This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
On Optimal Infinite Impulse Response Edge Detection Filters
November 1991 (vol. 13 no. 11)
pp. 1154-1171

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters, operating in two orthogonal directions. The implementation is very simple and computationally efficient. has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

[1] T. Poggio, H. Voorhees, and A. Yuille, "A regularized solution to edge detection," Tech. Rep. MA, Rep. AIM-833, MIT Artificial Intell. Lab., May 1985.
[2] P. Bouthemy, "A maximum likelihood framework for determining moving edges,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, pp. 499-511, May 1989.
[3] H. H. Baker and T. O. Binford, "Depth from edge and intensity based stereo," inProc. 7th Int. Joint Conf. Artificial Intell., 1979, pp. 631-636.
[4] H. Barrow and J. Tenenbaum, "Interpreting line drawings as 3-d surfaces,"Artificial Intell., vol. 17, pp. 75-116, 1981.
[5] S. T. Barnard and M. A. Fischler, "Computational stereo,"Comput. Surveys, vol. 14, no. 4, pp. 553-572, 1982.
[6] W. E. L. Grimson,From Images to Surfaces: A Computational Study of the Human Early visual System. Cambridge, MA: MIT Press, 1981.
[7] W. E. L. Grimson, "Computing stereopsis using feature point contour matching," inTechniques for 3-D Machine Perception(A. Rosenfeld, Ed.), New York: Elsevier, 1986, pp. 75-111.
[8] J. E. W. Mayhew and J. P. Frisby, "Psychological and computational studies toward a theory of human stereopsis,"Artificial Intell., vol. 17, pp. 349-385, 1981.
[9] D. Marr and T. Poggio, "A theory of human stereopsis,"Proc. Royal Soc. London, 1980, pp. 187-217, vol. 207.
[10] D. Marr,VISION: A Computational Investigation into the Human Representation and Processing of Visual Information. San Fransisco, CA: W. H. Freeman, 1981.
[11] Y. Yakimovsky and R. Cunningham, "A system of extracting three-dimensional measurements from a stereo pair of TV cameras,"Comput. Graphics Image Processing, vol. 7, pp. 195-210, 1978.
[12] K. L. Boyer and G. E. Sotak, "Structural stereo matching of Laplacian-of-Gaussian contour segments for 3D perception," inProc. SPIE, 1988, pp. 219-226, vol. 1005.
[13] A. C. Kak, "Depth perception for robots," inHandbook of Industrial Robotics(S. Nof, Ed.), New York: Wiley, 1986, pp. 272-319.
[14] L. S. Davis, "A survey of edge detection techniques,"Comput. Graphics Image Processing, vol. 4, pp. 248-270, Sept. 1975.
[15] M. Brady, "Computational approaches to image understanding,"Comput. Surveys, vol. 14, pp. 3-71, Mar. 1982.
[16] V. S. Nalwa and T. O. Binford, "On detecting edges,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 699-714, 1986.
[17] R. M. Haralick, "Digital step edges from zero crossings of second directional derivatives,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 58-68, Jan. 1984.
[18] J. W. Modestino and R. W. Fries, "Edge detection in noisy images using recursive digital filtering,"Comput. Graphics Image Processing, vol. 6, pp. 409-433, 1977.
[19] D. Marr and E. Hildreth, "Theory of edge detection," inProc. Royal Soc. London, 1980, pp. 187-217, vol. 207.
[20] J. F. Canny, "Finding lines and edges in images," Artificial Intell. Lab., Massachusetts Inst. Technol., Tech. Rep. TM-720, 1983.
[21] J. S. Huang and D. H. Tseng, "Statistical theory of edge detection,"Comput. Vision Graphics Image Processing, vol. 43, pp. 337-346, 1988.
[22] N. E. Nahi and M. H. Jahanshahi, "Image boundary estimation,"IEEE Trans. Comput., vol. C-26, pp. 772-781, Aug. 1977.
[23] F. R. Hansen and H. Elliot, "Image segmentation using simple markov field models,"Comput. Graphics Image Processing, vol. 20, pp. 101-132, 1982.
[24] N. E. Nahi and T. Assefi, "Bayesian recursive image estimation,"IEEE Trans. Comput., pp. 734-738, July 1972.
[25] A. C. Bovik, T. S. Huang, and D. C. Munson Jr., "Nonparametric tests for edge detection in noise,"Patt. Recogn., vol. 19, no. 1, pp. 209-219, 1986.
[26] J. S. Chen, A. Huertas, and G. Medioni, "Fast convolution with Laplacian-of-Gaussian masks,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 584-590, July 1987.
[27] G. E. Sotak and K. L. Boyer, "The Laplacian-of-Gaussian kernel: A formal analysis and design procedure for fast, accurate convolution and full-frame output,"Comput. Vision Graphics Image Processing, vol. 48, no. 2, pp. 147-189, 1989.
[28] K. S. Shanmugan, F. M. Dickey, and J. A. Green, "An optimal frequency domain filter for edge detection in digital pictures,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-1, pp. 37-49, Jan. 1979.
[29] W. Lunscher, "The asymptotic optimal frequency domain filter for edge detection,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-5, pp. 678-680, Nov. 1983.
[30] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
[31] R. Deriche, "Using Canny's criteria to derive a recursively implemented optimal edge detector,"Int. J. Comput. Vision, pp. 167-187, 1987.
[32] S.O. Rice, "Mathematical analysis of random noise,"Bell Syst. Tech. J., no. 24, pp. 46-156, 1945.
[33] H. D. Tagare and R. J. P. deFigueiredo, "On the localization performance measure and optimal edge detection,"IEEE Trans. Patt. Anal. Machine Intell., vol. 12, pp. 1186-1189, Dec. 1990.
[34] W. A. Gardner,Introduction to Random Processes with Applications to Signals and Systems, New York: McGraw-Hill, 1989.
[35] V. Torre and T. A. Poggio, "On edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147-163, Mar. 1986.
[36] L. Spacek, "The computation of visual motion," Ph.D. thesis, Univ. Essex, Colchester, U. K. 1984.
[37] R. Courant and D. Hilbert,Methods of Mathematical Physics. New York: Wiley, 1953.
[38] D. G. Luenberger,Introduction to Linear and Non-Linear Programming. Reading, MA: Addison-Wesley, 1973.
[39] W. M. Wells, "Efficient synthesis of Gaussian filters by cascaded uniform filters,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 234-239, Mar. 1986.
[40] P. J. Burt, "Fast algorithms for estimating local image properties," inProc. Conf. Patt. Recogn. Image Processing, 1982, pp. 669-671.
[41] L. A. Ferrari, P. V. Sankar, S. Shinnaka, and J. Sklansky, "Recursive algorithms for implementing digital image filters,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 461-466, May 1987.

Index Terms:
filter width; optimal infinite impulse response edge detection filters; Canny's high signal to noise ratio; localization criteria; spurious response; variational method; nonlinear constrained optimization; approximating recursive digital filtering; linear filters; computerised pattern recognition; digital filters; optimisation; variational techniques
Citation:
S. Sarkar, K.L. Boyer, "On Optimal Infinite Impulse Response Edge Detection Filters," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 11, pp. 1154-1171, Nov. 1991, doi:10.1109/34.103275
Usage of this product signifies your acceptance of the Terms of Use.