Weighted Spherical Harmonic Representation and Its Application to Cortical Analysis

We present a novel weighted spherical harmonic (SPHARM) representation of cortical surfaces and its application to a cortical thickness analysis in autism. The weighted-SPHARM is a hierarchical smoothing technique given as the solution to a parabolic partial differential equation. The weighted-SPHARM generalizes the classical-SPHARM with an additional parameter that modulates the high frequency content of data. We introduce a new algorithm called the iterative residual fitting (IRF) and address the problem of determining the optimal degree of the weighted-SPHARM. As an illustration, our unified framework has been applied in detecting the regions of abnormal behavior-structure correlation in a group of autistic subjects.