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Scaling Theorems for Zero-Crossings
January 1990 (vol. 12 no. 1)
pp. 46-54

Two scaling theorems are given. Instead of delta functions, polynomial functions are used as input. The advantages are twofold: the smoothness conditions on kernels are not required, so that kernels of the form e/sup -k mod X mod / can be included; the proofs are based on calculus completely and so can be more easily understood.

[1] A. Rosenfeld and M. Thurston, "Edge and curve detection for visual scene analysis,"IEEE Trans. Comput., vol. C-20, pp. 562-569, 1971.
[2] D. Marr,Vision. San Francisco, CA: Freeman, 1982.
[3] D. Marr and E. Hildreth, "Theory of edge detection,"Proc. Roy. Soc. London, vol. B207, pp. 187-217, 1980.
[4] A. P. Witkin, "Scale-space filtering, " inProc. IJCAI-8, 1983.
[5] 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.
[6] 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.

Index Terms:
pattern recognition; scaling theorems; zero-crossings; polynomial functions; smoothness conditions; pattern recognition; polynomials
Citation:
L. Wu, Z. Xie, "Scaling Theorems for Zero-Crossings," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 1, pp. 46-54, Jan. 1990, doi:10.1109/34.41383
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