Simulation and analysis of 3D microstructures by Minkowski functionals and deep learning

The core of the GEOFIELD project is to understand the geometry of random fields (denoted RF), in order to obtain practical tools for modeling and simulating actual spatial structures. Roughly speaking, a RF is denoted by a random variable in each physical point of a spatial domain and the correlation structure between neighbors. These random objects are practical when

modeling real structures like the surface of hip implants [1], human corneal endotheliums [4] and fuel cells [3]. This project focuses on Gaussian RFs because they are fully characterized by their covariance

function.

For stationary Gaussian RFs with given covariance structure, a fairly standard method using the Fourier transform can e fficiently speed-up the process [2]. To extend this e fficient approach for

non-stationary RFs, one could consider a RF G constructed by

the combination of several RFs (Gi; i = 1; : : : ;N), which is a sequence of independent, stationary Gaussian RFs, where the covariance of each is given by a window function (and thus localised in space).

Objective

Select the appropriate window functions fi and stationary covariance functions CGi to approximate a given covariance function CG e ciently. These RFs will be used to develop simulation models of Ni-YSZ anodes for fuel cells.

[1] O. Ahmad and J.-C. Pinoli. On the linear combination of the gaussian and student's t random eld and the integral

geometry of its excursion sets. Statistics & Probability Letters, 83(2):559{567, 2013.

[2] A. Lang and J. Pottho . Fast simulation of Gaussian random elds. Monte Carlo Methods and Applications,

17(3):195{214, 2011.

[3] H. Moussaoui, J. Laurencin, Y. Gavet, G. Delette, M. Hubert, P. Cloetens, T. L. Bihan, and J. Debayle. Stochastic

geometrical modeling of solid oxide cells electrodes validated on 3d reconstructions. Computational Materials Science,

143:262 { 276, 2018.

[4] K. Rannou, E. Crouzet, C. Ronin, P. Guerrero, G. Thuret, P. Gain, J. Pinoli, and Y. Gavet. Comparison of Corneal

Endothelial Mosaic According to the Age: The CorImMo 3D Project. IRBM, 37(2):124{130, 2016.

Funding category: Contrat doctoral



PHD title: Doctorat en Image, Vision, Signal

PHD Country: France