930-949, Jan. 1979.
[30] A. G. Radványi, "On the rectangular grid representation of general CNN networks," in Cellular Neural Networks and their Applications, IEEE International Workshop on, 1992 (CNNA'92), 1992, pp. 387-393.
[31] G. Seiler and J. A. Nossek, "Symmetry properties of cellular neural networks on square and hexagonal grids," in Cellular Neural Networks and their Applications, 1992. CNNA1992.
International Workshop on, 1992, pp. 258-263.
[32] G. Cauwenberghs and J. Waskiewicz, "Focal-plane analog VLSI cellular implementation of the boundary contour system," IEEE Transactions on Circuits and Systems - I, vol. 46, Feb.
1999.
[33] A. L. Nel, "Hexagonal image processing," in Communications and Signal Processing, Southern African Conference on, 1989 (COMSIG'89), 1989, pp. 109-113.
134
[34] T. Huang, "Two-dimensional nonrecursive filter design," in Applied Physics New York:
Springer-Verlag, 1981.
[35] W. Li and A. Fettweis, "Interpolation filters for 2-D hexagonally sampled signals,"
International Journals on Circuits Theories and their Applications, vol. C-18, pp. 733-740, 1997.
[36] D. V. Dille, T. Blu, M. Unser, W. Philips, I. Lemahieu, and R. V. Walle, "Hex-splines: a novel spline family for hexagonal lattices," IEEE Transactions on Image Processing, vol. 13, June 2005.
[37] R. M. Mersereau and D. E. Dudgeon, Multidimensional digital signal processing. New Jersey: Prentice-Hall, Inc., 1984.
[38] L. Middleton and J. Sivaswamy, "A framework for partical hexagonal-image processing,"
Journal on Electronic Imaging, 2001.
[39] R. Mersereau and T. Speake, "A unified treatment of Cooley-Turkey algorithms for the evaluation of the multi-dimensional DFT," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 29, pp. 1011-1018, 2005.
[40] I. Her, "Geometric transformations on hexagonal grid," IEEE Transactions on Image Processing, vol. 4, pp. 1213-1222, Sept. 1995.
[41] Z. Rahman, D. J. Jobson, and G. A. Woodell, "Retinex processing for automatic image processing," NASA 1986.
[42] J. Thumblin and G. Turk, "Tone reproduction for computer generated images," IEEE Computer Graphics and Applications, vol. 13, pp. 42-48, 1993.
[43] E. H. Land and J. L. Huertas, "Lightness theory," J. Opt. Soc., vol. 62, 1971.
[44] A. Zarándy, L. Orzo, E. Grawes, and F. Werblin, "CNN based early vision models for color vision and visual illusions," IEEE Transactions on Circuits and Systems - I: Special Issue on Bio-inspired Processors and Cellular Neural Networks, vol. 46, pp. 229-238, 1999.
[45] B. K. P. Horn, "Determining lightness from an image," Computer Graphics and Image Processing, pp. 277-299, 1974.
[46] B. Roska and F. S. Werblin, "Vertical interactions accross ten paralel, stacked representations in the mammalian retina," Nature, vol. 410, pp. 583-587, 2001.
[47] S. Shah and M. D. Levine, "Visual information processing in primate cone pathways - part i:
a model," IEEE Transactions on Systems, Man, and Sybernetics - Part B: Cybernetics, vol.
26, pp. 259-274, April 1996.
[48] A. K. Jain, "Unsupervised texture segmentation using Gabor filters," Pattern Recognition, vol. 24, pp. 1167-1186, 1991.
[49] A. Jacobs and F. S. Werblin, "Spatiotemporal patterns at the retinal output," Journal of Neurophysiology, vol. 80, pp. 447-451, 1998.
[50] H. Steklis and J. Erwin, "The primate retina," Comparative Primate Biology, Neuroscience, vol. 4, pp. 203-278, 1988.
[51] S. Shah and M. D. Levine, "The primate retina: a biological summary," in Center for
135
Intelligent Machines. vol. Ph.D. Montreal: McGill University, 1992.
[52] H. Kotera, Y. Yamada, and K. Shimo, "Sharpness improvement adaptive to edge strength of color images," in Color Imaging Conference 2000, Scottsdale, ZA, USA, 2000, pp. 149-154.
[53] R. Gershon, A. D. Jepson, and T. K. Tsotsos, "From {R, G, B} to surface reflectance:
computing color constant descriptors in images," in Artificial Intelligence, International Joint Conference on, 1987.
[54] G. Buchsbum, "A spatial processor model for object colour perception," Journal of the Franklin Institute, vol. 310, pp. 337-350, 1980.
[55] H. Tamura, S. Mori, and Y. Yamawaki, "Textural features corresponding to visual perception," IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-8, pp.
460-473, 1978.
[56] J. Sklansky, "Image segmentation and feature extraction," IEEE Transactions on Systems,Man, and Cybernetics, vol. SMC-8, pp. 237-247, 1978.
[57] J. K. Hawkins, "Picture Processing and Psychopictorics," in Textural Properties for Pattern Recognition, B. Lipkin and A. Rosenfeld, Eds. New York: Academic Press, 1969.
[58] A. C. Bovik, "Analysis of multichannel narrow-band fiters for image texture segmentation,"
IEEE Trans. Signal Process, vol. 39, pp. 2025-2043, 1990.
[59] D. Dunn and W. E. Higgins, "Optimal Gabor filter for texture segmentation," IEEE trans.
Image processing, vol. 4, pp. 947-964, Jul. 1995.
[60] T. N. Tan, "Texture edge detection by modelling visual cortical channels," Pattern Recognition, vol. 28, pp. 1283-1298, July 1995.
[61] P. Brodatz, Textures: a photographic album for artists and designers. New York: Dover Publications, 1966.
[62] ALADDIN CNN Software Library (Templates and Algorithms). Budapest: Analogic Computers Ltd., 2000.
[63] J. Daugman, "Uncertainty relation for resolution in space, spatial frequency, and orientation optimised by two-dimensional visual cortical filters," Journal of the Optical Society of America, vol. 2, pp. 1160-1169, 1985.
[64] I. Chen, "Texture perception: a linear system approach," University of California, Berkeley, 1994.
[65] ALADDIN CNN Software Library for ACE4K Chip (Templates and Algorithms). Budapest:
Analogic Computers Ltd., 2000.
[66] T. P. Weldon and W. E. Higgins, "Designing multiple Gabor filters for multi-texture image segmentation," Opt. Eng., vol. 35, pp. 2852-2863, Oct. 1996.
[67] A. Materka and M. Strzelecki, "Texture analysis methods - a review," University of Lodz, Institute of Electronics 1998.
[68] C. T. Lin, Neural Fuzzy Systems with Structure and Parameter Learning. New York: World Scientific, 1994.