Computation of weighting functions for smoothing two-dimensional data by local polynomial approximation techniques

Abstract

The problem of smoothing two-dimensional data by a local polynomial approximation technique (i.e., extension of Savitzky-Golay smoothing to two-dimensional applications) is considered. A simple analytical expression is proposed for computing the weighting functions used in the smoothing procedure with a polynomial of any degree and over any interval without loss of data at boundary points. The formulae obtained can be used for two dimensional smoothing by linear smoothing procedures, which considerably decreases the number of required operations.