Directional Fractal Dimension by Extended Box Counting Method

Abstract

The conventional fractal dimension is scalar-valued and cannot contain sufficient image information for image analysis. For example, spatial information such as the directionality and the configurative information are not represented by the fractal dimension. Overcoming these defects, in this paper, a new type of fractal feature, which we call the directional fractal dimension, is proposed and applied to image analysis. The feature is a generalization of box counting dimension and three fractal dimensions along x, y, z axis are calculated respectively, which contains directional information of the figure. The experiment verifies that the fractal feature is very useful for image analysis and classification.