Local approximation of curvature-bounded shape functions on S/sup 2/-diffeomorphic manifolds

Abstract

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 L/sup 2/ and bounded in norm with respect to their Laplacian by using local R/sup 2/ approximations to the S/sup 2/ shape functions. The approach used follows a line of argument presented by Daubechies (1990).<>