Fast B-Spline 2D Curve Fitting for unorganized Noisy Datasets
TypeCommunications sans actes
In the context of coordinate metrology and reverse engineering, freeform curve reconstruction from unorganized data points still offers ways for improvement. Geometric convection is the process of fitting a closed shape, generally represented in the form of a periodic B-Spline model, to data points [WPL06]. This process should be robust to freeform shapes and convergence should be assured even in the presence of noise. The convection's starting point is a periodic B-Spline polygon defined by a finite number of control points that are distributed around the data points. The minimization of the sum of the squared distances separating the B-Spline curve and the points is done and translates into an adaptation of the shape of the curve, meaning that the control points are either inserted, removed or delocalized automatically depending on the accuracy of the fit. Computing distances is a computationally expensive step in which finding the projection of each of the data points requires the determination of location parameters along the curve. Zheng et al [ZBLW12] propose a minimization process in which location parameters and control points are calculated simultaneously. We propose a method in which we do not need to estimate location parameters, but rather compute topological distances that can be assimilated to the Hausdorff distances using a two-step association procedure. Instead of using the continuous representation of the B-Spline curve and having to solve for footpoints, we set the problem in discrete form by applying subdivision of the control polygon. This generates a discretization of the curve and establishes the link between the discrete point-to-curve distances and the position of the control points. The first step of the association process associates BSpline discrete points to data points and a segmentation of the cloud of points is done. The second step uses this segmentation to associate to each data point the nearest discrete BSpline segment. Results are presented for the fitting of turbine blades profiles and a thorough comparison between our approach and the existing methods is given [ZBLW12, WPL06, SKH98].
Files in this item
Showing items related by title, author, creator and subject.
EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; DAMAK, Mohamed; GIBARU, Olivier (2014)Both contact and non-contact probes are often used in dimensional metrology applications, especially for roughness, form and surface profile measurements. To perform such kind of measurements with a nanometer level of ...
EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; GIBARU, Olivier; DAMAK, Mohamed (Elsevier, 2014)In the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an ...
EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; GIBARU, Olivier; DAMAK, Mohamed; BOURDET, Pierre (2014)Aspheric surfaces have become widely used in various fields ranging from imaging systems to energy and biomedical applications. Although many researches have been conducted to address their manufacturing and measurement, ...
EL HAYEK, Nadim; NOUIRA, Hichem; ANWER, Nabil; DAMAK, Mohamed; GIBARU, Olivier (IOP, 2014)The application of freeform surfaces has increased since their complex shapes closely express a product's functional specifications and their machining is obtained with higher accuracy. In particular, optical surfaces ...
Concept and architecture of a new apparatus for cylindrical form measurement with a nanometric level of accuracy VISSIERE, Alain; NOUIRA, Hichem; DAMAK, Mohamed; GIBARU, Olivier; DAVID, Jean-Marie (IOPSCIENCE, 2012)In relation to the industrial need and to the progress of technology, Laboratoire National de M´etrologie et d’Essais (LNE) would like to improve the measurement of its primary pressure standards, spherical and flick ...