March 17, 2010
Title: Multiresolution terrain representation by level curve elimination
Abstract: The most popular adaptive thinning algorithms for bivariate scattered data sets with corresponding function values are point removal schemes, where the points are recursively removed (1). Since level curves are still the most common form to represent elevation data for the Earth's surface, we propose a new method for computing a multiresolution representation of a digital terrain model using the connectivity information provided by contour lines.
The core of the presented multiresolution method is an algorithm for removing recursively the level curves according to some error criterion. It allows to obtain a sequence of approximations of the terrain where the difference between two consecutive approximations is only one curve: the less "important". In other words, the input curves are sorted in such a way that the n most relevant curves are contained in the n-th resolution level. For a given curve, the relevance criterion is the error computed using a function interpolating the remaining curves. Hence, to fully formulate the multiresolution algorithm it is necessary a function interpolating the contour lines of the terrain. In our method, we define the error measure associated with a level curve by means of the interpolant for terrain models introduced in (2).
To obtain an efficient implementation of the proposed method it was necessary to use adequate data structures and computational geometry algorithms in order to solve several subproblems, for instance the computation of the distance from a point to a polygon (with a huge amount of vertices), the simplification of the level curves and the point location problem.