Piecewise Linear (PL) approximation of curves sampled with statistical noise

a curve must be reconstructed from a statistically sampled
un-ordered point set. In addition, in the particular case of planar or
quasi-planar curves, the point sample may resemble the one of a self -
intersecting curve. In any case, the synthesized PL approximation must
be a set of 1-manifolds, which excludes the possiblity of
self-intersections. The current presentation discusses methods based
on statistical and deterministic approaches to determine the PL
1-manifold approximation of the statistically sampled curves.