Analyse spectrale de la complexité du cortex cérébral

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Date(s) - 26/09/2017
14 h 00 min - 16 h 00 min


Soutenance de thèse

Title: Spectral analysis of the cerebral cortex complexity

Abstract: Surface shape complexity is a morphological characteristic of folded surfaces. In this thesis, we aim at developing some spectral methods to quantify this feature of the human cerebral cortex reconstructed from structural MR images. First, we suggest some properties that a standard measure of surface complexity should possess. Then, we propose two clear definitions of surface complexity based on surface bending properties. To quantify these definitions, we extended the recently introduced graph windowed Fourier transform to mesh model of surfaces. Through some experiments on synthetic surfaces, we show that our curvature-based measurements overcome the classic surface area-based ones which may not distinguish deep folds from oscillating ones with equal area. The proposed method is applied to a database of 124 healthy adult subjects. We also define the surface complexity by the Hölder regularity of fractional Brownian motions defined on manifolds. Then, for the first time, we develop a spectral-regression algorithm to quantify the Hölder regularity of a given fractional Brownian surface by estimating its Hurst parameter H. The proposed method is evaluated on a set of simulated fractional Brownian spheres. Moreover, assuming the cerebral cortex is a fractional Brownian surface, the proposed algorithm is applied to estimate the Hurst parameters of a set of 14 fetal cerebral cortices.

PhD candidate at I2M (SI team), LSIS (I&M team) and INT (MeCA team)

*Membres du jury :

Pierre Borgnat, ENS Lyon, rapporteur
Umberto Castellani, University of Verona, rapporteur
Bruno Torresanni, I2M (AMU), examiner
Isabelle Bloch, Telecom ParisTech, examiner
Roberto Toro, Institut Pasteur, examiner
Julien Lefèvre, LSIS (AMU), supervisor
Olivier Coulon, LSIS (AMU), supervisor
Frédéric Richard, I2M (AMU), supervisor


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