Fractal Curvature Measures and Image Analysis

2015/01/03 by Peter Straka, Straka, Peter
Mathematics · #28A80 #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #math.MG #msc:28A80

paper · pdf · doi:10.48550/arxiv.1501.00530

95 pages, 23 figures

arxiv created 2015/01/03 · openalex publication_date 2015/01/03 · arxiv updated 2015/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_ε := \x∈ \mathbb R^d : d(x,F)≤ ε\ as ε \downarrow 0 is known, leading to the notion of fractal curvatures C_k^f(F), k∈ \0,…,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.

Related

• Fractal curvature measures of self-similar sets
• Fractal curvatures and Minkowski content of self-conformal sets
• Curvature Bounds for Neighborhoods of Self-Similar Sets
• Scaling exponents of curvature measures
• Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets