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Principal component analysis -PCA- and delone triangulations for PL approximation C-1-continuous 1-manifolds in R-N
(ACTA PRESS, 2004-01-01) Ruiz, OE; Cadavid, CA; Garcia, MJ; Martinod, R; Ruiz, OE; Cadavid, CA; Garcia, MJ; Martinod, R; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecánica Aplicada
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.