Enhancement of the Box-Counting Algorithm for fractal dimension estimation

The box-counting (BC) method is frequently used as a measure of irregularity and roughness of fractals with self-similarity property due to its simplicity and high reliability. It requires a proper choice of the number of box sizes, corresponding sizes, and size limits to guarantee the accuracy of the fractal dimension estimation. Most of the existing BC methods utilize the geometric-step method, which causes a lack of fitting data points and wasted pixels for images of large size and/or arbitrary size. This paper presents a BC algorithm in combination with a novel sampling method and fractional box-counting method which will allow us to overcome some of limitations evident in the conventional BC method. The new sampling method introduces a partial competition based on the coverage of box sizes and takes more number of box sizes than the geometric-step method. To circumvent the border problem occurring for images of arbitrary size, the fractional box-counting method allows the number of the boxes to be real, rather than integer. To show its feasibility, the proposed method is applied to a set of fractal images of exactly known fractal dimension.