Fractal properties from 2D-curvature on multiple scales

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.