Project: Statistical Invariances and Geometry Modeling for the Analysis of TEXtures (SIGMA-TEX) - 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 Rhone-Alps region in the terms of ARC6 grants (see 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 post-production 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 Fourier-Mellin 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 post-processing making conventional and hybrid engine systems cleaner and more performant.

Research investigations

SIGMA-TEX 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 public-sector research centre IFP Energies Nouvelles.

For more information, contact:


Abdourrahmane M. ATTO,,  LISTIC, University of Savoie, BP 80439, 74944 Annecy-le-Vieux Cedex, France,


Olivier ALATA,, Lab Hubert Curien, UMR CNRS 5516, University Jean Monnet, 18 Rue du Professeur Benoit Lauras, Saint-Etienne, France,


Maxime MOREAUD,, IFP Energies nouvelles, BP3 69390 SOLAIZE,


Zhangyun TAN,, LISTIC, University of Savoie, BP 80439, 74944 Annecy-le-Vieux Cedex, France.



[Ala98a] O. Alata, Texture Characterization from 2-D 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 Fourier-Mellin Transform, in Proc. IEEE Int. Conf. Image Proc. (ICIP), Vol. I, MA3, pp53-56, Oct. 98, Chicago, USA, 1998.

[Ala05] O. Alata and C. Ramananjarasoa, Unsupervised Textured Image Segmentation using 2-D Quarter Plane Autoregressive Support with Four Prediction Support, Pattern Recognition Letters, volume 26, pp. 1069-1081, 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. 239-251, May 1992.

[Do02] Do, M. N., & Vetterli, M., Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance, IEEE Transactions on Image Processing, 11(2), 146-158, 2002.

[Har79] R. M. Haralick ; Statistical and structural approaches to texture, Proc. IEEE, vol. 67, pp. 786-804, 1979.

[Hil06] A. Hillion, C. Roux, I. Donescu and O. Avaro, Generalized second-order invariance in texture modeling, Machine Graphics & Vision, vol. 15, n° 1, pp. 73-97, 2006.

[Kas86] R. L. Kashyap and A. Khotanzad, ‘ model-based method for rotation invariant texture classification, IEEE Trans. PAMI, vol. PAMI-8, no. 4, pp. 472-481, 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, 2-Dimensional 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. Chane-Ching, 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.