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Approximation theory applied to DEM vertical accuracy assessment / X. Liu in Transactions in GIS, vol 16 n° 3 (June 2012)  

Public [article]  inTransactions in GIS > vol 16 n° 3 (June 2012) . - pp 397 - 410 Titre : Approximation theory applied to DEM vertical accuracy assessment Type de document : Article/Communication Auteurs : X. Liu, Auteur ; P. Hu, Auteur ; H. Hu, Auteur ; J. Sherda, Auteur Année de publication : 2012 Article en page(s) : pp 397 - 410 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Applications photogrammétriques [Termes IGN] approximation [Termes IGN] estimation statistique [Termes IGN] interpolation linéaire [Termes IGN] modèle numérique de surface [Termes IGN] précision altimétrique [Termes IGN] précision du positionnement Résumé : (Auteur) Existing research on DEM vertical accuracy assessment uses mainly statistical methods, in particular variance and RMSE which are both based on the error propagation theory in statistics. This article demonstrates that error propagation theory is not applicable because the critical assumption behind it cannot be satisfied. In fact, the non-random, non-normal, and non-stationary nature of DEM error makes it very challenging to apply statistical methods. This article presents approximation theory as a new methodology and illustrates its application to DEMs created by linear interpolation using contour lines as the source data. Applying approximation theory, a DEM's accuracy is determined by the largest error of any point (not samples) in the entire study area. The error at a point is bounded by max(|?mode|+M2h2/8) where |?node| is the error in the source data used to interpolate the point, M2 is the maximum norm of the second-order derivative which can be interpreted as curvature, and h is the length of the line on which linear interpolation is conducted. The article explains how to compute each term and illustrates how this new methodology based on approximation theory effectively facilitates DEM accuracy assessment and quality control. Numéro de notice : A2012-283 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1111/j.1467-9671.2012.01343.x Date de publication en ligne : 28/05/2012 En ligne : https://doi.org/10.1111/j.1467-9671.2012.01343.x Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31729 [article]

Accuracy assessment of digital elevation models based on approximation theory / P. Hu in Photogrammetric Engineering & Remote Sensing, PERS, vol 75 n° 1 (January 2009)  

Public [article]  inPhotogrammetric Engineering & Remote Sensing, PERS > vol 75 n° 1 (January 2009) . - pp 49 - 56 Titre : Accuracy assessment of digital elevation models based on approximation theory Type de document : Article/Communication Auteurs : P. Hu, Auteur ; X. Liu, Auteur ; H. Hu, Auteur Année de publication : 2009 Article en page(s) : pp 49 - 56 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Applications photogrammétriques [Termes IGN] analyse comparative [Termes IGN] approximation [Termes IGN] données de terrain [Termes IGN] erreur de modèle [Termes IGN] estimation de précision [Termes IGN] interpolation bilinéaire [Termes IGN] interpolation linéaire [Termes IGN] interpolation polynomiale [Termes IGN] modèle numérique de surface [Termes IGN] précision altimétrique [Termes IGN] propagation d'erreur [Termes IGN] Triangulated Irregular Network Résumé : (Auteur) Empirical research in DEM accuracy assessment has observed that DEM errors are correlated with terrain morphology, sampling density, and interpolation method. However, theoretical reasons for these correlations have not been accounted for. This paper introduces approximation theory adapted from computational science as a new framework to assess the accuracy of DEMs interpolated from topographic maps. By perceiving DEM generation as a piecewise polynomial simulation of the unknown terrain, the overall accuracy of a DEM is described by the maximum error at any DEM point. Three linear polynomial interpolation methods are examined, namely linear interpolation in 1D, TIN interpolation, and bilinear interpolation in a rectangle. Their propagation error and interpolation error, whose sum is the total error at a DEM point, are derived. Based on the results, the theoretical basis for the correlation between DEM error and terrain morphology and source data density is articulated for the first time. Copyright ASPRS Numéro de notice : A2009-008 Affiliation des auteurs : non IGN Thématique : IMAGERIE Nature : Article DOI : 10.14358/PERS.75.1.49 En ligne : https://doi.org/10.14358/PERS.75.1.49 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=29638 [article]