Uniqueness of the Gaussian Kernel for Scale-Space Filtering
Babaud, Jean; Witkin, Andrew P.; Baudin, Michel; Duda, Richard O.
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Volume PAMI-8, Issue 1, Jan. 1986 Page(s):26 - 33
Digital Object Identifier   10.1109/TPAMI.1986.4767749
Summary: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.

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