Conformal spherical representation of 3D genus-zero meshes

This paper describes an approach of representing 3D shape by using a set of invariant Spherical Harmonic (SH) coefficients after conformal mapping. Specifically, a genus-zero 3D mesh object is first conformally mapped onto the unit sphere by using a modified discrete conformal mapping, where the modification is based on Möbius Factorization and is aimed at obtaining a canonical conformal mapping. Then a Spherical Harmonic Analysis is applied to the resulting conformal spherical meshes. The obtained SH coefficients are further made invariant to translation and rotation, while at the same time retain their completeness, so that the original shape information has been faithfully preserved. keyword: conformal mapping, shape invariant, spherical harmonics, shape representation.