The discrete thin plate spline smoother

The thin plate spline is a technique for interpolating and smoothing surface over scattered data in many dimensions. It is a type of polyharmonic splines that appears in various applications, including image processing and correspondence recovery. It has some favourable properties like being insensitive to noise in data. One major limitation of the thin-plate spline is that the resulting system of equations is dense and the size depends on the number of data points, which is impractical for large datasets. A discrete thin-plate spline smoother has been developed to approximate thin plate spline with piecewise linear basis functions. The resulting system of equations is sparse and the size depends only on the number of nodes in finite the element grid.