article
Ellipsebased principal component analysis for selfintersecting curve reconstruction from noisy point sets
Date
20110301Registration in:
01782789
14322315
WOS;000287450000004
SCOPUS;2s2.079951958575
10.1007/s003710100527x
Author
Ruiz, O.
Vanegas, C.
Cadavid, C.
Ruiz, O.
Vanegas, C.
Cadavid, C.
Institutions
Abstract
Surface reconstruction from cross cuts usually requires curve reconstruction from planar noisy point samples. The output curves must form a possibly disconnected 1manifold for the surface reconstruction to proceed. This article describes an implemented algorithm for the reconstruction of planar curves (1manifolds) out of noisy point samples of a selfintersecting or nearly selfintersecting planar curve C. C:[a,b]R?R 2 is selfintersecting if C(u)=C(v), u v, u,v (a,b) (C(u) is the selfintersection point). We consider only transversal selfintersections, i.e. those for which the tangents of the intersecting branches at the intersection point do not coincide (C (u)=C(v)). In the presence of noise, curves which selfintersect cannot be distinguished from curves which nearly selfintersect. Existing algorithms for curve reconstruction out of either noisy point samples or pixel data, do not produce a (possibly disconnected) Piecewise Linear 1manifold approaching the whole point sample. The algorithm implemented in this work uses Principal Component Analysis (PCA) with elliptic support regions near the selfintersections. The algorithm was successful in recovering contours out of noisy slice samples of a surface, for the Hand, Pelvis and Skull data sets. As a test for the correctness of the obtained curves in the slice levels, they were input into an algorithm of surface reconstruction, leading to a reconstructed surface which reproduces the topological and geometrical properties of the original object. The algorithm robustly reacts not only to statistical noncorrelation at the selfintersections (nonmanifold neighborhoods) but also to occasional high noise at the nonselfintersecting (1manifold) neighborhoods. © 2010 SpringerVerlag.
Subjects
Related items
Showing items related by title, author, creator and subject.

Reconstructing surface triangulations by their intersection matrices
Jorge L. Arocha; Javier Bracho; Natalia GarcíaColín; Isabel Hubard 
Ellipsebased principal component analysis for selfintersecting curve reconstruction from noisy point sets
Ruiz, O.; Vanegas, C.; Cadavid, C. (SPRINGER, 20110301)Surface reconstruction from cross cuts usually requires curve reconstruction from planar noisy point samples. The output curves must form a possibly disconnected 1manifold for the surface reconstruction to proceed. This ... 
Erratum: Ellipsebased principal component analysis for selfintersecting curve reconstruction from noisy point sets (Visual Computer DOI: 10.1007/s003710100527x)
Ruiz, O.; Vanegas, C.; Cadavid, C.; Ruiz, O.; Vanegas, C.; Cadavid, C. (SPRINGER, 20110101)[No abstract available]