Uniqueness of the Gaussian Kernel for Scale-Space Filtering

  • Authors:
  • J, Babaud;A P Witkin;M Baudin;R O Duda

  • Affiliations:
  • -;-;-;-

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 1986

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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驴or its image by a linear differential operator驴is analyzed in terms of zero-crossing contours of the transform in scale-space.