A metric of planar self-similar forms
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 wordsSelf-similar forms Iterative function system Botanical trees Distance measure
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