Project: Statistical Invariances and Geometry
Modeling for the Analysis of TEXtures (SIGMATEX) 
Application to high resolution Transmission Electron Microscopy (TEM) Imaging
Project abstract
In computer vision, image analysis,
virtual or augmented reality, the information content of images is mainly
defined by four components: texture, contours, contrast and color.
Texture plays a key role for visual
perception because it provides intrinsic information on the elements of the
scene imaged. Despite some decades of research on modeling the textural
information of images, texture characterization remains a challenge for the
scientific community: there exist no rigorous mathematical definition of
textures and texture modeling from statistical tools is not straightforward.
The aim of the project is the
investigation of a unified framework for texture characterization. This
framework is chosen to encompass natural and synthetic textures in both
grayscale and color cases associated with static and dynamic scenes. This
framework will integrate geometry transformations (rotation,
scale modification, perspectives ...) that are essential in defining
texture descriptors.
The project will consider applications at large, with a particular focus on
textures issued from high resolution transmission electron microscopy imaging.
The project is supported by RhoneAlps region in the terms of ARC6
grants (see http://www.arc6tic.rhonealpes.fr/ for more information). A PhD position is associated with the project.
Project motivation
The concept of texture is common to many
applications involving imaging systems, among which we can mention:

Monitoring the environment (forests, vegetation, farms, and buildings
are textured components in natural images),

Geosciences (textures of rocks, sediments, tectonic structures, etc.)

Composite materials (transmission electron microscopy, circuit diagrams
on electronic maps, aeronautics material, etc.),

Biology (tissues, cell structures, etc.),

Optics (interference fringes, distance perception, etc.),

Cosmology (topological defect of the universe, cosmic microwave
background radiation, etc.).
Texture plays a major role in modeling and
synthesis for virtual or augmented reality, in particular for video games.
Texture is also a main concept for increasing video definition in the stage of
postproduction of films. Because of its presence in several scientific and
technical fields, texture has motivated some trials on its definition, its
intrinsic properties and characterization from different formalisms, see
[Har79], Ala98a], [Do02], [Hil06],
[Jac11].
From the different mathematical formalisms
addressed in the literature on the topic, stochastic modeling allows both a
relevant texture description (it provides analytical tools relevant for
detection, recognition, segmentation...) [Ala05], [Att11], [Mor12], [Sor13] and
a reliable synthesis of this texture from computer simulation [Do02]. We will
consider such a stochastic modeling in the project.
It is worth noticing that there have been
relatively few attempts in taking into account geometric transformations
(rotation, scaling, perspective ...) in the statistical models proposed for
describing the distribution of texture components whereas such transformations
may affect textural information in both static and dynamic scenes [Kas86],
[Coh92], [Ala98b], [Hil06], [Mor08].
The project will address such joint
statistical and geometrical approaches to derive new properties such as the notion
of geometric stationarity (shape based stationarity or stationarity
associated with some given geometry invariance property) in order to propose
models adapted to digital processing, characterization and synthesis of
textures.
In addition, parsimonious functional
representations will play a main role in the project due to their capability in
enhancing texture features and simplifying statistical modeling. Indeed,
references [Ala98b], [Att13], have shown the suitability of FourierMellin and wavelet transforms to express more simply and to
estimate texture spectral features. These results, among others, justify the
role of functional representation spaces / transforms for effective
characterization of textures.
Among the application areas that require
the analysis and processing of textures, we will pay special attention to the
characterization of high resolution images of materials from the Transmission
Electron Microscopy (TEM). Two of the impacts described through the choice of
this application domain are: 1) the improvement of our understanding of fuel
based systems involving low environmental impact and 2) the postprocessing
making conventional and hybrid engine systems cleaner and more performant.
Research investigations
SIGMATEX project aims at proposing joint stochastic (random field analysis, cumulant
modeling, etc.) and geometry based (rotation, scale modification, perpectives, etc.) texture modeling. The notion of texture
invariances plays a key role in the research activities associated with
this project. The invariances are expected to derive from a unified
framework and to make possible a reliable texture synthesis from
invariance specifications. The project organization follows: a) the
investigation of generalized statistical frameworks including geometry
descriptions and b) the focus on an industrial context for TEM texture
analysis issued from the publicsector research centre
IFP Energies Nouvelles.
For more information,
contact:
Abdourrahmane M. ATTO, Abdourrahmane.Atto@univsavoie.fr, LISTIC, University
of Savoie, BP 80439, 74944 AnnecyleVieux Cedex, France, Olivier ALATA, olivier.alata@univstetienne.fr, Lab
Hubert Curien, UMR CNRS 5516, University Jean
Monnet, 18 Rue du Professeur Benoit Lauras,
SaintEtienne, France, Maxime MOREAUD, maxime.moreaud@ifpen.fr, IFP Energies nouvelles, BP3 69390 SOLAIZE, Zhangyun TAN, Zhangyun.Tan@univsavoie.fr, LISTIC, University of Savoie, BP 80439,
74944 AnnecyleVieux Cedex, France. 
References
[Ala98a] O. Alata, Texture Characterization from 2D reflexion coefficients. PhD Thesis, University de
Bordeaux I, 1998.
[Ala98b] O. Alata, C. Cariou, C. Ramananjarasoa and M. Najim, Classification of rotated and scaled
textures using HMHV spectrum estimation and the FourierMellin
Transform, in Proc. IEEE Int. Conf.
Image Proc. (ICIP), Vol. I, MA3, pp5356, Oct. 98,
Chicago, USA, 1998.
[Ala05] O. Alata and C. Ramananjarasoa, Unsupervised
Textured Image Segmentation using 2D Quarter Plane Autoregressive Support with
Four Prediction Support, Pattern
Recognition Letters, volume 26, pp. 10691081, 2005.
[Coh92] F. S. Cohen and Z. Fan, Maximum Likelihood unsupervised textured
image segmentation, CVGIP: Graphical models and image processing, vol. 54,
no. 3, pp. 239251, May 1992.
[Do02] Do, M. N., & Vetterli,
M., Waveletbased texture retrieval using
generalized Gaussian density and KullbackLeibler
distance, IEEE Transactions on Image Processing, 11(2), 146158, 2002.
[Har79] R. M. Haralick ; Statistical and structural approaches
to texture, Proc. IEEE, vol. 67, pp. 786804, 1979.
[Hil06] A. Hillion, C.
Roux, I. Donescu and O. Avaro,
Generalized secondorder invariance in texture modeling, Machine
Graphics & Vision, vol. 15, n° 1, pp. 7397, 2006.
[Kas86] R. L. Kashyap and A. Khotanzad, ‘ modelbased method for rotation invariant
texture classification, IEEE Trans. PAMI, vol. PAMI8, no. 4, pp. 472481,
July 1986.
[Att11] A. M. Atto and Y. Berthoumieu, How to
Perform Texture Recognition from Stochastic Modeling in the Wavelet Domain, IEEE International Conference on
Acoustics, Speech, and Signal Processing, ICASSP, Prague, Czech Republic, May
2011.
[Att13] A. M. Atto and Y.
Berthoumieu and P. Bolon, 2Dimensional
Wavelet Packet Spectrum for Texture Analysis, IEEE Transactions on Image
Processing, vol. 22, no. 6, June, 2013.
[Jac11] L. Jacques, L.
Duval, C. Chaux and G. Peyre,
A Panorama on Multiscale
Geometric Representations, Intertwining Spatial, Directional and Frequency
Selectivity, Signal Processing,
Special issue on Advances in Multirate Filter Bank
Structures and Multiscale Representations, December
2011.
[Mor08]
M. Moreaud, D. Jeulin, A. Thorel
and J . Y. ChaneChing, A
quantitative morphological analysis of nanostructured ceria–silica composite
catalysts, Journal of Microscopy, Vol. 232, Pt 2, pp. 293–305, 2008.
[Mor12] M. Moreaud, D. Jeulin, V.
Morard and R. Reval, TEM
image analysis and modeling: application to boehmites
nanoparticles, Journal of Microscopy, Vol. 245, Pt 2, pp. 186–199, 2012.
[Sor13]
L. Sorbier, A.S. Gay, A. Fecant,
M. Moreaud and N. Brodusch, Measurement of palladium
crust thickness on catalysts by optical microscopy and image analysis,
Microscopy and Microanalysis, 2013.