I am interested in parameterizing a surface without a mesh. One technique used in the field of optics is to use Radial Basis Functions (e.g. Gaussians).
From a naive point of view, the decomposition of a 2D scalar field into Gaussian functions centered at various spatial locations doesn't sound that much different than wavelet transforms.
Being a novice at both wavelets and RBF's, both appear to be decomposition into a series of functions with finite extent as opposed to Fourier decomposition, Bessel function decomposition, Legendre polynomials, ... which tend to be distributed over the entire area of the 2D field.