Abstract
Digital Elevation Models (DEMs) are considered as one of the most relevant geospatial data to carry out land-cover and land-use classification. This work deals with the application of a mathematical framework based on a Gaussian Markov Random Field (GMRF) to interpolate grid DEMs from scattered elevation data. The performance of the GMRF interpolation model was tested on a set of LiDAR data (0.87 points/m<sup>2</sup>) provided by the Spanish Government (PNOA Programme) over a complex working area mainly covered by greenhouses in Almería, Spain. The original LiDAR data was decimated by randomly removing different fractions of the original points (from 10% to up to 99% of points removed). In every case, the remaining points (scattered observed points) were used to obtain a 1 m grid spacing GMRF-interpolated Digital Surface Model (DSM) whose accuracy was assessed by means of the set of previously extracted checkpoints. The GMRF accuracy results were compared with those provided by the widely known Triangulation with Linear Interpolation (TLI). Finally, the GMRF method was applied to a real-world case consisting of filling the LiDAR-derived DSM gaps after manually filtering out non-ground points to obtain a Digital Terrain Model (DTM). Regarding accuracy, both GMRF and TLI produced visually pleasing and similar results in terms of vertical accuracy. As an added bonus, the GMRF mathematical framework makes possible to both retrieve the estimated uncertainty for every interpolated elevation point (the DEM uncertainty) and include break lines or terrain discontinuities between adjacent cells to produce higher quality DTMs.
Highlights
Statistical spatial analysis encompasses an expanding range of methods, being spatial interpolation of unknown elevations, referenced to a common vertical datum, one of the most widely studied because of its ability to produce highly demanded cartographic products such as Digital Terrain or Surface Models (DTM or Digital Surface Model (DSM) respectively; Digital Elevation Models (DEMs) in general) (e.g. Aguilar et al 2005)
The resulting DSM would look like over-smoothed, being convenient to diminish the stiffness of the interpolated surface by increasing the tolerance parameter
The same can be said about the results provided by the Triangulation with Linear Interpolation (TLI) method, if point density was much lower than the output cell size, some triangles of the triangular irregular network (TIN) model may be unpleasantly made out in the output DEM/DSM
Summary
Statistical spatial analysis encompasses an expanding range of methods, being spatial interpolation of unknown elevations, referenced to a common vertical datum, one of the most widely studied because of its ability to produce highly demanded cartographic products such as Digital Terrain or Surface Models (DTM or DSM respectively; DEMs in general) (e.g. Aguilar et al 2005). Photogrammetrically-derived DEMs have received a boost with the adaptable stereo imaging capability of the newest civilian VHR satellites that allows generating strong stereo geometry with adequate base-to-height ratio (Aguilar et al, 2014). Their agile pointing ability enables the generation of same-date in-track stereo images, reducing radiometric image variations and so improving the success rate in any matching process
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