Wenli Li, W. Randolph Franklin, Salles V. G. de Magalhães, and Marcus V. A. Andrade. Restricted bathymetric tracklines interpolation. In 24th Fall Workshop on Computational Geometry. U. Connecticut, Storrs CT, USA, 31 Oct – 1 Nov 2014. (extended abstract).
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In this paper, we propose a method to interpolate a small bathymetry with long and thin sand bars as distinctive features. Underwater terrain, or bathymetry, is measured by a single beam or multibeam echosounder attached under a boat. Measurement points are distributed along the a track of the boat and their positions and values constitute a trackline. Although full coverage is possible in multibeam surveys, tracklines are often sparse and thin, especially in single beam surveys, and it is expected to interpolate the bathymetry from tracklines. There are dozens of existing spatial interpolation methods with their strengths and weaknesses, and some are more widely used than others. One of the methods, overdetermined laplacian partial differentiation equations (ODETLAP), has been successfully used in bathymetry data interpolation and shown to be better than some of the popular methods. However, it is more suited for large-scale bathymetry without significant linear or continuous features.

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