title: Uniqueness of the gaussian kernel for scale-space filtering.
abstract: 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.
authors.affiliation: Schlumberger Computer Aided Systems, Palo Alto, CA 94304.
authors.forename: J
authors.initials: J
authors.lastname: Babaud
authors.forename: A P
authors.initials: AP
authors.lastname: Witkin
authors.forename: M
authors.initials: M
authors.lastname: Baudin
authors.forename: R O
authors.initials: RO
authors.lastname: Duda