Thin plate spline

Summary

A thin plate spline is a smooth function of two variables that interpolates scattered data with the least bending energy. It is a sum of translates of the radial function $r^2 \log r$ and an affine function, the case $d = 2$, $m = 2$ of a polyharmonic spline. The name comes from the physical picture of a thin metal sheet bent to pass through given heights. Thin plate splines are widely used for surface fitting and for smooth image warping.