3D shape analysis of the brain cortex with application to dyslexia

To discriminate more accurately between dyslexic and normal brains, we detect the brain cortex variability through a spherical harmonic analysis that represents a 3D surface supported by the unit sphere, having a linear combination of special basis functions, called spherical harmonics (SHs). The proposed 3D shape analysis is carried out in five steps: (i) 3D brain cortex segmentation, with a deformable 3D boundary, controlled by two probabilistic visual appearance models (the learned prior and the estimated current appearance one); (ii) 3D Delaunay triangulation to construct a 3D mesh model of the brain cortex surface; (iii) mapping this model to the unit sphere; (iv) computing the SHs for the surface, and (v) determining the number of the SHs to delineate the brain cortex. We describe the brain shape complexity with a new shape index, the estimated number of the SHs, and use it for the K-nearest classification into the normal and dyslexic brains. Initial experiments suggest that our shape index is a promising supplement to the current dyslexia diagnostic techniques.