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Uniqueness of the Gaussian Kernel for Scale-Space Filtering
January 1986 (vol. 8 no. 1)
pp. 26-33
Jean Babaud, Schlumberger Computer Aided Systems, Palo Alto, CA 94304.
Andrew P. Witkin, Schlumberger Computer Aided Systems, Palo Alto, CA 94304.
Michel Baudin, Schlumberger Computer Aided Systems, Palo Alto, CA 94304.
Richard O. Duda, Syntelligence. Sunnyvale, CA.
Scale-space filtering constructs hierarchic symbolic signal descriptions by transforming the signal into a continuum of versions of the original signal convolved with a kernal containing a scale or bandwidth parameter. It is shown that the Gaussian probability density function is the only kernel in a broad class for which first-order maxima and minima, respectively, increase and decrease when the bandwidth of the filter is increased. The consequences of this result are explored when the signal¿or its image by a linear differential operator¿is analyzed in terms of zero-crossing contours of the transform in scale-space.
Citation:
Jean Babaud, Andrew P. Witkin, Michel Baudin, Richard O. Duda, "Uniqueness of the Gaussian Kernel for Scale-Space Filtering," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 8, no. 1, pp. 26-33, Jan. 1986, doi:10.1109/TPAMI.1986.4767749
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