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Tessellations à base de champs aléatoires gaussiens. Application à la modélisation spatiale et temporelle de l'endothélium cornéen humain.

Abstract : Tessellations, also called mosaics, are used to model many structures, for example cellular arrangements in biology or grains in material science. The most known tessellation is the Voronoï diagram which partitions the space from a set of points, called germs. The innovative approach of this thesis is to use Gaussian random fields to generate germs and random distances. The use of random fields allows to simulate a great variety of tessellations in terms of cells forms and sizes.To study the properties of each type of tessellation, they are characterized: first, by studying the germs, including their spatial distribution, and then by analyzing the cells geometry and morphometry. These tessellations are also compared to other known tessellations.The human corneal endothelium is a mono-layer of cells forming a regular hexagonal mosaic at birth, and losing his regularity later. The corneal graft quality is given by some observations made on the endothelial mosaic (cells density, the homogeneity of cells sizes and shapes).A database of endothelium images allows to characterize the evolution with age of the corneal mosaic. The originality is to estimate the age of an endothelium based on the measures computed to characterize the tessellations, and finally to set up a promising method to evaluate if a corneal evolution is normal.
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Submitted on : Friday, December 15, 2017 - 3:46:26 PM
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Klervi Rannou. Tessellations à base de champs aléatoires gaussiens. Application à la modélisation spatiale et temporelle de l'endothélium cornéen humain.. Autre. Université de Lyon, 2016. Français. ⟨NNT : 2016LYSEM032⟩. ⟨tel-01665180⟩

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