ISPRS Journal of Photogrammetry and Remote Sensing 64 (2009) 398–406 Contents lists available at ScienceDirect ISPRS Journal of Photogrammetry and Remote Sensing journal homepage: www.elsevier.com/locate/isprsjprs Accuracy assessment of digital elevation models by means of robust statistical methods Joachim Höhle a,∗ , Michael Höhle b a Department of Development and Planning, Aalborg University, Denmark b Department of Statistics, Ludwig-Maximilians-Universität München, Germany article info Article history: Received 4 March 2008 Received in revised form 30 January 2009 Accepted 3 February 2009 Available online 19 March 2009 Keywords: DEM/DTM Laser scanning Photogrammetry Accuracy Specifications abstract Measures for the accuracy assessment of Digital Elevation Models (DEMs) are discussed and characteristics of DEMs derived from laser scanning and automated photogrammetry are presented. Such DEMs are very dense and relatively accurate in open terrain. Built-up and wooded areas, however, need automated filtering and classification in order to generate terrain (bare earth) data when Digital Terrain Models (DTMs) have to be produced. Automated processing of the raw data is not always successful. Systematic errors and many outliers at both methods (laser scanning and digital photogrammetry) may therefore be present in the data sets. We discuss requirements for the reference data with respect to accuracy and propose robust statistical methods as accuracy measures. Their use is illustrated by application at four practical examples. It is concluded that measures such as median, normalized median absolute deviation, and sample quantiles should be used in the accuracy assessment of such DEMs. Furthermore, the question is discussed how large a sample size is needed in order to obtain sufficiently precise estimates of the new accuracy measures and relevant formulae are presented. © 2009 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved. 1. Introduction Digital Elevation Models are today produced by digital pho- togrammetry or by laser scanning. Both methods are very efficient and accurate; the density of the elevations is very high. However, blunders may occur at both methods. From the raw data a Dig- ital Terrain Model (DTM) and a Digital Surface Model (DSM) are generated by means of filtering (for classifying into ground and off terrain points) and interpolation (for filling gaps). Errors may also occur during such a post-processing. The quality control should de- tect errors and outliers in order to eliminate them. As a final step it has to be checked, whether the edited DTM and DSM achieve the accuracy of the specification. For this purpose, accurate ref- erence values are required, and accuracy measures like the Root Mean Square Error (RMSE), mean error and the standard deviation have to be derived. The amount of data is huge, but the accuracy assessment has to be made with few check points only as it is very labour intensive to obtain them. However, the sample size should ∗ Corresponding address: 11 Fibigerstraede, DK-9220, Aalborg, Denmark. Tel.: +45 9940 8361; fax: +45 9815 6541. E-mail addresses: jh@land.aau.dk (J. Höhle), Michael.Hoehle@stat.uni-muenchen.de (M. Höhle). be large enough to guarantee reliable accuracy measures, which are valid for the whole DTM or DSM. Usually, the specification of ac- curacy measures is based on the assumption that the errors follow a Gaussian distribution and that no outliers exist. But all too often this is not the case, because objects above the terrain like vegeta- tion, buildings and unwanted objects (cars, people, animals, etc.) are present, and the filtering program may not label all ground el- evations correctly. Also system errors will occur: Photogrammetry needs structure and texture in the images and not all of the image parts fulfil this requirement. Laser light is not always reflected di- rectly by the points to be measured and the position and altitude of the sensor may be in error. Positional errors will cause vertical er- rors at terrain with steep slopes and buildings. Altogether, editing of the data has to detect and correct such errors, but even with the most careful editing errors will remain. The number or percentage of outliers should be documented, for example in metadata, so that one can judge whether the derived DTM is usable for the intended application (‘‘fit for purpose’’). The derivation of accuracy measures has to adapt to the fact that outliers may exist and that the distribution of the errors might not be normal. There is thus a need for accuracy measures, which are reliable without being influenced by outliers or a skew distribution of the errors. These facts are well known and mentioned in recently published textbooks and manuals, for example in Li et al. (2005) and Maune (2007). Recent publications, which deal in detail with 0924-2716/$ – see front matter © 2009 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved. doi:10.1016/j.isprsjprs.2009.02.003