We generalize techniques dating back to Duchon 4] for error estimates for interpolation by thin plate splines to basis functions with positive and algebraically decaying Fourier transform. We include L p-estimates for 1 p < 2 that can also be applied to thin plate spline approximation. x1. Introduction Radial basis functions are a well-established tool for multivariate approximation problems. A...

Surface smoothing applied to range/elevation data acquired using a variety of sources has been a very active area of research in computational vision over the past decade. Generalized splines have emerged as the single most popular approximation tool to this end. In this paper we present a new and fast algorithm for solving the surface smoothing problem using a membrane, a thin-plate, or a thin...

Morphometrics, a new branch of statistics, combines tools from geometry, computer graphics and biometrics in techniques for the multivariate analysis of biological shape variation. Although medical image analysts typically prefer to represent scenes by way of curving outlines or surfaces, the most recent developments in this associated statistical methodology have emphasized the domain of landm...

We present an approach to elastic registration of tomographic brain images which is based on thin plate splines and takes into account landmark errors The inclusion of error information is important in clin ical applications since landmark extraction is always prone to error In comparison to previous work our approach can cope with anisotropic er rors which is signi cantly more realistic than d...

A new multivariate approximation scheme to scattered data on arbitrary bounded domains in Rd is developed. The approximant is selected from a space spanned (essentially) by corresponding translates of the ‘shifted’ thin-plate spline (‘essentially,’ since the space is augmented by certain functions in order to eliminate boundary effects). This scheme applies to noisy data as well as to noiseless...

We introduce an approach to elastic registration of tomographic images based on thin-plate splines. Central to this scheme is a well-de ned minimizing functional for which the solution can be stated analytically. In this work, we consider the integration of anisotropic landmark errors as well as additional attributes at landmarks. As attributes we use orientations at landmarks and we incorporat...

We consider elastic registration of medical image data based on thin plate splines using a set of corresponding anatomical point land marks Previous work on this topic has concentrated on using interpola tion schemes Such schemes force the corresponding landmarks to exactly match each other and assume that the landmark positions are known exactly However in real applications the localization of...

We review the semiparametric approach previously proposed by Kong and Lee and extend it to a case in which the dose-effect curves follow the Emax model instead of the median effect equation. When the maximum effects for the investigated drugs are different, we provide a procedure to obtain the additive effect based on the Loewe additivity model. Then, we apply a bivariate thin plate spline appr...

Thin plate smoothing splines incorporating varying degrees of topographic dependence were used to interpolate 100 daily rainfall values, with the degree of data smoothing determined by minimizing the generalised cross validation. Analyses were performed on the square roots of the rainfall values. Model calibration was made difficult by short range correlation and the small size of the data set....