Encoding Cortical Surface by Spherical Harmonics

There is a lack of unified statistical modeling framework for cerebral shape asymmetry analysis in literature. Most previous approaches start with flipping the 3D magnetic resonance images (MRI). The anatomical correspondence across the hemispheres is then established by registering the original image to the flipped image. A difference of an anatomical index between these two images is used as a measure of cerebral asymmetry. We present a radically different asymmetry analysis that utilizes a novel weighted spherical harmonic representation of cortical surfaces. The weighted spherical harmonic representation is a surface smoothing technique given explicitly as a weighted linear combination of spherical harmonics. This new representation is used to parameterize cortical surfaces, establish the hemispheric correspondence, and normalize cortical surfaces in a unified mathematical framework. The methodology has been applied in characterizing the cortical asymmetry of a group of autistic subjects.