Abstract
Abstract. This study evaluates the horizontal positional accuracy of a new algorithm that defines a surface that approximates DEM data by means of a spline function. This algorithm allows evaluating the surface at any point in its definition domain and allows analytically estimating other parameters of interest, such as slopes, orientations, etc. To evaluate the accuracy achieved with the algorithm, we use a reference DEM 2 m × 2 m (DEMref) from which the derived DEMs are obtained at 4 m × 4 m, 8 m × 8 m and 16 m × 16 m (DEMder). For each DEMder its spline approximant is calculated, which is evaluated at the same points occupied by the DEMref cells, getting a resampled DEM 2 × 2 m (DEMrem). The horizontal accuracy is obtained by computing the area amongs the homologous contour lines derived from DEMref and DEMrem, respectively. It has been observed that the planimetric errors of the proposed algorithm are very small, even in flat areas, where you could expect major differences. Therefore, this algorithm could be used when an evaluation of the horizontal positional accuracy of a DEM product at lower resolution (DEMpro) and a different producing source than the higher resolution DEMref is wanted.
Highlights
Having a mathematical function that represents the terrain throughout its continuous definition domain has different advantages, among others the following: a) It is possible to sample regular meshes to generate digital elevation models (DEM) of both higher and lower resolution than the data from which the mathematical function was obtained; and this is achieved thanks to its definition domain is continuous, b) morphological variables of interest can be obtained from the corresponding mathematical formulas of the surfaces, such as slope, orientation, curvature and normal direction, c) You could intersect two surfaces corresponding to homologous DEMs from different dates and calculate the increase or decrease in the terrain volume
Procedures are available to extract information directly from a DEM, we propose a new algorithm to build a surface with low computational cost that adjusts the elevations in order to have an explicit expression from which to find the elements of interest
We propose to construct a spline surface by means of a tensor product of 1D spline approximants, defining the surface patches directly in the Bernstein basis
Summary
Having a mathematical function that represents the terrain throughout its continuous definition domain has different advantages, among others the following: a) It is possible to sample regular meshes to generate digital elevation models (DEM) of both higher and lower resolution than the data from which the mathematical function was obtained; and this is achieved thanks to its definition domain is continuous, b) morphological variables of interest can be obtained from the corresponding mathematical formulas of the surfaces, such as slope, orientation, curvature and normal direction, c) You could intersect two surfaces corresponding to homologous DEMs from different dates and calculate the increase or decrease in the terrain volume. The provision of functions of this type has allowed resampling through bilinear (Maune, 2007) and bicubic (Keys, 1981) interpolations that have been used in different applications both to obtain DEMs of higher and lower resolution. Procedures are available to extract information directly from a DEM, we propose a new algorithm to build a surface with low computational cost that adjusts the elevations in order to have an explicit expression (function) from which to find the elements of interest. The regular structure of the DEM allows to define a piecewise surface defined on a quadrangular partition of the terrain. In this work we will study the horizontal accuracy achieved by the new algorithm that we have proposed. We will use the automatic algorithm based on homologous contour lines introduced in Reinoso, 2010 and rigorously demonstrated in Reinoso, 2011 for evaluating the horizontal accuracy
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