Digital Elevation Model Interpolation Research Articles

OPTIMIZATION OF DEM INTERPOLATION

Digital Elevation Models (DEMs) are simply regular grids of elevation measurements over the land surface. DEMs are mainly extracted by applying the technique of stereo measurements on images available from photogrammetry and remote sensing. DEMs play a vital role in many scientific, environmental, engineering as well as military applications which need accurate and dense DEMs. However, generating a dense and accurate DEM comes with the price of spending both time and money on the field measurements. Fortunately, advanced space technology has provided much single (if not stereo) high resolution satellite imageries almost worldwide with the available global or local DEMs. This study included evaluating both DEM produced from topographic map and raster DEM after resolution enhancement by using single satellite image. According to the results of these experiments, a strategy was proposed for using the reflectance data to enhance the accuracy of DEM interpolation. The proposed the reflectance data models were implemented in a software package and successfully tested.

Effects of digital elevation model spatial resolution on distributed calculations of solar radiation loading on a High Arctic glacier

AbstractHigh-resolution airborne lidar data are used to produce digital elevation models (DEMs) of an arctic valley glacier (midre Lovénbreen, Svalbard) at resolutions of 2.5–2000 m, using three different interpolation schemes. These data are used in a distributed model of solar radiation loading for glaciers. When the mean of all lidar measurements within a DEM cell is used to calculate cell height, the differences between the finest- (2.5 m) and coarsest-resolution (2000 m) DEMs for the calculated annual whole-glacier spatial means of total potential direct-beam solar radiation, potential duration of direct-beam solar radiation, and intensity of potential direct-beam solar radiation are 20%, 56% and −23% of the 2.5 m DEM values respectively. A resolution change from 2.5 m to 200 m affects the whole-glacier spatial mean summer net solar radiative flux by an average of 5%, and the summer melt production from the glacier by an average of 3% compared with the 2.5 m DEM values, for the years 2001–03. These changes are largely driven by underestimation of shading by surrounding topography at coarser DEM resolutions. This dependency is reduced in the second and third interpolation schemes, especially at resolutions finer than 50 m, which use the maximum lidar height measurement in some or all DEM cells. These results suggest that resolutions of ∼50 m are the coarsest that should be adopted in high-resolution glacier surface energy-balance models for glaciers of similar size and in similar topographic situations to midre Lovénbreen, and that the impact of DEM resolution on calculated solar radiation receipts can be reduced by an appropriate choice of DEM interpolation scheme.

Evaluating error associated with lidar-derived DEM interpolation

Light detection and ranging (lidar) technology is capable of precisely measuring a variety of vegetation metrics, the estimates of which are usually based on relative heights above a digital elevation model (DEM). As a result, the development of these elevation models is a critical step when processing lidar observations. A number of different algorithms exist to interpolate lidar ground hits into a terrain surface. We tested seven interpolation routines, using small footprint lidar data, collected over a range of vegetation classes on Vancouver Island, British Columbia, Canada. The lidar data were randomly subsetted into a prediction dataset and a validation dataset. A suite of DEMs were then generated using linear, quintic, natural neighbour, regularized spline, spline with tension, a finite difference approach (ANUDEM), and inverse distance weighted interpolation routines, at spatial resolutions of 0.5, 1.0 and 1.5 m. In order to examine the effects of terrain and ground cover on interpolation accuracies, the study area was stratified by terrain slope, vegetation structural class, lidar ground return density, and normalized difference vegetation indices (NDVI) derived from Quickbird and Landsat7 ETM+ imagery. The root mean square (RMS) and mean absolute errors of the residuals between the surfaces and the validation points indicated that the 0.5 m DEMs were the most accurate. Of the tested approaches, the regularized spline and IDW algorithms produced the most extreme outliers, sometimes in excess of ±6 m in sloping terrain. Overall, the natural neighbour algorithm provided the best results with a minimum of effort. Finally, a method to create prediction uncertainty maps using classification and regression tree (CART) analysis is proposed.

Uncertainties associated with digital elevation models for hydrologic applications: a review

Abstract. Digital elevation models (DEMs) represent the topography that drives surface flow and are arguably one of the more important data sources for deriving variables used by numerous hydrologic models. A considerable amount of research has been conducted to address uncertainty associated with error in digital elevation models (DEMs) and the propagation of error to derived terrain parameters. This review brings together a discussion of research in fundamental topical areas related to DEM uncertainty that affect the use of DEMs for hydrologic applications. These areas include: (a) DEM error; (b) topographic parameters frequently derived from DEMs and the associated algorithms used to derive these parameters; (c) the influence of DEM scale as imposed by grid cell resolution; (d) DEM interpolation; and (e) terrain surface modification used to generate hydrologically-viable DEM surfaces. Each of these topical areas contributes to DEM uncertainty and may potentially influence results of distributed parameter hydrologic models that rely on DEMs for the derivation of input parameters. The current state of research on methods developed to quantify DEM uncertainty is reviewed. Based on this review, implications of DEM uncertainty and suggestions for the GIS research and user communities are offered.

Reconstruction of DEMs From ERS-1/2 Tandem Data in Mountainous Area Facilitated by SRTM Data

A new approach is presented in this paper to produce Digital Elevation Model (DEM) in mountainous areas with steep slope using ERS-1/2 tandem data. In order to reduce the impact of phase errors on the Interferometric Synthetic Aperture Radar (InSAR)-generated DEM, an external DEM such as that from Shuttle Radar Topography Mission (SRTM) is utilized in this approach. The proposed algorithm includes two steps: The first step is to model and remove phase trends with a linear regression analysis before converting phase to height; the second step is to filter unreliable height points before interpolating the DEM from the InSAR height map. The critical points are the following: 1) determining the one-to-one correspondence between the interferogram and the SRTM DEM before knowing the InSAR-derived elevation values and 2) estimating the elevation range of every pixel from SRTM DEM. To solve the first problem, an iteratively geocoding algorithm is performed. A DEM interpolation error model solves the second one. For InSAR data processing, the SRTM DEM is not only usable for modeling systematic phase errors but also for filtering gross height errors. The experiments in Zhangbei and the Three Gorges areas in China show that our approach has improved the accuracy of the resulting DEMs significantly without any ground control points.

Effects of Terrain Morphology, Sampling Density, and Interpolation Methods on Grid DEM Accuracy

This paper explores the effects of terrain morphology, sampling density, and interpolation methods for scattered sample data on the accuracy of interpolated heights in grid Digital Elevation Models (DEM). Sampled data were collected with a 2 by 2 meters sampling interval from seven different morphologies, applying digital photogrammetric methods to large scale aerial stereo imagery (1:5000). The experimen- tal design was outlined using a factorial scheme, and an analysis of variance was carried out. This analysis yielded the following main conclusions: DEM accuracy (RMSE) is affected significantly by the variables studied in this paper according to morphologysampling densityinterpola- tion method. Multiquadric Radial Basis Function (RBF) was rated as the best interpolation method, although Multilog RBF performed similarly for most morphologies. The rest of RBF interpolants tested (Natural Cubic Splines, Inverse Multiquadric, and Thin Plate Splines) showed numerical instability working with low smoothing factors. Inverse Distance Weighted interpolant performed worse than RBF Multiquadric or RBF Multilog. In addition, it is found that the relationship between the RMSE and the sampling density N is adjusted to a decreasing potential function that may be expressed as RMSE/Sdz � 0.1906(N/M) � 0.5684 (R 2 � 0.8578), being Sdz the standard deviation of the heights of the M check points used for accuracy estimation, and N the number of sampling points used for creating the DEM. The results obtained in this study allow us to observe the possibility of establishing empirical relationships between the RMSE expected in the interpolation of a Grid DEM and such variables as terrain ruggedness, sampling density, and the interpolation method, among others that could be added. Therefore, it would be possible to establish a priori the optimum grid size required to generate or storage a DEM of a particular accuracy, with the economy in computing time and file size that this would signify for the digital flow of the mapping information.

Artificial Lineaments in Digital Terrain Modelling: Can Operators of Topographic Variables Cause Them?

Digital terrain modeling is widely used in geological studies. In some cases, orthogonal and diagonal linear patterns appear on maps of local topographic variables. These patterns may be both portrayals of geological structures and artefacts. Some researchers speculated that possible anisotropy of operators of local topographic variables might be a cause of these artefacts. Using a principle for testing derivative operators in image processing, we gave proof to isotropy (rotation invariability) of operators of a majority of local topographic attributes of the complete system of curvatures (i.e., slope gradient, horizontal curvature, vertical curvature, mean curvature, Gaussian curvature, accumulation curvature, ring curvature, unsphericity curvature, difference curvature, minimum curvature, maximum curvature, horizontal excess curvature, and vertical excess curvature). Rotating an elevation function about z-axis and then applying these operators cannot lead to variations in both values of the topographic variables and patterns in their maps, comparing with results of applying these operators to an unrotated elevation function. This demonstrates that linear artefacts with preferable directions in maps of the topographic attributes specified cannot be caused by intrinsic properties of their operators. Other possible sources for false linear patterns in maps of topographic variables are briefly discussed: (a) errors in the compilation of digital elevation models (DEMs), (b) grid geometry of digital terrain models (DTMs), (c) errors in DEM interpolation, (d) imperfection of algorithms for DTM derivation, and (e) aliasing errors.

Preserving first and second moments of the slope area relationship during the interpolation of digital elevation models

Accurate representation of terrain with appropriate reproduction of topographic characteristics is important for increasingly sophisticated physically-based models of natural processes. Recently investigators have successfully enforced slope area relationships to interpolate more realistic topographies from the sparse data. The limitation of those procedures is that, for the most part, they preserve only the first moment (the mean), when scaling slope with contributing area. Here we present a simple approach to also enforce the second moment, the variance, during landscape evolution simulations or physically-based spatial interpolations.

Errors of signal processing in digital terrain modelling

We present new interpretation of three classes of errors in digital terrain models (DTMs) which can be sources of artefacts in DTM-based studies: (a) errors in interpolation of digital elevation models (DEMs) caused by the Gibbs phenomenon; (b) errors in DTM derivation from DEMs with ‘enhanced’ resolution due to noise increase after DEM differentiation; (c) errors in DTM derivation caused by displacement of a DEM grid. Explanation of artefact roots and ways to avoid them are carried out in the context of the theory of signal processing. The Gibbs phenomenon is a specific behaviour of some functions manifested as over- and undershoots near a jump discontinuity. Any DEM includes jump discontinuities of the elevation, such as escarpments and pronounced errors of DEM generation. There are four main ways to prevent or reduce DEM errors caused by the Gibbs phenomenon: (a) decreasing the jump discontinuity before DEM interpolation; (b) using interpolation functions which do not generate the Gibbs phenomenon; (c) omitting over- and undershoots after DEM interpolation; (d) filtering the Gibbs phenomenon. Derivation of topographic variables from DEMs marked by ‘enhanced’ resolution can lead to artefacts. If a DEM of this kind is interpolated by triangulation-based algorithms, triangular patterns may be revealed on maps of topographic variables. If an ‘enhanced’ resolution of DEM is achieved by the weighted average methods of interpolation, contour ‘traces’ may be seen on maps. This is because partial derivatives used to calculate some topographic variables are very responsive to high-frequency components of a DEM. To prevent these errors one should use a regular DEM with a grid space relating to an average distance between points in an irregular DEM. Displacement of a grid of points, wherein elevation values are interpolated or determined, influences the derivation of topographic variables (e.g. map design of horizontal and vertical curvatures). Some patterns break, merge, and change their width and length. Small dots, lines, and particles of big patterns can appear and disappear on maps. These effects should be taken into account in the application of these maps to DTM-based geological studies.

Interpolation of digital elevation models using AMLE and related methods

Interpolation of digital elevation models becomes necessary in many situations, for instance, when constructing them from contour lines (available e.g., from nondigital cartography), or from disparity maps based on pairs of stereoscopic views, which often leaves large areas where point correspondences cannot be found reliably. The absolutely minimizing Lipschitz extension (AMLE) model is singled out as the simplest interpolation method satisfying a set of natural requirements. In particular, a maximum principle is proven, which guarantees not to introduce unnatural oscillations which is a major problem with many classical methods. The authors then discuss the links between the AMLE and other existing methods. In particular, they show its relation with geodesic distance transformation. They also relate the AMLE to the thin-plate method, that can be obtained by a prolongation of the axiomatic arguments leading to the AMLE, and addresses the major disadvantage of the AMLE model, namely its inability to interpolate slopes as it does for values. Nevertheless, in order to interpolate slopes, they have to give up the maximum principle and authorize the appearance of oscillations. They also discuss the possible link between the AMLE and Kriging methods that are the most widely used in the geoscience literature.

Optimising the degree of data smoothing for locally adaptive finite element bivariate smoothing splines

Finite difference and finite element schemes for bivariate thin plate smoothing splines are described. Nested grid SOR iterative methods are known to be able to solve these systems efficiently for large data sets. An iterative Newton procedure for optimising the smoothing parameter to achieve a prescribed residual sum of squares from the data is obtained. It can be added to the SOR iteration with little additional computational cost and is demonstrated on test data to work for a wide range of smoothing parameters. An apparently more accurate version of this procedure, which requires more memory, converges slightly less quickly than the simpler approximation. The simpler method appears to be directly compatible with the SOR iterative method. The Newton method is shown to also work for locally adaptive versions of finite difference smoothing splines. The roughness penalty can be made locally adaptive to respect process-based constraints, such as minimum profile curvature, which depends on the local aspect of the fitted surface. This can be applied to the interpolation of digital elevation models. The weighted residual sum of squares can be made locally adaptive to allow for positional error in data, whether arising from actual data error, or from a finite difference discretisation. This has given rise to an objective method for optimising the grid resolution to the information content of the data.

DEM Interpolation Using Inverse Spectrum Constraints

ABSTRACT Generation of a Digital Elevation Model (DEM) in remote sensing is an important application. The process of DEM generation often requires interpolation. This paper introduces Claerbout's interpolation algorithm that uses spectral information, which is widely used in geophysical applications, and examines the applicability of the method to DEM interpolation. The interpolation process can be explained in two steps. The first step is for finding spectral information from the known data and the second step is finding missing data so as to follow the spectral trend found in the previous step. The interpolation algorithm was tested for a real DEM data and compared with other conventional DEM interpolation method such as kriging method.

Towards Context- Dependent Interpolation of Digital Elevation Models

The fractional Brownian motion (fBm) model has become increasingly popular in recent years as a mechanism for the synthesis of many natural phenomena. Unfortunately, the required interdependence of neighbouring points over an unbounded area (context dependence) renders valid approximations to fBm extremely inefficient. This paper describes a technique for the interpolation of digital elevation models to an arbitrarily high spatial resolution. This is achieved using an efficient recursive subdivision algorithm which has the ability to permit some degree of context dependence within, and across the boundaries of interpolation areas. The application of this technique to flight simulation is described and the technique is evaluated based on its ability to reduce run-time storage requirements.