On the Validity of Fractal Dimension Measurements in Image Analysis

Fractal dimension is a parameter frequently used to analyze textures at different scales. There are several alternative definitions of the fractal dimension and consequently many algorithms have been proposed to determine its value. In this paper, we assess the robustness of all these algorithms. This is achieved by comparing their respective behavior under linear transformations of the image intensity values. A theoretical comparison shows that algorithms invariant to these transformations are restricted to Flat Structuring Element, Variogram, and Power Spectrum methods. This comparison is illustrated by experiments performed on simulated and natural images.