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Evolutionary computation for optimal knots allocation in smoothing splines of one or two variables

P. Gonzalez, H. Idais, M. Pasadas, M. Yasin
2018 International Journal of Computational Intelligence Systems  
When approximating, or fitting, a surface to a given data set inside a rectangle using B-splines, the main idea is to use an appropriate multi-objective genetic algorithm to optimize both the number of  ...  In this paper, a new methodology is presented for optimal knots' placement when approximating functions of one or two variables.  ...  The method in 17 describes the unified averaging technique, for both approximation and interpolation problems, concerning knots placement for B-spline curves.  ... 
doi:10.2991/ijcis.11.1.96 fatcat:32pxhcuatrdejcst6vmjaflwki

Page 6227 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
Using knot interval notation, the paper introduces MD-splines, which are B-spline- like curves that are comprised of polynomial segments of various degrees (MD stands formulti-degree’).  ...  Summary: “This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot in- sertion, differentiation  ... 

Multiscale B-spline snakes for general contour detection

Patrick Brigger, Michael A. Unser, Andrew F. Laine, Michael A. Unser, Akram Aldroubi
1998 Wavelet Applications in Signal and Imaging Processing VI  
The optimization procedure is embedded into a multi-resolution image representation, where the number of snake points is adapted to the image grid spacing by correctly adjusting the spline knot spacing  ...  We propose an alternative formulation using cubic B-splines, where the knot spacing is variable and controlled by the user.  ...  The authors would like to thank Akram Aldroubi for his numerous inputs with respect to mathematically related problems, Murray Eden for his valuable discussions, and Philippe Thevenaz for his suggestions  ... 
doi:10.1117/12.328127 fatcat:rp6fe7yojra5leew5g5qiw66cu

A High-Accuracy Single Patch Representation of Multi-Patch Geometries with Applications to Isogeometric Analysis

Jinlan Xu, Ningning Sun, Gang Xu
2020 CMES - Computer Modeling in Engineering & Sciences  
This paper presents a novel approximating method to construct highprecision single-patch representation of B-spline surface from a multi-patch representation for isogeometric applications.  ...  With the proposed approximating method, isogeometric analysis results using the new single-patch can be obtained efficiently compared with the original multi-patch structure.  ...  They optimized the position of control points to merge two B-spline curves as precisely as possible, and adjusted the knots to avoid superfluous knots. Harish et al.  ... 
doi:10.32604/cmes.2020.010341 fatcat:cn2ejmj2l5cghlatp6s7noj5ce

B-Spline Curve Fitting with Intelligent Water Drops (IWD)

Kübra Uyar, Erkan Ülker, Ahmet Arslan
2016 International Journal of Intelligent Systems and Applications in Engineering  
It is obvious that the selection of knot points in B-spline curve approximation has an important and considerable effect on the behaviour of final approximation.  ...  The curve behind of the model can be obtained by doing approximation of control points, approximation of knot points or parameterization.  ...  This work was also accepted among the "selected papers".  ... 
doi:10.18201/ijisae.2016specialissue-146975 fatcat:6lersfxiozf5plkcn2ks44rjlm

Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: Explicit time-stepping and efficient mass matrix inversion

Jesse Chan, John A. Evans
2018 Computer Methods in Applied Mechanics and Engineering  
We show how the use of optimal knot vectors can improve both approximation properties and the maximum stable timestep, and present a simple heuristic method for approximating optimal knot positions.  ...  Finally, we explore the use of optimal knot vectors based on L2 n-widths.  ...  Acknowledgments The authors thank Joseph Benzaken help in constructing the three-dimensional pipe elbow geometry.  ... 
doi:10.1016/j.cma.2018.01.022 fatcat:ben7okfqsrfzhnky3teaamptmu

Adaptive B-spline knot selection using multi-resolution basis set

Yuan Yuan, Nan Chen, Shiyu Zhou
2013 IIE Transactions  
However, how to place the knots appropriately in B-spline curve fitting remains a difficult problem.  ...  At the first stage, we selected a subset of basis functions from the pre-specified multi-resolution basis set using the statistical variable selection method-Lasso.  ...  In the literature, many research works in B-spline curve fitting focused on how to optimize the control points when the knots vector is given.  ... 
doi:10.1080/0740817x.2012.726758 fatcat:42iqupmvrzeqpaa3pzclsr3xzm

B-Spline Curve Approximation Using Pareto Envelope-Based Selection Algorithm – PESA

Erkan Ülker
2013 International Journal of Computer and Communication Engineering  
An Application environment which is collected reverse engineering methods and approaches of the algorithm was improved and the node estimation process of B-spline curves is introduced using PESA.  ...  The most common problems which constitute the subject of research in the field of computer-based modeling are to predict the desired shape of the curve for a set of given points.  ...  B-SPLINE CURVE KNOT APPROXIMATION Process step of B-spline curve node estimation are following [Ülker, 2007]; 1) Firstly, among the available points offered of outside is selected and centripetal  ... 
doi:10.7763/ijcce.2013.v2.137 fatcat:4rvqfe374bcoro4ilpecqgmhga

Automatic smoothing by optimal splines

Ricardo Biloti, Lúcio T. Santos, Martin Tygel
2003 Revista Brasileira de Geofisica  
From an a priori selection of the number of knots that define the adjusting spline, but not their location in that curve, the method automatically determines the adjusting cubic spline in a least-squares  ...  The method is fast and easily allows for selection of various possible number of knots, adding a desirable flexibility to the procedure.  ...  Acknowledgements This work was kindly supported by CNPq & FAPESP (Brazil) and the sponsors of the Wave Inversion Technology (WIT) Consortium, Karlsruhe, Germany.  ... 
doi:10.1590/s0102-261x2003000200006 fatcat:js6sp5554zhu7fp6i3mx7zu2vq

An Artificial Immune System Approach for B-Spline Surface Approximation Problem [chapter]

Erkan Ülker, Veysi İşler
2007 Lecture Notes in Computer Science  
In surface fitting problems, the selection of knots in order to get an optimized surface for a shape design is well-known.  ...  This paper presents an application of another computational intelligence technique known as "Artificial Immune Systems (AIS)" to the surface fitting problem based on B-Splines.  ...  Acknowledgements This study has been supported by the Scientific Research Projects of Selcuk University (in Turkey).  ... 
doi:10.1007/978-3-540-72586-2_7 fatcat:gaccud6r7nbhfi2japnp4nz744

The Joint Estimation of Term Structures and Credit Spreads

Patrick Houweling
1999 Social Science Research Network  
We present a new framework for the joint estimation of the default-free government term structure and corporate credit spread curves.  ...  To determine the 'optimal' model specification, we use a newly developed test statistic that compares spread curves from competing models. q  ...  Acknowledgements Part of the research was conducted while the first author was affiliated with the Quantitative Research Department of the Robeco Group.  ... 
doi:10.2139/ssrn.157652 fatcat:xqqulcxpujdjjnbnyrqdcfgity

The joint estimation of term structures and credit spreads

Patrick Houweling, Jaap Hoek, Frank Kleibergen
2001 Journal of Empirical Finance  
We present a new framework for the joint estimation of the default-free government term structure and corporate credit spread curves.  ...  To determine the 'optimal' model specification, we use a newly developed test statistic that compares spread curves from competing models. q  ...  Acknowledgements Part of the research was conducted while the first author was affiliated with the Quantitative Research Department of the Robeco Group.  ... 
doi:10.1016/s0927-5398(01)00026-3 fatcat:zxbha632crdmrhwp7fohynu57a

Knot calculation for spline fitting via sparse optimization

Hongmei Kang, Falai Chen, Yusheng Li, Jiansong Deng, Zhouwang Yang
2015 Computer-Aided Design  
Our experiments show that the approximation spline curve obtained by our approach has less number of knots compared to existing methods.  ...  This paper presents a framework for computing knots (including the number and positions) in curve fitting based on a sparse optimization model.  ...  Acknowledgments The authors thank the reviewers for providing useful comments and suggestion.  ... 
doi:10.1016/j.cad.2014.08.022 fatcat:3kw5xsjtjne6lhpplb2tgo5h2e

Parametric Surface Modelling for Tea Leaf Point Cloud Based on Non-Uniform Rational Basis Spline Technique

Wenchao Wu, Yongguang Hu, Yongzong Lu
2021 Sensors  
The PSF was firstly fitted as B-spline surface and then was transformed to NURBS form by minimizing fitting error, which was solved by particle swarm optimization (PSO).  ...  Finally, the PSF was fitted into non-uniform rational B-spline (NURBS) surface. Two methods were developed to generate the ordered PSF and the unordered PSF, respectively.  ...  (a) B-spline curve approximations in udirection; (b) B-spline curve approximations in v-direction; (c) Fitted B-spline surface for the unordered PSF and the SLPC.  ... 
doi:10.3390/s21041304 pmid:33670354 pmcid:PMC7918418 fatcat:5gsjkq7atbeljhcdzgurlwqq3m

A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting

Van Than Dung, Tegoeh Tjahjowidodo, Rongling Wu
2017 PLoS ONE  
OPEN ACCESS Citation: Dung VT, Tjahjowidodo T (2017) A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting.  ...  This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed.  ...  Acknowledgments The authors acknowledge the support of Nanyang Technological University and the Advanced Remanufacturing and Technology Centre (ARTC) in this research work. Software: VTD.  ... 
doi:10.1371/journal.pone.0173857 pmid:28319131 pmcid:PMC5358887 fatcat:yjlib6fwzbcq7blg4v47j423re
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