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This paper presents a new model called Autoregressive Fractional Brownian Field (ARFBF) for analyzing textures which contain stationary and non-stationary components. The paper also proposes two estimation methods for the parameter of an isotropic fractional Brownian field based on Wavelet Packet (WP) spectrum: the Log-Regression on Diagonal WP spectrum (Log-RDWP) and the Log-Regression on Polar representation of WP spectrum (Log-RPWP). The Log-RPWP method provides a better estimation performance for small size images. We show the interest of ARFBF model and Log-RPWP for characterizing High-Resolution Transmission Electron Microscopy (HRTEM) images.

This paper addresses the characterization of spatial arrangements of fringes in catalysts imaged by High Resolution Transmission Electron Microscopy (HRTEM). It presents a statistical model-based approach for analyzing these fringes. The proposed approach involves Fractional Brownian Field (FBF) and 2-D AutoRegressive (AR) modeling, as well as morphological analysis. The originality of the approach consists in identifying the image background as an FBF, subtracting this background, modeling the residual by 2-D AR so as to capture fringe information and, finally, discriminating catalysts from fringe characterizations obtained by morphological analysis. The overall analysis is called ARFBF (Auto-Regressive Fractional Brownian Field) based morphology characterization.