Recently there has emerged a need to compute multimodal non-rigid registrations in a lot of clinical applications. To date, the viscous fluid algorithm is perhaps the most adept method at recovering large local misregistrations that exist between two images. However, this model can only be used on images from the same modality as it assumes similar intensity values between images. This paper pr...

This paper presents a novel minutiae matching method that describes elastic distortions by means of a thin-plate spline model and uses that model to normalize the shape of the test fingerprint with respect to the template. The method first determines possible matching minutiae pairs by means of comparing local neighborhoods of the minutiae. Next, a thin-plate spline model is used to describe th...

2 The Calculus of Variations 2 2.1 Functionals of f and f ′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Functionals of f , f ′, and f ′′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Cubic Splines and Green’s Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Euler-Lagrange Equations for Multi...

While direct theorems for interpolation with radial basis functions are intensively investigated, little is known about inverse theorems so far. This paper deals with both inverse and saturation theorems. For an inverse theorem we especially show that a function that can be approximated sufficiently fast must belong to the native space of the basis function in use. In case of thin plate spline ...

Recently there has emerged a need to compute multimodal non-rigid registrations in a lot of clinical applications. To date, the viscous fluid algorithm is perhaps the most adept method at recovering large local misregistrations that exist between two images. However, this model can only be used on images from the same modality as it assumes similar intensity values between images. This paper pr...

This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which i...

We suggest a method of fitting of the zero-range model of the tectonic plate under the boundary stress based on comparison of the theoretical formulae for the corresponding eigenfunctions/eigenvalues with the results of instrumental measurements of frequency and the shape and the shape of the relevant seismo-gravitational modes in the remoted zone. Comparison of the data of the instrumental mea...

Vector field approximation is a problem involving the reconstruction of physical fields from a set of scattered observed data. In this paper, we address the problem of interpolation of divergence-free vector fields in three dimensional space by thin plate spline under tension. The problem is formulated as a minimization problem where the cost is related to the equilibrium energy of thin plate w...

Splines can be used to approximate noisy data with a few control points. This paper presents a new curve matching method for deformable shapes using two-dimensional splines. In contrast to the residual error criterion [7], which is based on relative locations of corresponding knot points such that is reliable primarily for dense point sets, we use deformation energy of thin-plate-spline mapping...

Our aim is to establish accurate correspondences between temporal mammograms in order to improve the detection of tumours. We propose a method for detecting abnormalities after aligning a pair of mammograms using thin-plate spline interpolation based on corresponding points on the breast boundary. We also suggest a method for the automatic detection of landmarks within the breast tissue. We sho...