Spherical Harmonics are a set of orthonormal basis functions defined over a sphere.
A function is a harmonic function if it satisfies Laplace's equation:
- The Laplacian (or trace of the hessian) is zero.
Spherical Harmonics are a set of orthonormal basis functions defined on the sphere.
Below are some explicit formulas for Laplace spherical harmonics stolen from 
There are functions for each band.
- where are the associated Legendre Polynomials
- l is the band, m is the function
For a real valued basis,
Below are distorted sphere visualizations where the radius corresponds to the value at each point.
Ruofei did a project on Saliency using Spherical Harmonics as part of his PhD dissertation.