Normal Multiresolution Approximation of Curves

ABSTRACT. A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction. In this paper we study properties such as regularity, convergence, and stability of a normal multiresolution analysis. In particular we show that these properties critically depend on the underlying subdivision scheme and that in general the convergence of normal multiresolution approximations equals the convergence of the underlying subdivision scheme.