Verifying convergence rates of discrete thin-plate splines in 3D.

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...

3D tooth shape from radiographs using thin-plate splines.

Current methods to produce 3-dimensional tooth root models involve conversion from radiographic means (computed tomography) or creation using computer-assisted design (CAD) software. The former lacks detail while the second is manually fabricated and can bear little resemblance to the original. Thin-plate splines have been used in morphometrics to define changes of shape between subjects of the...

Finite Element Thin Plate Splines

Verifying Numerical Convergence Rates

2 Determining the order of accuracy We are often faced with the problem of how to determine the order p given a sequence of approximations ũh1 , ũh2 , . . . This is can be a good check that a method is correctly implemented (if p is known) and also a way to get a feeling for the credibility of an approximation ũh (high p means high credibility). We can either be in the situation that the exact ...