This paper is concerned with approximation properties of linear combinations of scattered translates of the thin-plate spline radial basis function | · | log | · | where the translates are taken in the unit disc D in R. We show that the Lp approximation order for this kind of approximation is 2+1/p (for sufficiently smooth functions), which matches Johnson’s upper bound and, thus, gives the sat...

Optic flow computation is one of the most fundamental problems in the realm of visual motion. In this contribution, we present a novel optic flow computation method based on a thin-plate spline representation of image brightness data. Using a spline-based description of image brightness data removes the need for presmoothing and provides an algebraic means to compute the optic flow (explicitly)...

This paper presents an algorithm for the rapid evaluation of the vector spline in two dimensions. Our work is an extension of the fast evaluation of thin-plate spline by Beatson and Newsam. The algorithm is based on the fast multipole method and has an asymptotic CPU time estimate of O(N), while the direct calculation requires an amount of work of the order O(N 2), where N is the number of the ...

Non-rigid registration requires a smoothness or regularization term for making the warp field regular. Standard models in use here include b-splines and thin plate splines. In this paper, we suggest a regularizer which is based on first principles, is symmetric with respect to source and destination, and fulfills a natural semi-group property for warps. We construct the regularizer from a distr...

This paper describes a method for estimating insurance claims or risk premiums allowing for spatial dependence as well as explanatory factors. The concepts are related to those used for graduation of mortality tables using cubic splines but extended to spatial dependence as found in many insurance products. Firstly techniques for measuring spatial dependence are reviewed. Then models with bivar...

The paper discusses the sensitivity of the height assignment of optically thin cirrus clouds to satellite calibration errors. Thin cirrus are often used as tracers for the derivation of high-level wind vectors. The height assignment is based on bi-spectral techniques, which in the case of Meteosat use both the IR (10.5 12.5 μm) and WV (5.7 7.1 μm) channels. Height allocation errors for typical ...

Image registration is inherently ill-posed, and lacks a unique solution. In the context of medical applications, it is desirable to avoid solutions that describe physically unsound deformations within the patient anatomy. Among the accepted methods of regularizing non-rigid image registration to provide solutions applicable to medical practice is the penalty of thin-plate bending energy. In thi...

In this paper, we develop a fast algorithm for a smoothing spline estimator in multivariate regression. To accomplish this, we employ general concepts associated with roughness penalty methods in conjunction with the theory of radial basis functions and reproducing kernel Hilbert spaces. It is shown that through the use of compactly supported radial basis functions it becomes possible to recove...

Two methods for registering laser-scans of human heads and transforming them to a new semantically consistent topology defined by a user-provided template mesh are described. Both algorithms are stated within the Iterative Closest Point framework. The first method is based on finding landmark correspondences by iteratively registering the vicinity of a landmark with a re-weighted error function...

We present in this paper an algorithm for surface reconstruction using thin plate splines on scattered patches or points on smooth surfaces. The algorithm is an improved version of Szeliski’s Variational Spline Fitting algorithm (SVSF). In particular, we introduce a different derivation of the discrete equations for the energy corresponding to the thin plat model. The results obtained on simula...