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Localization and Noise in Edge Detection
October 1989 (vol. 11 no. 10)
pp. 1106-1117

Two aspects of edge detection are analyzed, namely accuracy of localization and sensitivity to noise. The detection of corners and trihedral vertices is analyzed for gradient schemes and zero-crossing schemes. It is shown that neither scheme correctly detects corners of trihedral vertices, but that the gradient schemes are less sensitive to noise. A simple but important conclusion is that the noise present in digital images of typical indoor scenes is small and the signal-to-noise ratio is high. The noise present in digital images is so small as to make the performances of a variety of filters almost indistinguishable. As a consequence small filters can be used and the exact shape of the filter is not critical.

[1] R. Abraham and J. Robbin,Transversal Mappings and Flows. New York: Benjamin, 1967.
[2] L. Basano, P. Ottonello, and M. Straforini, "Power-of-two FIR filters in edge detection," (in preparation).
[3] M. Bertero, T. Poggio and V. Torre, "Ill-posed problems in early vision,"Proc. IEEE, 1988.
[4] V. Berzins, "Accuracy of Laplacian edge detectors,"Comput. Graph. Image Processing, vol. 27, pp. 195-201, 1984.
[5] J. F. Canny, "Finding lines and edges in images," Artificial Intell. Lab., Massachusetts Inst. Technol., Tech. Rep. TM-720, 1983.
[6] L. Davis, "A survey of edge-detection techniques,"Comput. Graph. Image Processing, vol. 4, pp. 248-270, 1975.
[7] E. De Micheli and G. Sandini, "On edge detection of trihedral vertexes,"Proc. III Int. Conf. Image Anal. Proc., Rapallo, Italy, 1986.
[8] R. Deriche, "Using Canny's criteria to derive an optimal edge detector recursively implemented,"Int. J. Comput. Vision, 1987.
[9] B. R. Frieden, "Linear and circular prolate functions," inProgress in Optics IX, E. Wolf, Ed., Amsterdam, The Netherlands: North Holland, pp. 312-408, 1971.
[10] R. M. Haralick, "Edge and region analysis for digital image data,"Comput. Graph. Image Proc., vol. 12, pp. 60-73, 1980.
[11] R. M. Haralick, "The digital edge,"Proc. Conf. Pattern Recogn. Image Proc., pp. 285-294, Dallas, TX, 1981.
[12] R. M. Haralick, "Zero-crossing of second directional derivative edge operator,"SPIE Proc. Robot Vision, Arlington, VA, 1982.
[13] A. Herskowitz and T. O. Binford, "On boundary detection," M.I.T., Cambridge, A.I. Memo 183, 1980.
[14] E. C. Hildreth, "Implementation of a theory of edge detection,"AI-TR- 579, AI Lab, Mass. Inst. Technol., 1980.
[15] B. K. P. Horn, "The Binford-Horn edge finder," M.I.T., Cambridge, A.I. Memo 285, 1972.
[16] W. H. H. Lunscher, "The asymptotic optimal frequency domain filter for edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 678-680, 1983.
[17] D. Marr and E. C. Hildreth, "Theory of edge detection,"Proc. Roy. Soc., vol. 207, pp. 187-217, 1980.
[18] V. S. Nalwa and T. O. Binford, "On detecting edges,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 699-714, 1986.
[19] K. F. Shanmugan, F. M. Dichey, and J. A. Green, "An optimal frequency domain filter for edge detection in digital pictures,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-1, pp. 37-49, 1979.
[20] D. Slepian, "Some asymptotic expansions for prolate spheroidal wave functions,"J. Math. Phys., vol. 44, pp. 99-149, 1965.
[21] R. Thom, "Quelques proprietes globales des varietes differentiables,"Commun. Math. Helv., vol. 28, pp. 17-86, 1954.
[22] A. N. Tikhonov and V. Y. Arsenin, "Solutions of ill-posed problem," Winston, Washington, D.C., 1977.
[23] V. Torre and T. A. Poggio, "On edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147-163, Mar. 1986.

Index Terms:
computerised picture processing; computerised pattern recognition; noise; edge detection; localization; sensitivity; trihedral vertices; gradient schemes; zero-crossing schemes; digital images; filters; computerised pattern recognition; computerised picture processing
E. De Micheli, B. Caprile, P. Ottonello, V. Torre, "Localization and Noise in Edge Detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 10, pp. 1106-1117, Oct. 1989, doi:10.1109/34.42841
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