Spherical harmonic decomposition for surfaces of arbitrary topology

Spherical harmonics have many valuable theoretic and practical applications in data and signal processing and modeling. It decomposes a given function defined on a sphere into a set orthogonal spherical harmonics. However, the given signal/function needs to be defined on a sphere domain. This paper studies the spherical harmonic decomposition for functions defined on general 2-dimensional manifold surfaces. We parameterize a surface with non-trivial topology onto a sphere domain, upon which the spherical harmonic decomposition can be conducted effectively. We demonstrate the effectiveness of our framework via progressive surface reconstruction.