In previous works, we proposed a method to characterize jointly self-similarity and anisotropy properties of a large class of self--similar Gaussian random fields. We provide here a mathematical analysis of our approach, proving that the sharpest way of measuring smoothness is related to these anisotropies and thus to the geometry of these fields.
@article{arxiv.1302.0819,
title = {A strong optimality result for anisotropic self--similar textures},
author = {M. Clausel and B. Vedel},
journal= {arXiv preprint arXiv:1302.0819},
year = {2013}
}