Fractal properties from 2D curvature on multiple scales

Erhardt Barth; Christoph Zetzsche; Mario Ferraro; Ingo Rentschler

doi:10.1117/12.146648

23 June 1993 Fractal properties from 2D curvature on multiple scales

Erhardt Barth, Christoph Zetzsche, Mario Ferraro, Ingo Rentschler

Proceedings Volume 2031, Geometric Methods in Computer Vision II; (1993) https://doi.org/10.1117/12.146648
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

Basic properties of 2-D-nonlinear scale-space representations of images are considered. First, local-energy filters are used to estimate the Hausdorff dimension, D_H, of images. A new fractal dimension, D_N, defined as a property of 2-D-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 analyze the stability of curvature maxima across scale and to illustrate that spurious resolution can be avoided by extracting 2-D-curvature features.

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Erhardt Barth, Christoph Zetzsche, Mario Ferraro, and Ingo Rentschler "Fractal properties from 2D curvature on multiple scales", Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); https://doi.org/10.1117/12.146648

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