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On the Edge Location Error for Local Maximum and Zero-Crossing Edge Detectors
December 1994 (vol. 16 no. 12)
pp. 1207-1212

Examines the localization criterion for edge detection and determine the probability density function describing the edge location error. Canny (1986) defines the measure of localization as the reciprocal of the root-mean-square edge location error and formulates an expression of this measure for local maximum detectors. However, Tagare and deFigueiredo (1990) point out that an incorrect assumption is made in the calculation. The same procedure is used by Sarkar and Boyer (1991) for their localization measure for zero-crossing detectors. We modify the analysis and obtain a closed-form solution of the probability density function of the edge location error. Examination of the density function indicates the variance of the edge location error does not exist, and hence cannot be used directly as a measure of localization.

[1] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
[2] S. Sarkar and K. L. Boyer, "Optimal infinite impulse response zero crossing based edge detectors,"Comput. Vision, Graphics and Image Processing Image Understanding, vol. 54, pp. 224-243, Sept. 1991.
[3] H. D. Tagare and R. J. P. deFigueiredo, "On the localization performance measure and optimal edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. 12, no. 12, Dec. 1990.
[4] A. Papoulis,Probability, Random Variables and Stochastic Processes. New York: McGraw-Hill, 1965.
[5] A. Huertas, and G. Medioni, "Detection of intensity changes with subpixel accuracy using Laplacian-Gaussian masks,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, no. 5, pp. 651-664, Sept. 1986.
[6] D. Marr and E. Hildreth, "Theory of edge detection,"Proc. Roy. Soc. Lon., vol. 207, pp. 187-217, 1980.
[7] S. Sarkar and K. Boyer, "On optimal infinite impulse response edge detection filters,"IEEE Trans. Pattern Anal. Machine Intell., vol. 13, no. 11, Nov. 1991.
[8] R. M. Haralick, "Digital step edges from zero crossings of second directional derivatives,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 1, Jan. 1984.
[9] V. Torre and T. A. Poggio, "On edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147-163, Mar. 1986.
[10] S. O. Rice, "Mathematical analysis of random noise,"Bell Syst. Tech. J., vol. 24, pp. 46-156, 1945.
[11] J. Koplowitz and X. Lee, "Edge detection with subpixel accuracy,"Proc. SPIE, vol. 1471, pp. 452-463, 1991.
[12] A. J. Tabatabai and O. R. Mitchell, "Edge location to subpixel values in digital imagery,"IEEE Trans. Pattern Anal. Machine Intell., vol. 6, no. 2, 1984.
[13] E. P. Lyvers, O. R. Mitchell, M. L. Akey, and A. P. Reeves, "Subpixel measurements using a moment-based edge operator,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, no. 12, 1989.
[14] A. Yuille and T. Poggio, "Scaling theorems for zero crossings,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 1, pp. 15-25, 1986.
[15] J. Babaud, A. P. Witkin, M. Baudin, and R. O. Duda, "Uniqueness of the Gaussian kernel for scale-space filtering,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 26-33, Jan. 1986.
[16] H. R. Wilson and S. C. Geise, "Threshold visibility of frequency gradient patterns,"Vision Res., vol. 17, pp. 1177-1190.

Index Terms:
edge detection; errors; probability; feature extraction; image segmentation; edge location error; local maximum detectors; zero-crossing edge detectors; localization criterion; probability density function; root-mean-square error; closed-form solution; variance; localization measure; feature extraction; image processing; image segmentation
Citation:
J. Koplowitz, V. Greco, "On the Edge Location Error for Local Maximum and Zero-Crossing Edge Detectors," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 12, pp. 1207-1212, Dec. 1994, doi:10.1109/34.387487
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