Error indicators and adaptive refinement of the discrete thin plate spline smoother

Error Estimates for Thin Plate Spline Approximation in the Disc

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...

Approximate Thin Plate Spline

Approximation of a Thin Plate Spline Smoother Using Continuous Piecewise Polynomial Functions

A new smoothing method is proposed which can be viewed as a finite element thin plate spline. This approach combines the favourable properties of finite element surface fitting with the ones of thin plate splines. The method is based on first order techniques similar to mixed finite element techniques for the biharmonic equation. The existence of a solution to our smoothing problem is demonstra...

Approximate Thin Plate Spline Mappings

The thin plate spline (TPS) is an e ective tool for modeling coordinate transformations that has been applied successfully in several computer vision applications. Unfortunately the solution requires the inversion of a p p matrix, where p is the number of points in the data set, thus making it impractical for large scale applications. As it turns out, a surprisingly good approximate solution is...

Thin-plate spline analysis of mandibular growth.

The analysis of mandibular growth changes around the pubertal spurt in humans has several important implications for the diagnosis and orthopedic correction of skeletal disharmonies. The purpose of this study was to evaluate mandibular shape and size growth changes around the pubertal spurt in a longitudinal sample of subjects with normal occlusion by means of an appropriate morphometric techni...