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Local Reproducible Smoothing Without Shrinkage
March 1993 (vol. 15 no. 3)
pp. 307-312

A simple local smoothing filter is defined for curves or surfaces, combining the advantages of Gaussian smoothing and Fourier curve description. Unlike Gaussian filters, the filter described has no shrinkage problem. Repeated application of the filter does not yield a curve or surface smaller than the original but simply reproduces the approximate result that would have been obtained by a single application at the largest scale. Unlike Fourier description, the filter is local in space. The wavelet transform of Y. Meyer (1989) is also shown to have these properties.

[1] G. Battle, "A block spin construction of ondelettes, Part 1: Lemairie functions,"Comm. Mach. Phys., vol. 110, pp. 601-615, 1987.
[2] R. Chellappa and R. Bagdazian, "Optimal Fourier coding of image boundaries," inProc. Conf. Patt. Recogn. Image Processing(Las Vegas), June 1982.
[3] B. K. P. Horn and E. J. Weldon, "Filtering closed curves,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, pp. 665-668, 1986.
[4] D. G. Lowe, "Organization of smooth image curves at multiple scales,"Int. J. Comput. Vision, vol. 3, pp. 119-130, 1989.
[5] P. G. Lemmairie, "Une Nouvelle Base d'Ondelettes deL2(Rn),"J. Math Pures Appl., vol. 67, pp. 221-236, 1988.
[6] S. G. Mallat, "Multiresolution approximations and wavelet orthornormal bases ofL2(R),"Trans. Amer. Math. Soc., vol. 315, no. 1, pp. 69-87, 1989.
[7] Y. Meyer, "Wavelets and operators, " inAnalysis at Urbana 1, London Mathematical Society Lecture Note Series 137(E. R. Berkson, N. T. Peck, and J. Uhl, Eds.). Cambridge, UK: Cambridge University Press, 1989.
[8] D. H. Marimont, "A representation for image curves," inProc. AAAI-84(Austin, TX), 1984, pp. 237-242.
[9] F. Moktarian and A. Mackworth, "Scale-based description and recognition of planar curves and two-dimensional shapes,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 1, pp. 34-43, Jan. 1986.
[10] E. Persoon and K. Fu, "Shape discrimination using Fourier descriptors,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, no. 3, pp. 388-397, May 1986.
[11] C. W. Richard and H. Hermami, "Identification of three-dimensional objects using Fourier descriptors of the boundary curve,"IEEE Trans. Syst. Man Cybern., vol. SMC-4, pp. 371-378, 1974.
[12] R. Szeliski,Bayesian Modeling of Uncertainty in Low-Level Vision, Boston: Kluwer, 1989.
[13] A. P. Witkin, "Scale-space filtering," inProc. IJCAI-83(Karlsruhe, West Germany), 1983, pp. 1019-1022.
[14] C. T. Zahn and R. Z. Roskies, "Fourier descriptors for plane closed curves,"IEEE Trans. Comput., vol. C-21, pp. 269-281, 1972.

Index Terms:
local reproducible smoothing filter; image processing; curves; surfaces; Gaussian smoothing; Fourier curve description; Fourier description; filtering and prediction theory; Fourier analysis; image processing
Citation:
J. Oliensis, "Local Reproducible Smoothing Without Shrinkage," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 3, pp. 307-312, March 1993, doi:10.1109/34.204914
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