Ellipse-based principal component analysis for self-intersecting curve reconstruction from noisy point sets
| Autor: | O. Ruiz, C. Cadavid, Carlos A. Vanegas |
|---|---|
| Přispěvatelé: | Universidad EAFIT. Departamento de Ingeniería Mecánica, Laboratorio CAD/CAM/CAE |
| Rok vydání: | 2010 |
| Předmět: |
Surface (mathematics)
ANÁLISIS ESTOCÁSTICO CURVAS PLANAS Geometry Ellipse Topology CORRELACIÓN (ESTADÍSTICA) Nube de puntos Piecewise linear function Manifolds (Mathematics) Intersection Functions Point (geometry) VARIEDADES (MATEMÁTICAS) Curves Reconstrucción superficial Mathematics Mathematical analysis Curves plane Tangent Stochastic analysis Computer Graphics and Computer-Aided Design TOPOLOGÍA Functions elliptic Transversal (combinatorics) COLECTORES (INGENIERÍA) Correlation (statistics) FUNCIONES ELÍPTICAS plane Computer Vision and Pattern Recognition elliptic Software Surface reconstruction |
| Zdroj: | Repositorio EAFIT Universidad EAFIT instacron:Universidad EAFIT |
| ISSN: | 1432-2315 0178-2789 |
| DOI: | 10.1007/s00371-010-0527-x |
| Popis: | 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 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink