One conventional tool for interpolating surfaces over scattered data, the thin-plate spline, has an elegant algebra expressing the dependence of the physical bending energy of a thin metal plate on point constraints. For interpolation of a surface over a fixed set of nodes in the plane, the bending energy is a quadrat ic form in the heights assigned to the surface. The spline is the superpositi...

Accurate registration of cortical structures plays a fundamental role in statistical analysis of brain images across population. This paper presents a novel framework for the non-rigid intersubject brain surface registration, using conformal structure and spherical thin-plate splines. By resorting to the conformal structure, complete characteristics regarding the intrinsic cortical geometry can...

Landmark placement is crucial in manual demarcation and registration of anatomical structures, registration of different image modalities (i.e. MRI/CT), labeling training data for lip and face principal component models, training for neural networks, and signal interpolation to name some applications. Although landmark placement at curvature and coordinate extrema (e.g. corners of the mouth, lo...

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)...

An algorithm for selection of knot point locations for approximation of functions from large sets of scattered data by least squares Thin Plate Splines is given. The algorithm is based on the idea that each data point is equally important in defining the surface, which allows the knot selection process to be decoupled from the least squares. Properties of the algorithm are investigated, and exa...

A list of technical reports, including some abstracts and copies of some full reports may be found at:

We study a vectorial approximation problem based on thin plate splines with tension involving two positive parameters: one for the control of the oscillations and the other for the control of the divergence and rotational components of the field. The existence and uniqueness of the solution are proved and the solution is explicitly given. As special cases, we study the limit problems as the par...

In this contribution, a scattered data approximation problem, chosen from the literature and using Radial Basis Function (RBF) approach, is considered for application of point cloud modelling. Three solutions are investigated problem. First, technique known linear combination thin-plate splines polynomials, with additional constraint equations. Then, same function as before, developed rigorous ...

We extend Schoenberg’s family of polynomial splines with uniform knots to all fractional degrees α > −1. These splines, which involve linear combinations of the one-sided power functions x+ = max(0, x) α, are α-Hölder continuous for α > 0. We construct the corresponding B-splines by taking fractional finite differences and provide an explicit characterization in both time and frequency domains....