Comments on the two-dimensional smoothing of data Original Research Article

A general treatment for 2D smoothing of equally or nonequally spaced data is presented. It is shown that the two techniques already known in literature and developed by Ratzlaff–Johnoson and Kuo et al. are limiting cases of this treatment obtained when the orthogonal functions of the trial function are expressed as a sum or a product of one-dimensional orthogonal functions, respectively. The smoothing capabilities of these two techniques were tested using both experimental and artificial data. We found a very peculiar and unexpected behavior. Although Ratzlaff–Johnoson’s smoothing method fails completely to smooth an individual 2D set of data, something, which can be done effectively by Kuo’s approach, it may give better results than Kuo’s approach if it is used with the moving window technique. This is due to the fact that Ratzlaff–Johnoson’s method smoothes effectively only the central point of each subset of data.