scholarly journals Characterisation theorem for best polynomial spline approximation with free knots

2017 ◽  
Vol 369 (9) ◽  
pp. 6389-6405 ◽  
Author(s):  
Nadezda Sukhorukova ◽  
Julien Ugon
Keyword(s):  
Spline Approximation ◽  
Polynomial Spline

L 1 C 1 polynomial spline approximation algorithms for large data sets

2014 ◽  
Vol 67 (4) ◽  
pp. 807-826 ◽  
Author(s):  
Laurent Gajny ◽  
Olivier Gibaru ◽  
Eric Nyiri
Keyword(s):  
Approximation Algorithms ◽  
Spline Approximation ◽  
Large Data ◽  
Polynomial Spline ◽  
Large Data Sets ◽  
Data Sets

scholarly journals Polynomial Spline-Approximation of Clarke's Model

2004 ◽  
Vol 52 (5) ◽  
pp. 1198-1208 ◽  
Author(s):  
Y.V. Zakharov ◽  
T.C. Tozer ◽  
J.F. Adlard
Keyword(s):  
Spline Approximation ◽  
Polynomial Spline

scholarly journals Weighted Quasi-Interpolant Spline Approximations of Planar Curvilinear Profiles in Digital Images

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3084
Author(s):  
Andrea Raffo ◽  
Silvia Biasotti
Keyword(s):  
Digital Images ◽  
Spline Approximation ◽  
Detection Algorithm ◽  
Polynomial Spline ◽  
Automatic Method ◽  
Data Perturbation ◽  
Spline Curves ◽  
Curve Approximation ◽  
Local Approximations ◽  
Edge Points

The approximation of curvilinear profiles is very popular for processing digital images and leads to numerous applications such as image segmentation, compression and recognition. In this paper, we develop a novel semi-automatic method based on quasi-interpolation. The method consists of three steps: a preprocessing step exploiting an edge detection algorithm; a splitting procedure to break the just-obtained set of edge points into smaller subsets; and a final step involving the use of a local curve approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), chosen for its robustness to data perturbation. The proposed method builds a sequence of polynomial spline curves, connected C0 in correspondence of cusps, G1 otherwise. To curb underfitting and overfitting, the computation of local approximations exploits the supervised learning paradigm. The effectiveness of the method is shown with simulation on real images from various application domains.

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