An Isotropic Areal Filter Based on High-Order Thin-Plate Spline for Surface Metrology

An Areal Isotropic Spline Filter for Surface Metrology

This paper deals with the application of the spline filter as an areal filter for surface metrology. A profile (2D) filter is often applied in orthogonal directions to yield an areal filter for a three-dimensional (3D) measurement. Unlike the Gaussian filter, the spline filter presents an anisotropic characteristic when used as an areal filter. This disadvantage hampers the wide application of ...

Approximate Thin Plate Spline

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 Approximation for Image Registration

The point based registration technique of Book stein can be seen as an interpolation problem With this technique an elastic transformation based on thin plate splines is determinedwhich maps the source and target land marks exactly to each other However in real applications the positions of the landmarks can only be determined ap proximately Therefore in this case an interpolation scheme is ina...

An improved order of approximation for thin-plate spline interpolation in the unit disc

We show that the Lp-norm of the error in thin-plate spline interpolation in the unit disc decays like O(h p), where p := minf2; 1 + 2=pg, under the assumptions that the function to be approximated is C1 and that the interpolation points contain the nite grid fhj : j 2Z; jhjj < 1 hg.