Local approximation of curvature-bounded shape functions on S2 -diffeomorphic manifolds

The explosive growth in the availability of three-dimensional imaging technologies (such as magnetic resonance imagery (MRI) and computer-assisted tomography (CAT)) has transformed the issue of three-dimensional shape description from a purely abstract exercise in differential geometry to one with practical implications. The paper explores the problem of constructing a rotationally-invariant “sampling lattice” for objects which are diffeomorphic to the unit sphere whose shape functions are L² and bounded in norm with respect to their Laplacian by using local R² approximations to the S² shape functions. The approach used follows a line of argument presented by Daubechies (1990)