A Fractal-Based Approach to Network Characterization Applied to Texture Analysis

This work proposes a new method for texture analysis that combines fractal descriptors and complex network modeling. At first, the texture image is modeled as a network. Then, the network is converted into a surface where the Cartesian coordinates and the vertex degree is mapped into a 3D point in the surface. Then, we calculate a description vector of this surface using a method inspired by the Bouligand-Minkowski technique for estimating the fractal dimension of a surface. Specifically, the descriptor corresponds to the evolution of the volume occupied by the dilated surface, when the radius of the spherical structuring element increases. The feature vector is given by the concatenation of the volumes of the dilated surface for different radius values. Our proposal is an enhancement of the classic complex networks descriptors, where only the statistical information was considered. Our method was validated on four texture datasets and the results reveal that our method leads to highly discriminative textural features.