<title>Wavelets and multiresolution analysis on sphere-like surfaces</title>

Abstract

We construct a multiresolution analysis and wavelets on the manifolds S² and SO(3). For C¹-functions on S² we derive the differentiability conditions for the singular points of their coordinate representation depending on polar coordinates. This leads in a natural way to tensor products of E-spline wavelets and wavelets on the interval. By using quaternion parameterization the case of SO(3) is reduced to the case of S³, which can be dealt with in the same way as S² using a special parameterization.