A fast hybrid approach for approximating a thin-plate spline surface

Thin-plate spline (TPS) is a common method to smooth interpolation of bivariate scattered data. However, this method has been associated with very high computational cost, particularly when number of scattered data becomes large and interpolation function must be evaluated on a large grid. This paper describes a hybrid approach for computing a C²-continuous surface using combination of thin-plate spline and cubic spline interpolation that approximates the thin-plate spline interpolation function. Experimental results show that this method significantly speeds up the evaluation of thin-plate spline interpolation function in comparison with direct evaluation, particularly in the cases that interpolation function must be evaluated on a large grid.