Surface fitting by pseudo-potential functions

A method for fitting surfaces to two-dimensional data is presented. The underlying model is composed of a finite sum of pseudo-potential elements which play a role similar to that of sources and sinks in potential field theory. The local behavior of the data is exploited along with the structure of the pseudo-potential function in converting the nonlinear parameter estimation problem into linear subproblems, which are solved by standard techniques. A criterion for selecting the number of field elements to be used in the representation is proposed. The resolution of the proposed technique as a function of the number of elements used and the data size is illustrated by solving a problem of topographical mapping from radar altimetry data.