A recently developed weighted spherical harmonic (SPHARM) representation will be presented. The weighted-SPHARM is a partial differential equation based shape representation technique that incorporates surface parameterization, surface data smoothing, and surface normalization in a unified framework. The weighted-SPHARM represents surface data as a weighted linear combination of spherical harmonics in such a way that the representation reduces the Gibbs phenomenon associated with Fourier series. Using the inherent angular symmetry of the spherical harmonics, surface shape can be decomposed into symmetric and asymmetric components. The resulting shape asymmetry index is given as the ratio of positive and negative order harmonics. As an illustration, the methodology is applied in characterizing and detecting abnormal cortical asymmetry pattern of autistic brain.
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