Statistical analysis of irregular anisotropic and heterogeneous textures

In this talk, I will review some statistical methods I developed for the analysis of the anisotropy or the heterogeneity of image textures.

I will present extended fractional Brownian field models that account for directional or spatial variations of the fields. I will then describe analysis methods based on observed field increments and their local and directed quadratic variations. I will then state some asymptotic normality results highlighting linear relations between theses quadratic variations and model parameters of interest.

Finally, I will present methods for testing or characterizing the anisotropy and heterogeneity, as well as their applications. To conclude, I will bring a new interpretation of these methods in a framework of deep neural networks and will trace some research perspectives opened by this interpretation.