If the manifolds are euclidean, the energy functional reduces to the classical thin plate spline energy. We show how the resulting optimization problems can be. Image warping plays an extremely important role in face. Approximate thin plate spline mappings cornell vision pages. I discuss the production of low rank smoothers for d 1 dimensional data, which can be. Approximation methods for thin plate spline mappings and. A thinplate spline is a physically motivated 2d inter polation scheme for arbitrarily spaced tabulated data xi,yi,fxi,yi.
The construction is based on choosing a function that minimizes an integral that represents the bending energy of a surface. The thin plate spline tps is a commonly used basis function for representing coordinate mappings from r2 to r2. Thin plate splines tps are a splinebased technique for data interpolation and smoothing. The smoothers allow the use of approximate thin plate spline models with large data sets, avoid the problems that are associated with knot placement that usually complicate modelling with regression splines or penalized regression splines, provide a sensible way of modelling interaction terms in generalized additive models, provide low.
I discuss the production of low rank smoothers for d. The thin plate spline tps is an interpolation approach that has been developed to investigate a frequently occurring problem in geosciences. Therefore, thin plate splines approximate surfaces with minimal bending energy and they are widely considered as the standard fair surface model. If the manifolds are euclidean, the energy functional reduces to the classical thinplate spline energy. Thin plate splines tps are a spline based technique for data interpolation and smoothing. A set of basis functions emerges directly from the demand to minimize the residual sum of squares, plus a smoothness penalty that is a multiple of the multivariate. Robust point matching rpm is a common extension and shortly known as the tpsrpm algorithm. We present a simple, pdebased proof of the result 17 by m. Consistent thinplate spline image registration the university of. The smoothers are constructed by a simple transformation and truncation of the basis that arises. Fifth proofs fair 2009108 pagev i i i i i i i i contents fair listingsxi fair examplesxiii listoffigures xvii listoftables xix preface xxi 1 introduction 1. Wood university of st andrews, uk received october 2001.
They were introduced to geometric design by duchon. Thin plate splines, alexwarp, interpolation, applet, java programming language. The thin plate spline tps is an effective tool for modeling coordinate transformations that has been applied successfully in several computer vision applications. Manifoldvalued thinplate splines with applications in computer. Thin plate regression splines wood 2003 journal of. These splines are the generalization of the natural cubic splines in 1d. I am trying to figure out how to create a three dimensional plot of a thin plate spline, similar to the visualizations which appear on pages 2425 of introduc. They are an important special case of a polyharmonic spline.