Whittle maximum likelihood estimator for isotropic fractional Brownian images

Fractional Brownian motion (fBm) of H parameter is a stochastic fractal process that can be used to create virtual landscapes or to model 2D physical phenomenon. In this communication, we explore the Whittle maximum likelihood estimator (WMLE) to assess the H parameter of isotropic fBm images. We have compared a 1D estimator assessed from the lines increments of the image, to a 2D estimator of the 2D increments of the image. These 2 estimators were tested on 2D fBm generated using the exact Stein method. Results are of high quality. The mean H values are very close to the true ones for both estimators. The standard deviations of the 2D estimates are 2 times smaller than in 1D and should be preferred for practical application as for example texture analysis.