On the interpolation algorithm ranking

On the interpolation algorithm ranking
Carlos López-Vázquez

LatinGEO Lab, SGM+Universidad ORT del Uruguay (carlos.lopez@ieee.org)

Abstract: Interpolation of data gathered at a finite number of locations is an everyday issue with spatial data. The choice of the best interpolation algorithm has been a topic of interest for a long time. Typical papers take a single dataset, a single set of data points, and a handful of algorithms. They report results of considering a subset A of the data points, application of each algorithm to the complement of A, and evaluating the MAD/RMSE over such points. The lower the better, so a ranking among methods (without confidence level) can be derived based upon it. We believe that the best interpolation algorithm should consider not merely the function value at some designated points, but also the spectral properties of the original field. We have used a metric named ESAM for that. Using a sample of N = 500, 2500 and 5000 irregularly distributed points taken from a reference DEM, we applied a number of interpolation methods and create a ranking among them using MAD, RMSE and ESAM as the figure of merit. ESAM ranking does not agree with the others. In addition, in this paper we will show how to build a ranking with a confidence level.

Keywords: Interpolation, RMSE, MAD, ESAM, ranking

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