Soutenance de la thèse de RABIEI Hamed

26 septembre 2017

Spectral analysis of the cerebral cortex complexity

Mardi 26 Septembre, 14h00, Amphithéatre de la faculté d’Odontologie, Campus de La Timone


Jury :

  • Pierre Borgnat, ENS Lyon, rapporteur
  • Umberto Castellani, Université de Vérone, rapporteur
  • Bruno Torresanni, I2M (AMU), examinateur
  • Isabelle Bloch, Telecom ParisTech, examinateur
  • Roberto Toro, Institut Pasteur, examinateur
  • Julien Lefèvre, LSIS, directeur de thèse
  • Olivier Coulon, LSIS, directeur de thèse
  • Frédéric Richard, I2M, directeur de thèse

Résumé :

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.

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