Thin Plate Spline Interpolation on Large 2D Grids

In the early 1990s BCS was involved in some image processing and detection projects arising in both natural resource and defense settings. We were convinced that thin plate spline (TPS) functions could play an important role in developing effective software for image registration and change detection, but initially we encountered some computational challenges when using TPS functions on mid-size to large problems. Fortunately, we were able to enlist the assistance of Professor M. J. D. Powell of Cambridge University; the end result is that BCS has very efficient, numerically stable software for solving the underlying problem of TPS evaluation on large 2D grids (such as raster images). This note provides background to, and some mathematical details of, the algorithms involved.