Texture analysis using complex system models: fractal dimension, swarm systems and non-linear diffusion

Texture is one of the primary visual attributes used to describe patterns found in nature. Several texture analysis methods have been used as powerful tools for real applications involving computer vision. However, existing methods do not successfully discriminate the complexity of texture patterns. Such methods disregard the possibility of describing image structures by fractal dimension. Fractality-based measures allow a noninteger geometric interpretation with applications in areas such as mathematics, physics, and biology. The central hypothesis of this work is that textures can be described as irregular fractal surfaces due to their complex geometry. Pushing the limits of the state-of-the-art, the results achieved in the four methodologies described in this work demonstrated the potential of using texture features in tasks of pattern recognition. The contributions of this work shall support significant advances in materials engineering, computer vision, and agriculture. Keywords-texture analysis; fractal dimension; swarm system; non-linear diffusion; complex networks