Scale Space Smoothing, Image Feature Extraction and Bessel Filters

  • Sasan Mahmoodi
  • Steve Gunn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6688)


The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian filters. The features extracted by the Bessel filter are therefore scale invariant. Edges, blobs, and junctions are features considered here to show that the extracted features remain unchanged by varying the scale of a Bessel filter. The scale invariance property of Bessel filters for edges is analytically proved here. We conjecture that Bessel filters also enjoy this scale invariance property for other kinds of features. The experimental results presented here confirm our conjecture of the scale invariance property of the Bessel filters.


Scale Space Linear Filtering Bessel Filter Feature Extraction 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sasan Mahmoodi
    • 1
  • Steve Gunn
    • 1
  1. 1.School of Electronics and Computer Science, Building 1Southampton UniversitySouthamptonUK

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