PRINCIPAL COMPONENT ANALYSIS -PCA- AND DELONE TRIANGULATIONS FOR PL APPROXIMATION C~1- CONTINUOUS 1-MANIFOLDS IN R~N

摘要

A Method is presented which combines statistical (Principal Component Analysis) and deterministic (Voronoi-Delone) methods to find Piecewise Linear approximations of curves C_i(u) in R~3 sampled with statistical noise. If the curves are self-intersecting, there are a finite number of points in which they are not 1-manifolds. Otherwise, they are 1-manifolds in all extents. The combination presented, of PCA and V-D methods, allows the recovery of 1-manifold approximations for C_i (u) for self-intersecting quasi-planar and non self-intersecting curves. In the later case the PCA alone succeeds in finding 1-manifold PL approximations for them. The algorithm implemented finds applications in contour and shape reconstruction from noisy data, subject to sampling errors or blockage.