Ellipse-based Principal Component Analysis for Self-intersecting Curve Reconstruction from Noisy Point Sets

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 sel-fintersecting or nearly sel-fintersecting planar curve C -- C:[a,b]⊂R→R is self-intersecting if C(u)=C(v), u≠v, u,v∈(a,b) (C(u) is the self-intersection point) -- We consider only transversal self-intersections, 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 self-intersect cannot be distinguished from curves which nearly sel fintersect -- 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 self-intersections(nonmanifold neighborhoods) but also to occasional high noise at the nonselfintersecting (1manifold) neighborhoods

• Autores: Ruíz, O.; Vanegas, C.; Cadavid, C.
• Fecha de publicación: 2011
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: eng
• OAI Identifier: oai:repository.eafit.edu.co:10784/9681
• Acceso en línea: http://hdl.handle.net/10784/9681
• Palabra clave: CURVAS PLANAS; COLECTORES (INGENIERÍA); TOPOLOGÍA; VARIEDADES (MATEMÁTICAS); CORRELACIÓN (ESTADÍSTICA); ANÁLISIS ESTOCÁSTICO; FUNCIONES ELÍPTICAS; Curves, plane; Topology; Manifolds (Mathematics); Correlation (statistics); Stochastic analysis; Functions, elliptic; Curves; plane; Topology; Manifolds (Mathematics); Correlation (statistics); Stochastic analysis; Functions; elliptic; Reconstrucción superficial; Nube de puntos
• License: Springer-Verlag 2010