Authors:
Oscar E. Ruiz
1
;
C. Cortés
1
;
M. Aristizábal
1
;
Diego A. Acosta
1
and
Carlos A. Vanegas
2
Affiliations:
1
Universidad EAFIT, Colombia
;
2
University of California, United States
Keyword(s):
Parametric Curve Reconstruction, Noisy Point Cloud, Principal Component Analysis, Minimization.
Related
Ontology
Subjects/Areas/Topics:
CAGD/CAD/CAM Systems
;
Computer Vision, Visualization and Computer Graphics
;
Geometric Computing
;
Geometry and Modeling
;
Modeling and Algorithms
Abstract:
Curve reconstruction from noisy point samples is central to surface reconstruction and therefore to reverse engineering, medical imaging, etc. Although Piecewise Linear (PL) curve reconstruction plays an important role, smooth (C^1-, C^2-,...) curves are needed for many applications. In reconstruction of parametric curves from noisy point samples there remain unsolved issues such as (1) high computational expenses, (2) presence of artifacts and outlier curls, (3) erratic behavior of self-intersecting curves, and (4) erratic excursions at sharp corners. Some of these issues are related to non-Nyquist (i.e. sparse) samples. In response to these shortcomings, this article reports the minimization-based fitting of parametric curves for noisy point clouds. Our approach features: (a) Principal Component Analysis (PCA) pre-processing to obtain a topologically correct approximation of the sampled curve. (b) Numerical, instead of algebraic, calculation of roots in point-to-curve distances. (
c) Penalties for curve excursions by using point cloud – to - curve and curve – to – point cloud. (d) Objective functions which are economic to minimize. The implemented algorithms successfully deal with self - intersecting and / or non-Nyquist samples. Ongoing research includes self-tuning of the algorithms and decimation of the point cloud and the control polygon.
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