Faster fast evaluation of thin plate splines in two dimensions

Fast Evaluation of Vector Splines in Two Dimensions

This paper presents an algorithm for the rapid evaluation of the vector spline in two dimensions. The algorithm is based on the fast multipole method and has an asymptotic CPU time estimate of O(N), where N is the number of data points. The main idea of the algorithm is to combine a cluster of evaluation kernels at diierent data sources into a single kernel in the form of a multipole expansion ...

Thin-Plate Splines

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...

Thin plate regression splines

I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thinplate spline smoothing problem, and are optimal in the sense that the truncation is designed to result in the minimum possible pe...

The role of inner summaries in the fast evaluation of thin-plate splines

The driving force behind fast evaluation of thin-plate splines is the fact that a sum Pn2 j=n1 λjφ(x − ξj), where φ(x) = ‖x‖ 2 log ‖x‖, can be efficiently and accurately approximated by a truncated Laurent-like series (called an outer summary) when the data sites {ξj} n2 j=n1 are clustered in a disk and when the evaluation point x lies well outside this disk. We present a means (called an inner...

Finite Element Thin Plate Splines