A Method of Calculating Image Fractal Dimension Based on Fractal Brownian Model

Abstract

DBC (Differential Box-Counting) has been proved the least complex and the most convenient way to calculate the fractal dimension of images. However, for images with low resolution, the existence of empty boxes will influence the accuracy of fractal dimension. In order to reduce its effect, a new approach ADBC (Actual Differential Box-counting) is proposed in this paper. First, the empty boxes are classified into two categories: real empty boxes and potential ones. Then, the probability of the empty boxes being potential ones under higher resolution is determined by associating the spatial domain relations between the Fractional Brownian surface model and the pixel’s gray-level. Thus, the more accurate fractal dimension can be obtained even if the image resolution is not high enough. Experimental tests also indicate that with the complexity of calculation being basically the same, ADBC can effectively improve the accuracy of fractal dimension.