Principal Component Analysis -PCA- and Delone Triangulations for PL Approximation C1-continuous 1-Manifolds in RN

O.E. Ruiz, C.A. Cadavid, M.J. Garcia, and R. Martinod (Colombia)

Keywords

Manifold Reconstruction, Principal Component Analysis, VoronoiDelaunay Methods, Medial Axis, Stochastic Geometry

Abstract

A Method is presented which combines statistical (Prin cipal Component Analysis) and deterministic (Voronoi Delone) methods to find Piecewise Linear approxima tions of curves Ci(u) in 3 sampled with statistical noise. If the curves are self-intersecting, there are a finite num ber of points in which they are not 1-manifolds. Oth erwise, they are 1-manifolds in all extents. The com bination presented, of PCA and V-D methods, allows the recovery of 1-manifold approximations for Ci(u) for self-intersecting quasi-planar and non self-intersecting curves. In the later case the PCA alone succeeds in find ing 1-manifold PL approximations for them. The al gorithm implemented finds applications in contour and shape reconstruction from noisy data, subject to sampling errors or blockage.

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