A metric of planar self-similar forms

  • Atsushi Imiya
  • Yasumitsu Fujiwar
  • Toshiyuki Kawashima
Morpology and Mathematical Approaches to Pattern Recognition
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1121)


In this paper, we define a metric of planar self-similar forms. Self-similarity is one of the fundamental geometric properties which define configurations of geometric elements on the planes and in the space, such as line segments, parts of curves, and blocks. Thus, as the first step in the discrimination of complex objects, which are constructed from basic elements by their structures, we define a metric of self-similarity forms. The iterative function system, IFS, is a method for describing self-similar forms. Since a set of metrices defines an IFS, we define a metric among self-similar forms using the matrix norm of metrices which define IFS's. We also introduce a method for the estimation of parameters of IFS's from measured data of planar trees.

Key words

Self-similar forms Iterative function system Botanical trees Distance measure 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Atsushi Imiya
    • 1
  • Yasumitsu Fujiwar
    • 1
  • Toshiyuki Kawashima
    • 1
  1. 1.Dept. of Information and Computer SciencesChiba UniversityChibaJapan

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