Fractal properties from 2D-curvature on multiple scales
Erhardt Barth, Christoph Zetzsche, Mario Ferraro,
and Ingo Rentschler
ABSTRACT: Basic properties of 2D-nonlinear scale-space representations
of images are considered. First, local-energy filters are used to estimate
the Hausdorff dimension of images. A new fractal dimension, defined as
a property of 2D-curvature representations on multiple scales, is introduced
as a natural extension of traditional fractal dimensions, and it is shown
that the two types of fractal dimensions can give a less ambiguous description
of fractal image structure. Since fractal analysis is just one (limited)
aspect of scale-space analysis, some more general properties of curvature
representations on multiple scales are considered. Simulations are used
to analyse the stability of curvature maxima across scale and to illustrate
that spurious resolution can be avoided by extracting 2D-curvature features.
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