Abstract:
Joint work with Peter Straka and Steffen Winter.
Most of the known methods for estimating fractal dimensions are based on the evaluation of a
single geometric characteristic, usually the volume. We propose a method involving the evaluation of
several geometric characteristics, namely all the Minkowski functionals (i.e. volume, surface area,
Euler characteristic etc.). Motivated by recent results on the limiting behaviour of Minkowski functionals of
the parallel sets of self-similar fractals, we use these functionals to estimate the fractal dimension of sets
from digital images by regression and time series methods. Simultaneously, we also obtain estimates of the fractal curvatures of these sets, some
fractal counterpart of Minkowski functionals, allowing for a finer classification of fractal sets than fractal
dimension only.
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