Fractal Curvature Measures and Image Analysis

Abstract

Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_{\epsilon }:=\{x\in {\mathbb{R}}^d:d(x,F)\le \epsilon \}$ as $\epsilon \downarrow 0$ is known, leading to the notion of fractal curvatures $C_k^f(F)$, $k\in \{0,\dots ,d\}$. The dependence of the growth behaviour on the fractal dimension $s=\dim F$ is exploited, and estimators for $s$ and $C_k^f(F)$ are derived. The performance of these estimators is tested on binary images of self-similar sets.

95 pages, 23 figures

Cited by in corpus (1)

• Estimation of fractal dimension and fractal curvatures from digital images