Surface Harmonics for Shape Modeling

We present an approach for three dimensional (3D) shape modeling using Jacobi polynomials based surface harmonics. Because we construct a set of complete hemispherical harmonic basis functions on a hemisphere domain from the associated Jacobi polynomials, our shape modeling method work efficiently on the open hemisphere-like objects that often exist in medical anatomical structures (e.g., ventricles, atriums, etc.). We demonstrate the effectiveness of our approach through theoretic and experimental exploration of a set of medical image applications.