An extension of thin-plate splines for image registration with radial basis functions

2012 ◽  
Author(s):  
Karl Rohr ◽  
Stefan Worz
Keyword(s):  
Image Registration ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Basis Functions ◽  
Thin Plate Splines ◽  
Radial Basis

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.

INTERACTIVE REGISTRATION OF INTRACELLULAR VOLUMES WITH RADIAL BASIS FUNCTIONS

2010 ◽  
Vol 09 (03) ◽  
pp. 207-224 ◽  
Author(s):  
SHIN YOSHIZAWA ◽  
SATOKO TAKEMOTO ◽  
MIWA TAKAHASHI ◽  
MAKOTO MUROI ◽  
SAYAKA KAZAMI ◽  
...  
Keyword(s):  
Image Registration ◽  
Radial Basis Functions ◽  
Plasma Membranes ◽  
Mapping Function ◽  
Basis Functions ◽  
Cell Geometry ◽  
Registration System ◽  
Barycentric Interpolation ◽  
Novel Approach ◽  
Radial Basis

We propose a novel approach to 3D image registration of intracellular volumes. The approach extends a standard image registration framework to the curved cell geometry. An intracellular volume is mapped onto another intracellular domain by using two pairs of point set surfaces approximating their nuclear and plasma membranes. The mapping function consists of the affine transformation, tetrahedral barycentric interpolation, and least-squares formulation of radial basis functions for extracted cell geometry features. An interactive volume registration system is also developed based on our approach. We demonstrate that our approach is capable of creating cell models containing multiple organelles from observed data of living cells.

Multilevel RBF collocation method for the fourth-order thin plate problem

2020 ◽  
pp. 2050079
Author(s):  
Lanling Ding ◽  
Zhiyong Liu ◽  
Qiuyan Xu
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Fourth Order ◽  
Basis Function ◽  
Research Method ◽  
Meshfree Method ◽  
Basis Functions ◽  
Radial Basis

The radial basis functions meshfree method is a research method for thin plate problem which has gradually developed into a more mature meshfree method. It includes finite element, radial basis functions meshfree collocation method, etc. In this paper, we introduce the multilevel radial basis function collocation method for the fourth-order thin plate problem. We use nonsymmetric Kansa multilevel radial basis function collocation method to solve the fourth-order thin plate problem. Two numerical examples based on Wendland’s [Formula: see text] and [Formula: see text] functions are given to examine that the convergence of the multilevel radial basis function collocation method which is good for solving the fourth-order thin plate problem.

COMPARATIVE STUDY OF THE MULTIQUADRIC AND THIN-PLATE SPLINE RADIAL BASIS FUNCTIONS FOR THE TRANSIENT-CONVECTIVE DIFFUSION PROBLEMS

2006 ◽  
Vol 17 (08) ◽  
pp. 1151-1169 ◽  
Author(s):  
A. DURMUS ◽  
I. BOZTOSUN ◽  
F. YASUK
Keyword(s):  
Radial Basis Functions ◽  
Thin Plate ◽  
Numerical Solutions ◽  
Convective Diffusion ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Thin Plate Spline ◽  
Collocation Methods ◽  
Radial Basis ◽  
Diffusion Problems

The numerical solutions of the unsteady transient-convective diffusion problems are investigated by using multiquadric (MQ) and thin-plate spline (TPS) radial basis functions (RBFs) based on mesh-free collocation methods with global basis functions. The results of radial basis functions are compared with the mesh-dependent boundary element and finite difference methods as well as the analytical solution for high Péclet numbers. It is reported that for low Péclet numbers, MQ-RBF provides excellent agreement, while for high Péclet numbers, TPS-RBF is better than MQ-RBF.

scholarly journals Image registration using radial basis functions with adaptive radius

2012 ◽  
Vol 39 (11) ◽  
pp. 6542-6549 ◽  
Author(s):  
Nadezhda Shusharina ◽  
Gregory Sharp
Keyword(s):  
Image Registration ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis ◽  
Adaptive Radius
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