scholarly journals A mixed finite element discretisation of thin-plate splines

2011 ◽  
Vol 52 ◽  
pp. 518 ◽  
Author(s):  
Bishnu P. Lamichhane ◽  
Stephen Roberts ◽  
Linda Stals
Keyword(s):  
Finite Element ◽  
Thin Plate ◽  
Mixed Finite Element ◽  
Thin Plate Splines

scholarly journals Distortion correction of MR data in whole-body small animal PET-MR using 3D thin-plate splines

2014 ◽  
Vol 1 (S1) ◽  
Author(s):  
Lynn Frohwein ◽  
Verena Hoerr ◽  
Cornelius Faber ◽  
Klaus Schäfers
Keyword(s):  
Thin Plate ◽  
Small Animal ◽  
Distortion Correction ◽  
Small Animal Pet ◽  
Whole Body ◽  
Thin Plate Splines ◽  
Animal Pet

scholarly journals Magnetometer Calibration and Field Mapping through Thin Plate Splines

Sensors ◽  
2019 ◽  
Vol 19 (2) ◽  
pp. 280 ◽  
Author(s):  
Marco Muraccini ◽  
Anna Mangia ◽  
Maurizio Lannocca ◽  
Angelo Cappello
Keyword(s):  
Magnetic Field ◽  
Thin Plate ◽  
Indoor Localization ◽  
Information Source ◽  
Attitude Estimation ◽  
Local Magnetic Field ◽  
Simultaneous Estimation ◽  
Thin Plate Splines ◽  
Field Mapping ◽  
Magnetometer Calibration

While the undisturbed Earth’s magnetic field represents a fundamental information source for orientation purposes, magnetic distortions have been mostly considered as a source of error. However, when distortions are temporally stable and spatially distinctive, they could provide a unique magnetic landscape that can be used in different applications, from indoor localization to sensor fusion algorithms for attitude estimation. The main purpose of this work, therefore, is to present a method to characterize the 3D magnetic vector in every point of the measurement volume. The possibility of describing the 3D magnetic field map through Thin Plate Splines (TPS) interpolation is investigated and demonstrated. An algorithm for the simultaneous estimation of the parameters related to magnetometer calibration and those describing the magnetic map, is proposed and tested on both simulated and real data. Results demonstrate that an accurate description of the local magnetic field using TPS interpolation is possible. The proposed procedure leads to errors in the estimation of the local magnetic direction with a standard deviation lower than 1 degree. Magnetometer calibration and magnetic field mapping could be integrated into different algorithms, for example to improve attitude estimation in highly distorted environments or as an aid to indoor localization.

DIV-CURL WEIGHTED MINIMIZING SPLINES

2007 ◽  
Vol 05 (02) ◽  
pp. 95-122 ◽  
Author(s):  
M. N. BENBOURHIM ◽  
A. BOUHAMIDI
Keyword(s):  
Vector Field ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Approximation Problem ◽  
Scattered Data ◽  
Scalar Function ◽  
Basis Functions ◽  
Thin Plate Splines ◽  
Numerical Examples ◽  
Radial Basis

The paper deals with a div-curl approximation problem by weighted minimizing splines. The weighted minimizing splines are an extension of the well-known thin plate splines and are radial basis functions which allow the approximation or the interpolation of a scalar function from given scattered data. In this paper, we show that the theory of the weighted minimizing splines may also be used for the approximation or for the interpolation of a vector field controlled by the divergence and the curl of the vector field. Numerical examples are given to show the efficiency of this method.

scholarly journals Approximation of vectors fields by thin plate splines with tension

2005 ◽  
Vol 136 (2) ◽  
pp. 198-229 ◽  
Author(s):  
M.N. Benbourhim ◽  
A. Bouhamidi
Keyword(s):  
Thin Plate ◽  
Thin Plate Splines
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