Local Polynomial Interpolation Method Optimization in the Process of Digital Terrain Model Creation Based on Data Collected From a Multibeam Echosounder

Abstract

This article describes a local polynomial interpolation (LPI) optimization used to create digital terrain models (DTM) of the seabed based on data collected via a multibeam echosounder (MBES) during a sea survey. In the studies presented in this article, the optimal parameters of this interpolation are sought in terms of the accuracy of the created models and the calculation time. The parameters to be optimized are: the size of the area from which we select the points for interpolation (radius size), the number of points involved in the local interpolation (no), and the polynomial degree used in the interpolation (poly degree). Based on the obtained results, it was shown that the optimal values of these parameters can be selected for this type of input data, and their value depends mainly on grid resolution and the density of measurement points collected during the sea survey. Based on research using various test surfaces, it has been shown that the use of properly selected interpolation parameters enables the creation of models with slightly higher accuracy. During the research, attention was also paid to the speed of calculations, which is an important aspect of the process of creating bathymetric models. It was assumed that the new method should not significantly increase the calculation time. Finally, the author proposed using a new point selection technique (named the growing radius) during LPI, which made it possible to further increase the accuracy of the created models and the speed of calculations. The results obtained are compared with other commonly used interpolation methods using the same test data, showing the good and the bad features of the optimized LPI method. The final results of the research and the conclusions presented in this article indicate that the use of the optimized LPI together with the new technique of selecting points (the growing radius) can be a better alternative to other interpolation methods used in the process of creating bathymetric models based on data from MBES.