Preserving Relative Dimension Rankings in the Presence of Noise Using the Box-Counting Algorithm

Abstract

Fractal dimension is a number that describes the degree of self-similarity, or "complexity", of a particular geometry. In digital image processing, fractal dimension is often used to provide quantitative comparisons between digital images. The Box-Counting Algorithm is one of the more widely used methods for estimating fractal dimension, although it has been shown to be highly sensitive to digital filtering and noise. This research investigates the variability in fractal dimension estimates obtained from the Box-Counting Algorithm as noise is applied to an image. In the case of increasing uniform noise, three distinct relationships emerge between dimensional estimates and their variability. It is then shown how these relationships may be leveraged to improve relative rankings among dimensional estimates when using the Box-Counting Algorithm.