We present a generalization of thin-plate splines for interpolation and approximation of manifold-valued data, and demonstrate its usefulness in computer graphics with several applications from different fields. The cornerstone of our theoretical framework is an energy functional for mappings between two Riemannian manifolds which is independent of parametrization and respects the geometry of b...

The thin plate spline is a popular tool for the interpolation and smoothing of scattered data. In this paper we propose a novel stabilized mixed finite element method for the discretization of thin plate splines. The mixed formulation is obtained by introducing the gradient of the smoother as an additional unknown. Working with a pair of bases for the gradient of the smoother and the Lagrange m...

A numcncal methodfor smooth interpolation oj scattered data over afinite two dimensional domain Q is presented The interpolating function is defined by minimizatwn of a Dinchlettype intégral oj order ^ 2 over Q, nieasuring the rougîmes s oj the surface The case cor r esponding to Q = R results in the so-called « thin plate » sphne A Ritz-type method for approximating the fimte domain interpolat...

Thin plate splines are utilized in the construction of a non-oscillatory finite volume method for the inviscid Burgers' equation which is a prototype nonlinear conservation law. To capture the sharp features that occur during numerical simulation, the method is implemented on an adaptive triangulation. An a posteriori error indicator is used to detect regions where the solution varies rapidly.

We describe a model-based method of generating realistic mass lesions and placing them in appropriate locations on normal mammogram backgrounds. These lesions are highly irregular in shape and have no consistent internal landmarks. Thin plate splines are used both in modelling the background to each lesion, and to warp examples when training an appearance model.

By coupling the flexibility of Thin-Plate Splines interpolation with Green’s integral formula, we obtain a meshless cubature method from scattered samples of small/moderate size, on convex as well as nonconvex and even multiply connected polygonal domains. 2000 AMS subject classification: 65D05, 65D32.