2‐D Linear Stochastic Modeling

Alata, Olivier; Cariou, Claude

doi:10.1002/9780470611067.ch2

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-D Ar Model1

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2018

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“…At a fixed order, the parameters of θ QP M 1 ,M 2 , ∈ {1, 2}, are estimated thanks to minimization in the least-squares sense of prediction errors, see Ranganath and Jain (1985); Alata and Cariou (2008a). This procedure involves Yule-Walker equations and it is equivalent to the maximum likelihood estimation, when the random variables are Gaussian.…”

Section: -D Ar Modelmentioning

confidence: 99%

Arfbf Morphological Analysis - Application to the Discrimination of Catalyst Active Phases

Tan¹,

Moreaud²,

Alata³

et al. 2018

Image Anal Stereol

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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.

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Section: -D Ar Modelmentioning

confidence: 99%