Various Mathematical Approaches to Extract Information from Textures of Increasing Complexities

Dealing with several structures of different complexities, we adopt various strategies to extract information. The general idea is to find appropriate tools to analyze the variation of the corresponding autocorrelation functions. First, for homogeneous media under different conditions, we recover, in a statistical way, a relationship between porosity and the autocorrelation function. Then, for low-complexity textures, we exploit this relationship to extract complementary parameters from the autocorrelation function beyond porosity using spectral analysis. For fractal-like structures, we process them according to their porosity. For fat fractals,usually used as synthetic models of porous media, we combine the regularization dimension, a method proposed to estimate the curve variation, with the autocorrelation function. This leads to a more robust classification. For fractals of negligible porosity, such as fractals of non-integer dimension, we discuss how the method HMSF we developed serves as an original means to estimate the Hausdorff dimension and how it can be exploited to give complementary characteristic parameters.