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Learnt knot placement in B-spline curve approximation using support vector machines

  • Knot placement for curve approximation is a well known and yet open problem in geometric modeling. Selecting knot values that yield good approximations is a challenging task, based largely on heuristics and user experience. More advanced approaches range from parametric averaging to genetic algorithms. In this paper, we propose to use Support Vector Machines (SVMs) to determine suitable knot vectors for B-spline curve approximation. The SVMs are trained to identify locations in a sequential point cloud where knot placement will improve the approximation error. After the training phase, the SVM can assign, to each point set location, a so-called score. This score is based on geometric and differential geometric features of points. It measures the quality of each location to be used as knots in the subsequent approximation. From these scores, the final knot vector can be constructed exploring the topography of the score-vector without the need for iteration or optimization in the approximation process. Knot vectors computed with our approach outperform state of the art methods and yield tighter approximations.

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Metadaten
Author:Pascal Laube, Matthias O. FranzORCiDGND, Georg UmlaufORCiDGND
DOI:https://doi.org/10.1016/j.cagd.2018.03.019
ISSN:0167-8396
Parent Title (English):Computer Aided Geometric Design
Volume:62
Document Type:Article
Language:English
Year of Publication:2018
Release Date:2019/01/18
First Page:104
Last Page:116
Institutes:Institut für Optische Systeme - IOS
Open Access?:Nein
Relevance:Peer reviewed Publikation in Thomson-Reuters-Listung
Licence (English):License LogoLizenzbedingungen Elsevier