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Authenticating Edges Produced by Zero-Crossing Algorithms
January 1989 (vol. 11 no. 1)
pp. 43-57

It is shown that zero-crossing edge detection algorithms can produce edges that do not correspond to significant image intensity changes. Such edges are called phantom or spurious. A method for classifying zero crossings as corresponding to authentic or phantom edges is presented. The contrast of an authentic edge is shown to increase and the contrast of phantom edges to decrease with a decrease in the filter scale. Thus, a phantom edge is truly a phantom in that the closer one examines it, the weaker it becomes. The results of applying the classification schemes described to synthetic and authentic signals in one and two dimensions are given. The significance of the phantom edges is examined with respect to their frequency and strength relative to the authentic edges, and it is seen that authentic edges are denser and stronger, on the average, than phantom edges.

[1] V. Berzins, "Accuracy of laplacian edge detectors,"Comput. Vision, Graphics, Image Processing, vol. 27, pp. 195-210, 1984.
[2] J. Canny, "Finding edges and lines in images," M.S. thesis, Mass. Inst. Technol., Cambridge, MA, 1983.
[3] J. J. Clark, "Singularities of contrast functions in scale space," inProc. First Int. Conf. Comput. Vision, London, UK, pp. 491-495, 1987.
[4] J. J. Clark, "Singularity theory and phantom edges in scale space,"IEEE Trans. Pattern Anal. Mach. Intell., to be published.
[5] R. M. Haralick, "Digital step edges from zero crossings of second directional derivatives,"IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-6, pp. 58-68, 1984.
[6] R. A. Hummel and B. C. Gidas, "Zero crossings and the heat equation," Div. Comput. Sci., Courant Inst. Math. Sci., New York Univ., Tech. Rep. 111, 1984.
[7] D. Marr and E. C. Hildreth, "Theory of edge detection,"Proc. Roy. Soc. London, Ser. B, vol. 207, pp. 187-217, 1980.
[8] D. Marr and T. Poggio, "A computational theory of human stereo vision,"Proc. Roy. Soc. London, Ser. B, vol. 204, pp. 301-328, 1979.
[9] V. S. Nalwa and T. O. Binford, "On detecting edges,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 699-714, 1986.
[10] S. O. Rice, "Mathematical analysis of random noise,"Bell Syst. Tech. J., vol. 24, pp. 46-156, 1945.
[11] J. Richter and S. Ullman, "Non-linearities in cortical simple cells and the possible detection of zero-crossings,"Biol. Cybern., vol. 53, pp. 195-202, 1986.
[12] J. J. Stoker,Differential Geometry. New York: Wiley-Interscience, 1969.
[13] V. Torre and T. A. Poggio, "On edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147-163, Mar. 1986.
[14] A. Witkin, "Scale space filtering," inProc. 8th Int. Joint Conf. Ar-tif. Intell., Karlsruhe, West Germany, 1983, pp. 1019-1022.
[15] A. L. Yuille and T. Poggio, "Scaling theorems for zero-crossings," M.I.T. Artificial Intell. Lab., Memo 772, June 1983.

Index Terms:
edge authentication; picture processing; pattern recognition; zero-crossing edge detection algorithms; phantom edges; authentic edges; pattern recognition; picture processing
J.J. Clark, "Authenticating Edges Produced by Zero-Crossing Algorithms," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 1, pp. 43-57, Jan. 1989, doi:10.1109/34.23112
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