Gabor-Type Filtering in Space and Time - Department of Electronic ...

132 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 45, NO. 2, FEBRUARY 1998filters tuned to different velocities can be obtained by cascadingthe spatial filter outputs with appropriately designedtemporal bandpass filters.Ongoing work includes the design and fabrication of thearchitecture described in Example 1 using the 2.0- m processprovided by MOSIS [39]. Future work includes incorporatingthis into a chip implementing a spatio–temporal filter,as described in Example 4. We are also investigating theapplication of these chips to various computer-vision taskssuch as binocular stereo vergence control and computation oftime-to-contact [26].REFERENCES[1] D. Gabor, “Theory of communication,” J. Inst. Elect. Eng. London, vol.93, pp. 429–457, 1946.[2] S. Marceljia, “Mathematical description of the responses of simplecortical cells,” J. Opt. Soc. Amer., vol. 70, pp. 1297–1300, Nov. 1980.[3] J. G. Daugman, “Two-dimensional spectral analysis of cortical receptivefield profiles,” Vision Res., vol. 20, pp. 847–856, 1980.[4] E. H. Adelson, and J. R. Bergen, “Spatiotemporal energy models forthe perception of motion,” J. Opt. Soc. Amer. A, Opt. Image Sci., vol.2, pp. 284–299, Feb. 1985.[5] J. Barron, D. S. Fleet, S. S. Beauchemin, and T. A. Burkitt, “Performanceof optical flow techniques,” in Proc. IEEE CVPR, Champaign,IL, 1992, pp. 236–242.[6] L. O. Chua and L. Yang, “Cellular neural networks: Theory,” IEEETrans. Circuits Syst., vol. 35, pp. 1257–1272, Oct. 1988.[7] , “Cellular neural networks: Applications,” IEEE Trans. CircuitsSyst., vol. 35, pp. 1273–1290, Oct. 1988.[8] L. O. Chua and T. Roska, “The CNN paradigm,” IEEE Trans. CircuitsSyst. I, vol. 40, pp. 147–156, Mar. 1993.[9] J. M. Cruz and L. O. Chua, “A CNN chip for connected componentdetection,” IEEE Trans. Circuits Syst., vol. 38, pp. 812–817, July 1991.[10] S. Espejo, R. Carmona, R. Dominguez-Castro, and A. Rodriguez-Vazquez, “A CNN universal chip in CMOS technology,” Int. J. CircuitTheory Applicat., vol. 24, pp. 93–109, 1996.[11] P. Kinget and M. Steyaert, “An analog parallel array processor for realtimesensor signal processing,” in IEEE Int. Solid-State Circuits Conf.Dig. Tech. Papers, San Francisco, CA, 1996, pp. 92–93.[12] T. Sanger, “Stereo disparity computation using Gabor filters,” Biol.Cybern., vol. 59, no. 6, pp. 405–418, 1988.[13] R. Wilson and H. Knutsson, “A multiresolution stereopsis algorithmbased on the Gabor representation,” in 3rd Int. Conf. Image ProcessingApplicat., Warwick, U.K., July 1989, pp. 19–22.[14] A. D. Jepson and M. Jenkin, “The fast computation of disparity fromphase differences,” in Computer Vision-ECCV90, O. Faugeras, Ed.Berlin, Germany: Springer-Verlag, 1990, pp. 50–55.[15] K. Langley, T. J. Atherton, R. G. Wilson, and M. H. E. Larcombe,“Vertical and horizontal disparities from phase,” in Computer Vision-ECCV90, O. Faugeras, Ed. Berlin, Germany: Springer-Verlag, 1990,pp. 315–325.[16] D. J. Fleet, A. D. Jepson, and M. R. M. Jenkin, “Phase-based disparitymeasurement,” CVGIP Image Understanding, vol. 53, no. 2, pp.198–210, Mar. 1991.[17] C. Chang and S. Chatterjee, “Ranging through Gabor logons—A consistent,hierarchical approach,” IEEE Trans. Neural Networks, vol. 4,pp. 827–43, Sept. 1993.[18] C.-J. Westelius, H. Knutsson, J. Wiklund, and C.-F. Westin, “Phasebaseddisparity estimation,” in Vision as Process, J. L. Crowley and H.I. Christensen, Eds. Berlin, Germany: Springer-Verlag, 1995, Ch. 11,pp. 157–178.[19] W. M. Theimer and H. A Mallot, “Phase-based binocular vergencecontrol and depth reconstruction using active vision,” CVGIP: ImageUnderstanding, vol. 60, no. 3, pp. 343–358, Nov. 1994.[20] M. Porat and Y. Y. Zeevi, “Localized texture processing in vision:Analysis and synthesis in Gaborian space,” IEEE Trans. Biomed. Eng.,vol. 36, pp. 115–29, Jan. 1989.[21] N. Petkov, P. Kruizinga, and T. Lourens, “Biologically motivatedapproach to face recognition,” in New Trends Neural Computation, Int.Workshop Artificial Neural Networks, Seville, Spain, 1993, pp. 68–77.[22] D. J. Heeger, “Model for the extraction of image flow,” J. Opt. Soc.Amer. A, vol. 4, pp. 1455–1471, Aug. 1987.[23] N. M. Gryzwacz and A. L. Yuille, “A model for the estimate of localimage velocity by cells in the visual cortex,” in Proc. R. Soc. Lond. B,vol. 239, 1990, pp. 129–161.[24] D. J. Fleet, Measurement of Image Velocity. Norwell, MA: Kluwer,1992.[25] B. K. P. Horn, Robot Vision. Cambridge, MA: MIT Press, 1986.[26] B. E. Shi, “Second-order CNN arrays for estimation of time to contact,”in Proc. 4th IEEE Int. Workshop Cellular Neural Networks, Seville,Spain, June 1996, pp. 427–432.[27] R. N. Bracewell, The Fourier Transform and Its Applications. NewYork: McGraw-Hill, 1986.[28] L. Raffo, “Resistive network implementing maps of Gabor functions ofany phase,” Electron. Lett., vol. 31, no. 22, pp. 1913–1914, Oct. 1995.[29] T. Delbruck, “Silicon retina with correlation-based, velocity-tuned pixels,”IEEE Trans. Neural Networks, vol. 4, pp. 529–541, May 1993.[30] B. E. Shi, “Spatio–temporal filtering with cellular neural networks,”Ph.D. dissertation, Dept. Elect. Eng. Computer Sci., Univ. CaliforniaBerkeley, 1994.[31] K. R. Crounse and L. O. Chua, “Methods for image processing andpattern formation in cellular neural networks: A tutorial,” IEEE Trans.Circuits Syst. I, vol. 42, pp. 583–601, Oct. 1995.[32] C. Mead, Analog VLSI and Neural Systems. Reading, MA: Addison-Wesley, 1989.[33] B. E. Shi and L. O. Chua, “Resistive grid image filtering: input/outputanalysis via the CNN framework,” IEEE Trans. Circuits Syst. I, vol. 39,pp. 531–548, July 1992.[34] B. Shi, “Gabor-type image filtering with cellular neural networks,” Proc.IEEE Int. Symp. Circuits Syst., vol. 3, pp. 558–561, May 1996.[35] K. F. Hui and B. E. Shi, “Robustness of CNN implementations forGabor-type filtering,” in IEEE Asia–Pacific Conf. Circuits Syst., Seoul,Korea, Nov. 1996, pp. 105–108.[36] H. Kobayashi, J. L. White, and A. A. Abidi, “An active resistor networkfor Gaussian filtering of images,” IEEE J. Solid-State Circuits, vol. 26,pp. 738–748, May 1991.[37] T. Poggio, H. Voorhees, and A. Yuille, “A regularized solution to edgedetection,” MIT, Cambridge, A.I. Memo 833, May 1985.[38] B. E. Shi, “Spatio–temporal image filtering with cellular neural networks,”Proc. IEEE Int. Conf. Neural Networks, vol. 3, Washington,DC, June 1996, pp. 141–1415.[39] , “An analog neural network for Gabor-type image filtering,” inProc. Int. Conf. Neural Inform. Processing, vol. 1, Hong Kong, Sept.1996, pp. 417–422.Bertram E. Shi (S’93–M’95) received the B.S.and M.S. degrees in electrical engineering fromStanford University, Stanford, CA, in 1987 and1988, respectively, and the Ph.D. degree in electricalengineering from the University of California atBerkeley, in 1994.Since 1994, he has been an Assistant Professorin the Department of Electrical and Electronic Engineering,Hong Kong University of Science andTechnology, Kowloon, Hong Kong. His researchinterests are in CNN’s, image processing, computervision, and speech recognition.