Numerical Surface Model Precision: Case of DEM's

摘要

A Digital Surface Model (DSM) is a numerical surface model which is formed by a set of points -point cloud-, arranged as a regular or irregular grid, to study some physical surface, Digital Elevation Models (DEM), or other possible applications, such as a face, or some anatomical organ, etc. The study of the precision of these models, which is of particular interest for DEMs, has been the object of several studies in the last decades. The measurement of the precision of a DSM model, in relation to another model of the same physical surface, consists in estimating the expectancy of the squares of differences between pairs of points, called homologous points, one in each model which corresponds to the same feature of the physical surface. But these pairs are not easily discernable, the grids may not be coincident, and the differences between the homologous points, corresponding to benchmarks in the physical surface, might be subject to special conditions such as more careful measurements than on ordinary points, which imply a different precision. The generally used procedure to avoid these inconveniences has been to use the squares of vertical distances between the models, which only address the vertical component of the error, thus giving a biased estimate when the surface is not horizontal. The Perpendicular Distance Evaluation Method (PDEM) which avoids this bias, provides estimates for vertical and horizontal components of errors, and is thus a useful tool for detection of discrepancies in Digital Surface Models (DSM) like DEMs. The solution includes a special reference to the simplification which arises when the error does not vary in all horizontal directions. Taking some precautions, the PDEM may be employed in the cases of DEM's obtained by means of the Interferometry SAR Technique and the LISAR technique.