This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Primitive Features by Steering, Quadrature, and Scale
November 1998 (vol. 20 no. 11)
pp. 1161-1173

Abstract—The impulse response of neurons in the visual cortex of the mammalian brain has been known for some time. How to make use of these as filters has led to many hypotheses. The response of a single filter is ambiguous because the result depends on stimulus type, contrast, position, orientation, and scale. We show that a set of quadrature filters at sparse positions can be constructed so that it is possible to disambiguate the 2D responses of the individual filters. Detecting edges is not the goal of the present work; rather, we seek to detect relevant edges. Thus, we make the assumption that at the scale of interest, a local image patch consists predominantly of an edge or a bar. When this patch is processed by five or seven oriented filters, one can compute the exact orientation and centroid position of the feature. When the set of filters is applied at two different scales, it is possible to distinguish edges from ridges and to identify the polarity, intensity, and width. It is also possible to find corners and blobs. These computations are stable under image shifts in position and orientation and can be made to subpixel resolution.

[1] E.H. Adelson and J.R. Bergen, "The Plenoptic Function and the Elements of Early Vision," Computational Models of Visual Processing, M.S. Landy and J.A. Movshon, eds., pp. 3-20.Cambridge, Mass.: MIT Press, 1991.
[2] J.A. Movshon, I.D. Thompson, and D.J. Tolhurst, "Spatial Summation in the Receptive Fields of Simple Cells in the Cat's Striate Cortex," J. Physiology, vol. 283, pp. 53-77, 1978.
[3] E.R. Kandel and J.H. Schwartz, Principles of Neural Science, 2nd ed. New York: Elsevier, 1985.
[4] S. Marcelja, "Mathematical Descriptions of the Responses of Simple Cortical Cells," J. Optical Soc. Am., vol. 70, pp. 1,297-1,300, 1980.
[5] J.J. Kulikowski, S. Marcelja, and P.O. Bishop, "Theory of Spatial Position and Spatial Frequency Relations in the Receptive Fields of Simple Cells in the Visual Cortex," Biological Cybernetics, vol. 43, pp. 187-198, 1982.
[6] J.G. Daugman, "Uncertainty Relation for Resolution in Space, Spatial Frequency, and Orientation Optimized by Two-Dimensional Visual Cortical Filters," J. Optical Soc. Am. A, vol. 2, pp. 1,160-1,169, 1985.
[7] 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, pp. 1,233-1,258, 1987.
[8] D. Gabor, "Theory of Communication," J. Institute of Electrical Eng., vol. 93, pp. 429-457, 1946.
[9] D. Marr, Vision.New York: W. H Freeman and Co., 1982.
[10] R.A. Young, "The Gaussian Derivative Model for Machine Vision: Visual Cortex Simulation," General Motors Research Publication GMR-5323, 1986.
[11] J.F. Canny, "A Computational Approach to Edge Detection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 679-698, 1986.
[12] D.H. Hubel and T.N. Wiesel, "Ferrier Lecture: Functional Architecture of Macaque Monkey Visual Cortex," Proc. Royal Soc. London, Series B, vol. 198, pp. 1-59, 1977.
[13] 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.
[14] T.C. Folsom, "Neural Networks Modeling Cortical Cells for Machine Vision," Ph.D. Thesis, Univ. of Washington, Seattle, Wash., 1994.
[15] C. Mead, Analog VLSI and Neural Systems. Addison-Wesley, 1989.
[16] B. Nabet, R.B. Darling, and R.B. Pinter, "Analog Implementation of Shunting Neural Networks," Advances in Neural Information Processing Systems, D.S. Touretzky, ed., pp. 695-702.San Mateo, Calif.: Kauffman, 1989.
[17] B. Nabet, R.B. Darling, and R.B. Pinter, "Optoelectronic Sensory Neural Network," U.S. Patent No. 5,130,563, 1991.
[18] K.K. DeValois, R.L. DeValois, and E.W. Yund, "Responses of Striate Cortex Cells to Gratings and Checkerboard Patterns," J. Physiology, vol. 291, pp. 483-505, 1979.
[19] D.M. MacKay, "Strife Over Visual Cortical Function," Nature, vol. 289, pp. 117-18, 1981.
[20] H.R. Wilson, D. Levi, L. Maffei, J. Rovamo, and R. DeValois, "The Perception of Form: Retina to Striate Cortex," Visual Perception: The Neurophysiological Foundations, L. Spillman and J.S. Werner, eds., pp. 231-272, 1990,.
[21] M.W. Levine and J.M. Shefner, Fundamentals of Sensation and Perception, 2nd ed. Pacific Grove, Calif.: Brooks/Cole, 1991.
[22] P. Seitz and G.K. Lang, "Using Local Orientation and Hierarchical Spatial Feature Matching for the Robust Recognition of Objects," SPIE Proc. Visual Communication and Image Processing 91: Image Processing, vol. 1,606, pp. 252-259, 1991.
[23] A. Dobbins, Difference Models of Visual Cortical Neurons, Ph.D. Thesis, McGill University, Canada, 1992.
[24] J.G. Daugman, “Complete Discrete 2D Gabor Transforms by Neural Networks for Image Analysis and Compression,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 36, no. 7, 1988.
[25] S. Mallat, "Multifrequency Channel Decomposition of Images and Wavelet Models," IEEE Trans. ASSP, vol. 37, no. 12, 1989, pp. 2091-2110.
[26] A.P. Pentland, "Spatial and Temporal Surface Interpolation Using Wavelet Bases," Geometric Methods in Computer Vision, SPIE, vol. 1,570, pp. 43-62, 1991.
[27] E.P. Simoncelli, W.T. Freeman, E.H. Adelson, and D.J. Heeger, “Shiftable Multi-Scale Transforms,” IEEE Trans. Information Theory, vol. 38, no. 2, pp. 587-607, Mar. 1992.
[28] T.C. Folsom and R.B. Pinter, "An Interpretation of Image Processing in Striate Cortex," IEEE Int'l Conf. Systems, Man, and Cybernetics,San Antonio, Oct. 1994.
[29] B. Nabet and R.B. Pinter, Sensory Neural Networks: Lateral Inhibition, CRC Press, 1991.
[30] E.L. Schwartz, "Computational Anatomy and Functional Architecture of Striate Cortex: A Spatial Mapping Approach to Perceptual Coding," Vision Research, vol. 20, pp. 645-669, 1980.
[31] J.G. Daugman, "Fortran Code for Gabor Transforms," unpublished, 1990.

Index Terms:
Edge finders, orientation, steerable filters, quadrature filters, Gabor functions, visual cortex, silicon retina.
Citation:
Tyler C. Folsom, Robert B. Pinter, "Primitive Features by Steering, Quadrature, and Scale," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 11, pp. 1161-1173, Nov. 1998, doi:10.1109/34.730552
Usage of this product signifies your acceptance of the Terms of Use.