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On the Location Error of Curved Edges in Low-Pass Filtered 2-D and 3-D Images
July 1994 (vol. 16 no. 7)
pp. 726-733

The authors study the location error of curved edges in two- and three-dimensional images after analog and digital low-pass filtering. The zero crossing of a second derivative filter is a well-known edge localization criterion. The second derivative in gradient direction (SDGD) produces a predictable bias in edge location towards the centers of curvature while the linear Laplace filter produces a shift in the opposite direction. Their sum called PLUS (PLUS=Laplace+SDGD) leads to an edge detector that finds curved edges one order more accurately than its constituents. This argument holds irrespective of the dimension. The influence of commonly used low-pass filters (such as the PSF originating from diffraction limited optics using incoherent light (2-D), the Gaussian filter with variable cutoff point (D-D), and the isotropic uniform filter (D-D)) is studied.

[1] D. Marr and E. C. Hildreth, "Theory of edge detection," inProc. Roy. Soc. Lon. B, vol. 207, 1980, pp. 187-217.
[2] D. Marr and T. Poggio, "A theory of human stereo vision," inProc. Roy. Soc. Lon. B., vol. 204, 1979, pp. 301-328.
[3] E. C. Hildreth, "The detection of intensity changes by computer and biological vision systems,"Comput. Vision, Graphics and Image Processing, vol. 22, pp. 1-27, 1983.
[4] J. Canny, "Finding edges and lines in images," M.S. thesis, M.I.T. Cambridge, MA, 1983.
[5] J. F. Canny, "A computational approach to edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 1986.
[6] W. H. H. J. Lunscher and M. P. Beddoes, "Optimal edge detector design I: Parameter selection and noise effects,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, pp. 164-177, 1986.
[7] F. M. Dickey and K. S. Shamugan, "Optimal edge detection filter,"Appl. Opt., vol. 16, no. 1, pp. 145-148, 1977.
[8] Z. Xu, "A further study on error probabilities of Laplacian-Gaussian edge detection," in8th Int. Conf. on Pattern Recognit., Paris, France, 1986, pp. 601-603.
[9] 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, pp. 1186-1190, 1990.
[10] S. Sarkar and K. L. Boyer, "On optimal infinite impulse response edge detection filters,"IEEE Trans. Pattern Anal. Machine Intell., vol. 13, no. 11, pp. 1154-1171, 1991.
[11] 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.
[12] A. Papoulis,Signal Analysis. New York: McGraw-Hill, 1977.
[13] 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.
[14] 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.
[15] V. Berzins, "Accuracy of Laplacian edge detectors,"Comput. Vision, Graphics and Image Processing, vol. 27, pp. 195-210, 1984.
[16] R. M. Haralick, "Digital step edges from zero crossing of second directional derivatives,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, no. 1, pp. 58-68, 1984.
[17] J. J. Clark, "Authenticating edges produced by zero-crossing algorithms,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, no. 1, pp. 43-57, 1989.
[18] V. Torre and T. A. Poggio, "On edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147-163, Mar. 1986.
[19] A. L. D. Beckers, "Parameter estimation for nonlinear object size filters in images," Master's thesis, (in Dutch) Faculty of Applied Physics, Delft Univ. of Technology, The Netherlands, 1986.
[20] J. Bernsen, "Dynamic thresholding of grey-level images," in8th Int. Conf. Pattern Recognit., Paris, France, 1986, pp. 1251-1255.
[21] L. J. van Vliet, I. T. Young, and A. L. D. Beckers, "An edge detection model based on nonlinear Laplace filtering," inPattern Recognition and Artificial Intelligence--Towards an Integration, E. S. Gelsema and L. N. Kanal, Eds. Amsterdam: Elsevier Science Publishers B. V. (North-Holland), 1988, vol. 7, pp. 63-73.
[22] L. J. van Vliet, I. T. Young , and A. L. D. Beckers, "A nonlinear Laplace operator as edge detector in noisy images,"Comput. Vision, Graphics, and Image Processing, vol. 45, no. 2, pp. 167-195, 1989.
[23] L. J. van Vliet, "Grey-Scale Measurements in Multi-Dimensional Digitized Images," Ph.D. thesis, Delft Univ. Press, Stevinweg 1, Delft, The Netherlands, 1993.
[24] P. W. Verbeek, "A class of sampling-error free measures in oversampled band-limited images,"Pattern Recognit. Lett., vol. 3, pp. 287-292, 1985.
[25] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering,Numerical Recipes in C: The Art of Scientific Computing. New York: Cambridge University Press, pp. 202-203.

Index Terms:
edge detection; low-pass filters; location error; curved edges; low-pass filtered 2-D images; 3-D images; digital low-pass filtering; analog low-pass filtering; zero crossing; second derivative filter; edge localization criterion; second derivative in gradient direction; edge location; centers of curvature; linear Laplace filter; edge detector; PSF; diffraction limited optics; incoherent light; Gaussian filter with variable cutoff point; isotropic uniform filter
Citation:
P.W. Verbeek, L.J. van Vliet, "On the Location Error of Curved Edges in Low-Pass Filtered 2-D and 3-D Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 7, pp. 726-733, July 1994, doi:10.1109/34.297954
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