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On Idempotence and Related Requirements in Edge Detection
May 1993 (vol. 15 no. 5)
pp. 484-491

The energy feature detectors described by R. Owens et al. (1989) are good candidates for idempotent edge detectors. However, some of them (in particular, the Gabor energy feature detector) suffer from a serious defect that is absent in gradient-type operators: their sensitivity to gray-level shift in the original image. This leads to errors in the localization of step edges. The Fourier phase and amplitude conditions outlined by M.C. Morrone and D.C. Burr (1988) for the class of energy feature detectors guarantee a zero DC level when the convolution masks are taken in L/sup 1/; therefore, the resulting energy feature detector is invariant under grey-level shift in the original image. Also, the properties of the underlying edge model are invariant under a smoothing of the image by a Gaussian or any function in L/sup 1/ having zero Fourier phase. In particular, such a smoothing does not deteriorate the idempotence of the edge detector. Some concrete examples of energy feature detectors satisfying the Morrone conditions are described.

[1] M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions with Formulas, Graphs and Mathematicals Tables. Washington, DC: Nat. Bureau Std., 1964, Applied Mathematics Series, vol. 55, 2nd printing.
[2] J. G. Daugman, "Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,"J. Opt. Soc. Amer., vol. 2, no. 7, pp. 1160-1169, July 1985. Ser. A.
[3] D. Gabor, "Theory of communication,"J. Inst. Elec. Eng., vol. 93, pp. 429-457, 1946.
[4] S. A. Klein and D. M. Levi, "Hyperacuity thresholds of 1 sec: Theoretical predictions and empirical validation,"J. Opt. Soc. Amer. Ser. A, vol. 2, no. 7, pp. 1170-1190, July 1985.
[5] A. Kundu, "Robust edge detection,"Patt. Recogn., vol. 23, no. 5, pp. 423-440, 1990.
[6] V. Lacroix, "The primary raster: A multiresolution image description," inProc. 10th. Int. Conf. Patt. Recogn.(Atlantic City, NJ), 1990, pp. 903-907, vol. I.
[7] D. Marr, "Early processing of visual information,"Phil. Trans. Royal Soc. London Ser. B, vol. 275, pp. 483-519, 1976.
[8] D. Marr,Vision. San Francisco: W. H. Freeman, 1982.
[9] D. Marr and E. Hildreth, "Theory of edge detection,"Proc. Royal Soc. London Ser. B, vol. 207, pp. 187-217, 1980.
[10] M. C. Morrone and D. C. Burr, "Feature detection in human vision: A phase-dependent energy model,"Proc. Royal Soc. London Ser. B, vol. 235, pp. 221-245, 1988.
[11] M. C. Morrone and R. A. Owens, "Feature detection from local energy,Patt. Recog. Lett., vol. 6, pp. 303-313, 1987.
[12] M. C. Morrone, J. Ross, D. C. Burr, and R. Owens, "Mach bands are phase dependent,"Nature, vol. 324, pp. 250-253, Nov. 20, 1986.
[13] R. Owens, S. Venkatesh, and J. Ross, "Edge detection is a projection,"Patt. Recogn. Lett., vol. 9, pp. 233-244, 1989.
[14] C. Ronse, One-dimensionalL1∪L2analysis of the Morrone model of edge detection in pictures," in preparation.
[15] J. Ross and R. Owens, "Sketches: man-made and machine-made,"Leonardo, to be published.
[16] W. Rudin,Real and Complex Analysis, second ed. New York: McGraw-Hill, 1974.
[17] J. Serra, "Morphological optics,"J. Microscopy, vol. 145, pt. 1, pp. 1-22, 1987.
[18] E. M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces. Princeton, NJ: Princeton University Press, 1971.
[19] S. Venkatesh and R. Owens, "On the classification of image features,"Patt. Recogn. Lett., vol. 11, pp. 339-349, 1990.

Index Terms:
image smoothing; feature extraction; idempotent edge detectors; Gabor energy feature detector; convolution masks; Fourier phase; Morrone conditions; edge detection; feature extraction
Citation:
C. Ronse, "On Idempotence and Related Requirements in Edge Detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 5, pp. 484-491, May 1993, doi:10.1109/34.211468
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