A statistical descriptor for texture images based on the box counting fractal dimension

This work proposes a method for supervised classification of grayscale texture images using the numerical computation of the box counting fractal dimension. Each pixel is mapped onto a point in a three-dimensional cloud, where the normalized gray level of each pixel is the third coordinate, and we analyze the distribution of points inside a mesh of boxes. Information at different resolutions are captured by varying the size of each box in the mesh. The texture descriptors are provided by a measure of organization of the points in the mesh, which is the entropy, and other statistical measures of this distribution, namely, mean, deviation and energy. We also propose a mathematical analysis of the model, which is accomplished here by employing techniques from Statistics and Combinatorics, quantifying the relation between the distribution of points and attributes classically associated to textures such as homogeneity and scale dependence. The proposed descriptors are applied to the classification of three well-known texture databases for benchmark purposes. In a comparison with other texture descriptors in the literature, the proposal demonstrated to be competitive, confirming the potential of a combination of box counting fractal dimension and statistics.