PhD Position (October 2013-September 2016)
Geometrical modeling and characterization of crystal populations using stochastic geometry
Location / Institution: Ecole Nationale Supérieure des Mines / LGF UMR CNRS 5307, Saint-Étienne, FRANCE Thesis Supervisor: Dr. Hab. Johan DEBAYLE Co-Supervisor: Prof. Jean-Charles PINOLI
Required Qualifications:
o Candidates should have a Master of Science in applied mathematics and/or image and pattern analysis o Programming skills with Matlab and C/C++
o A good level of written and spoken English
Application Procedure: Candidates should send a cover letter with a CV to Johan DEBAYLE ([email protected])
Description:
• Context
The knowledge of the shape and size distributions of solid particle populations has been of increasing interest (both theoretical and practical) over the last decade. More particularly, crystals in liquid suspension are frequently used in industrial processes (e.g. for pharmaceutical technology) and is one of the LGF CNRS laboratory preoccupations. Their geometrical characterization is required for exploring the physico-chemical properties of crystallization processes.
Ammonium oxalate crystals (Optical imaging)
Zinc sulfide crystals (SEM imaging)
• Objectives:
The objective of this PhD thesis is to mathematically model, simulate and characterize complex distributions of crystals, with the use of stochastic geometry, integral geometry and stereology. The geometrical modeling of such crystal populations (as exposed in the figures) is needed for investigating their geometrical and morphological properties. Indeed, the individualization (and further geometrical characterization) of superimposed crystals remains a difficult task for high population densities. An alternative consists in using stochastic geometry that provides useful models for simulating a distribution of random geometrical patterns. The proposed models should take into account the different scales into the crystal population (e.g. the different aggregation levels). Numerical simulations will be realized for fitting the models to the real data. These models will provide statistical geometrical characteristics of the individual crystals, which are required for exploring the physico-chemical properties of crystallization processes. Nevertheless, the geometrical characterization of such models is still an area of ongoing research.
• Related references:
[1] M. Berchtold. Modelling of Random Porous Media using Minkowski Functionals. PhD Thesis, ETH Zurich, Swiss (2008).
[2] M. Lagarrigue, S. Jacquier, J. Debayle, F. Gruy and J.C. Pinoli. Approximation for the light scattering cross section of optically hard aggregates. Journal of Quantitative Spectroscopy and Radiative Transfer, 113(9):704-714 (2012).
[3] K. Michielsen and H. De Raedt. Integral geometry morphological image analysis. Physical Reports, 347:461-538 (2001).
[4] B. Presles, J. Debayle, and J. C. Pinoli. Size and shape estimation of 3-D convex objects from their 2-D projections.
Application to crystallization processes. Journal of Microscopy, 248(2):140-155 (2012).
[5] D. Stoyan, W.S. Hendall and J. Mecke. Stochastic geometry and its applications. Wiley (1987).
[6] I. S. Molchanov. Statistics of the Boolean Model for Practitioners and Mathematicians. Wiley, Chichester (1997).
[7] R. Schneider and W. Weil. Stochastic and Integral Geometry. Springer, Berlin Heidelberg (2008).
[8] O. Ahmad, J. Debayle, and J.-C. Pinoli. "A geometric-based method for recognizing overlapping polygonal shaped and semi-transparent particles in gray tone images", Pattern Recognition Letters, 32(15):2068-2079 (2011).
[9] O. Ahmad and J.-C. Pinoli. "On the linear combination of the Gaussian and student’s t random field and the integral geometry of its excursion sets", Statistics & Probability Letters, 83(2):559-567 (2013).
[10] J. Ohser, W. Nagel, K. Schladitz. "Miles formulae for Boolean models observed on lattices", Image Analysis and Stereology, 28(2):77-92 (2009)
