ARFBF model for non stationary random fields and application in HRTEM images

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.

[1]  Patrick Flandrin,et al.  On the spectrum of fractional Brownian motions , 1989, IEEE Trans. Inf. Theory.

[2]  Maxime Moreaud,et al.  Measurement of Palladium Crust Thickness on Catalysts by Optical Microscopy and Image Analysis , 2013, Microscopy and Microanalysis.

[3]  Randy L. Vander Wal,et al.  A comparison of soot nanostructure obtained using two high resolution transmission electron microscopy image analysis algorithms , 2011 .

[4]  R. Revel,et al.  TEM image analysis and modelling: application to boehmite nanoparticles , 2012, Journal of microscopy.

[5]  D Jeulin,et al.  A quantitative morphological analysis of nanostructured ceria–silica composite catalysts , 2008, Journal of microscopy.

[6]  Jacques Lévy Véhel,et al.  The covariance structure of multifractional Brownian motion, with application to long range dependence , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[7]  Olivier Alata,et al.  Choice of a pertinent color space for color texture characterization using parametric spectral analysis , 2011, Pattern Recognit..

[8]  Olivier Alata,et al.  Unsupervised textured image segmentation using 2-D quarter plane autoregressive model with four prediction supports , 2005, Pattern Recognit. Lett..

[9]  Abdourrahmane M. Atto,et al.  Wavelet Packets of Fractional Brownian Motion: Asymptotic Analysis and Spectrum Estimation , 2010, IEEE Transactions on Information Theory.

[10]  J. L. Véhel,et al.  Stochastic fractal models for image processing , 2002, IEEE Signal Process. Mag..

[11]  Gabriel Rilling,et al.  Empirical mode decomposition, fractional Gaussian noise and Hurst exponent estimation , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[12]  Olivier Alata,et al.  Non-stationary texture synthesis from random field modeling , 2014, 2014 IEEE International Conference on Image Processing (ICIP).