The accuracy of grid digital elevation models linearly constructed from scattered sample data

Aguilar, Fernando J.; Aguilar, Manuel A.; Agüera, Francisco Orgaz; Sánchez, Jaime Almansa

doi:10.1080/13658810500399670

Cited by 47 publications

(47 citation statements)

References 22 publications

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“…In combining propagated error from source data points with interpolation error, it is commonly assumed that they are independent (e.g. Li, 1993;Huang, 2000;Aguilar et al, 2006).…”

Section: Discussionmentioning

confidence: 99%

“…Some researchers (Li, 1993;Huang, 2000;Aguilar et al, 2006) have adopted this assumption (independent and identical) for propagating error variances of node points into DEM. In some cases, error in data points acquired by some instruments may be independent.…”

Section: Error Propagation Methodsmentioning

confidence: 99%

“…Only the average error variance for a TIN model was evaluated in these studies (i.e. Zhu et al, 2005;Shi et al, 2005;Aguilar et al, 2006). Kyriakidis and Goodchild (2006) also investigated the average error variance of three linear interpolation methods (line linear, TIN linear and bilinear), and the propagation of vertical error variance at node points into a generic point using the geostatistics framework.…”

Section: Introductionmentioning

confidence: 99%

“…Shi et al (2005) estimated the propagated error variance from source data into DEMs created through higher-order interpolation (biquadratic and bicubic). Aguilar et al (2006) studied the accuracy of grid DEMs linearly constructed from scattered sample data. Only the average error variance for a TIN model was evaluated in these studies (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Fan

Smethurst

Atkinson

et al. 2014

International Journal of Geographical Information Science

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Digital elevation models (DEMs) have been widely used for a range of applications and form the basis of many GIS related tasks. An essential aspect of a DEM is its accuracy, which depends on a variety of factors, such as source data quality, interpolation methods, data sampling density and the surface topographical characteristics. In recent years, point measurements acquired directly from land surveying such as differential global positioning system (DGPS) and light detection and ranging (LiDAR) have become increasingly popular. These topographical data points can be used as the source data for the creation of DEMs at a local or regional scale. The errors in point measurements can be estimated in some cases. The focus of this article is on how the errors in the source data propagate into DEMs. The interpolation method considered is a triangulated irregular network (TIN) with linear interpolation. Both horizontal and vertical errors in source data points are considered in this study. An analytical method is derived for the error propagation into any particular point of interest within a TIN model. The solution is validated using Monte Carlo simulations and survey data obtained from a terrestrial laser scanner.

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“…In combining propagated error from source data points with interpolation error, it is commonly assumed that they are independent (e.g. Li, 1993;Huang, 2000;Aguilar et al, 2006).…”

Section: Discussionmentioning

confidence: 99%

Section: Error Propagation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Fan

Smethurst

Atkinson

et al. 2014

International Journal of Geographical Information Science

View full text Add to dashboard Cite

show abstract

“…In every case, the remaining scattered points (observed or map points) were used to obtain both 1 m grid spacing GMRF and TLI interpolated DSMs whose vertical accuracy (RMSEz and mean, maximum and minimum vertical error) was assessed on the set of previously extracted checkpoints by obtaining the z-differences (Zcheckpoint -ZDSM) (Aguilar et al, 2006). Every ZDSM corresponding to the easting and northing coordinates of the check points was calculated by applying bilinear interpolation from the GMRF or TLI computed 1 m grid spacing DSM.…”

Section: Dsm Accuracy Assessmentmentioning

confidence: 99%

Analysis and Validation of Grid Dem Generation Based on Gaussian Markov Random Field

Aguilar¹,

Aguilar²,

Blanco³

et al. 2016

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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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 2 ) 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.

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Effect of transect location, transect spacing and interpolation methods on river bathymetry accuracy

Glenn¹,

Tonina

Morehead³

et al. 2016

Earth Surf Processes Landf

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Digital elevation models (DEMs) of river channel bathymetries are developed by interpolating elevations between data collected at discrete points or along transects. The accuracy of interpolated bathymetries depends on measurement error, the density and distribution of point data, and the interpolation method. Whereas point measurement errors can be minimized by selecting the most efficient equipment, the effect of data density and interpolation method on river bathymetry is relatively unknown. Thus, this study focuses on transect-based collection methods and investigates the effects of transect location, the spacing between transects, and interpolation methods on the accuracy of interpolated bathymetry. This is accomplished by comparing four control bathymetries generated from accurate and high resolution, sub-meter scale data to bathymetries interpolated from transect data extracted from the control bathymetries using two transect locating methods and four interpolation methods. The transect locating methods are a morphologically-spaced and an equally-spaced model. The four interpolation methods are Ordinary Kriging, Delaunay Triangulation, and Simple Linear, which are applied in curvilinear coordinates (Delaunay Triangulation is also applied in Cartesian coordinates), and Natural Neighbor only in Cartesian Coordinates. The bathymetric data were obtained from morphologically simple and complex reaches of a large (average bankfull width = 90 m) and a small (average bankfull width = 17 m) river. The accuracy of the developed DEMs is assessed using statistical analysis of the differences between the control and interpolated bathymetries and hydraulic parameters assessed from bankfull water surface elevations. Results indicate that DEM accuracy is not influenced by the choice of transect location method (with same averaged cross-section spacing) or a specific interpolation method, but rather by the coordinate system for which the interpolation method is applied and the spacing between transects. They also show negligible differences between the mean depths and surface areas calculated from bathymetries with dense or coarse spacing.

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The accuracy of grid digital elevation models linearly constructed from scattered sample data

Cited by 47 publications

References 22 publications

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Propagation of vertical and horizontal source data errors into a TIN with linear interpolation

Analysis and Validation of Grid Dem Generation Based on Gaussian Markov Random Field

Effect of transect location, transect spacing and interpolation methods on river bathymetry accuracy

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