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To attenuate positional errors of LiDAR-derived datasets for constructing digital elevation models (DEMs), a feature-preserving point denoising algorithm (F-PDA) is developed in this paper. F-PDA i...

Digital elevation model (DEM) source data are subject to both horizontal and vertical errors owing to improper instrument operation, physical limitations of sensors, and bad weather conditions. These factors may bring a negative effect on some DEM-based applications requiring low levels of positional errors. Although classical smoothing interpolation methods have the ability to handle vertical errors, they are prone to omit horizontal errors. Based on the statistical concept of the total least squares method, a total error-based multiquadric (MQ-T) method is proposed in this paper to reduce the effects of both horizontal and vertical errors in the context of DEM construction. In nature, the classical multiquadric (MQ) method is a vertical error regression procedure, whereas MQ-T is an orthogonal error regression model. Two examples, including a numerical test and a real-world example, are employed in a comparative performance analysis of MQ-T for surface modeling of DEMs. The numerical test indicates that...

The classification of airborne laser scanning ALS point clouds is a necessary step in the process of digital elevation model DEM construction. Motivated by the surface interpolation filtering scheme, a multi-resolution hierarchical classification MHC method was developed to perform classification in our previous research. However, similar to almost all filtering methods, MHC suffers from the problem of misclassifying off-terrain and ground points in complex landscapes with steep slopes and large discontinuities. To improve the classification accuracy in the above landscapes, the original MHC is improved in this article by adopting a region growing-based segmentation method to maximally capture the initial ground seeds of MHC. Furthermore, considering the high sensitivity of principle component analysis PCA to outliers, a robust PCA approach based on least trimmed squares LTS is proposed to estimate point normals. Fifteen groups of data sets provided by the International Society for Photogrammetry and Remote Sensing ISPRS Working Group III/3 are utilized to compare the performances of the improved and original MHCs. Results indicate that the improved MHC is more accurate than the original MHC, irrespective of accuracy measures. In addition, we also compare the results of our method with three new filtering methods developed in the years 2013 and 2014. It is found that regardless of landscapes i.e. urban and rural samples, the improved MHC is averagely more accurate than the three filtering methods in terms of type II error, and irrespective of accuracy measures i.e. types I, II and total errors, our method outperforms the three filtering methods for the rural samples. In short, the robust segmentation-based MHC demonstrates great potential to ALS-derived DEM construction in rural areas.

A sequential adjustment (SA) method is employed to decrease the computational cost of high-accuracy surface modeling (HASM), and the SA of HASM (HASM-SA) is being developed. A mathematical surface was used to comparatively analyze the computing speed of SA and the classical iterative solvers provided by MATLAB 7.7 for solving the system of linear equations of HASM. Results indicate that SA is much faster than the classical iterative solvers. The computing time of HASM-SA is determined by not only the total number of grid cells but also the number of sampling points in the computational domain. A real-world example of surface modeling of digital elevation models (DEMs) with various resolutions shows that HASM-SA is averagely more accurate and much faster than the commonly used interpolation methods, such as inverse distance weighting (IDW), kriging, and three versions of spline, namely regularized spline (RSpline), thin-plate spline (TPS), and ANUDEM in terms of root mean square error (RMSE), mean absolute...

To smooth noises inherent in uniformly sampled dataset, the smoothness of high accuracy surface modeling HASM was explored, and a smoothing method of HASM HASM-SM was developed based on a penalized least squares method. The optimal smoothing parameter of HASM-SM was automatically obtained by means of the generalized cross-validation GCV method. For an efficient smoothing computation, discrete cosine transform was employed to solve the system of HASM-SM and to estimate the minimum GCV score, simultaneously. Two examples including a numerical test and a real-world example were employed to compare the smoothing ability of HASM-SM with that of GCV thin plate smoothing spline TPS and kriging. The numerical test indicated that the minimum GCV HASM-SM is averagely more accurate than TPS and kriging for noisy surface smoothing. The real-world example of smoothing a lidar-derived Digital Elevation Model DEM showed that HASM-SM has an obvious smoothing effect, which is on a par with TPS. In conclusion, HASM-SM provides an efficient tool for filtering noises in grid-based surfaces like remote sensing–derived images and DEMs.

A new method based on orthogonal least square OLS of multiquadric algorithm MOLS is proposed for digital elevation model DEM generalization by the retrieval of critical points from a grid-based DEM to construct a triangulated irregular network surface. The focus is on the method for accurately obtaining the critical points, which maximally retain the important terrain feature lines. The grid-based DEM to be generalized is first approximated in terms of multiquadric method, and then the significances of the grids are assessed based on OLS method with the merit that each selected grid point gives the maximal increment to the explained variance of the desired output. We used six study sites with different terrain complexities to comparatively analyze the generalization accuracies of MOLS and the classical methods including very important method and point-additive method Latticetin under different numbers of retrieved significant points. The results indicate that MOLS averagely performs better than the classical methods for the original DEM generalization in terms of root mean square error. The analytical results also show that MOLS has the better ability in maintaining the feature lines inherent in the original DEM than the classical methods in terms of streamline matching rate. The perfect performance of the newly proposed method can be attributed to the high accuracy of multiquadric method for surface approximation and the effectiveness of OLS for point significance assessment.

A new method for filling voids is developed by improving the approach to high-accuracy surface modelling (HASM), which is based on the first fundamental coefficients and the second fundamental coefficients of surfaces. The first fundamental coefficients are used to calculate the lengths of curves, angles of tangent vectors, areas of regions and geodesics on the surface. The second fundamental coefficients reflect the local warping of the surface, namely its deviation from the tangent plane at the point under consideration, which can be observed from outside the Earth. Nine regions with different landform complexities in hilly, plateau and mountainous areas are selected for testing the performance of HASM by comparing those ones of the classic methods such as triangulated irregular network (TIN), inverse distance weighted interpolation (IDW), advanced Spline method (ANUDEM), Spline and Kriging. The results demonstrated that the HASM void filling always has the highest accuracy regardless of the landform complexity, void area and auxiliary data.

A robust estimator based on the M-estimation principle (REMP) has been developed for digital elevation model (DEM) accuracy assessment. Adaptive weights were employed to respond to a broad class of DEM error distributions, and an iterative procedure in terms of REMP starting from robust initial estimates with a high breakdown point was introduced. Original DEMs with the resolution of 2 m were obtained by means of light detection and Ranging (LiDAR) from two study sites. DEM errors in each study site were, respectively, calculated based on 100 checkpoints captured by real-time kinematic (RTK) in terms of stratified random sampling strategy. Each group of DEM errors was, respectively, contaminated by five groups of outliers from different distributions. Thus, ten groups of simulated DEM errors were employed to comparatively assess the estimation accuracies of REMP and the classical estimators. The results indicated that under the non-normal distribution of DEM errors, the classical non-robust estimators are seriously influenced by the non-normality. Some robust estimators such as 10%-trimmed or Winsorized mean and normalized median absolute deviation (MADN) are not very robust to resist the influence of outliers. REMP, slightly affected by the non-normal distribution of DEM errors, is more accurate than the classical estimators. The robust methodology can adapt to the DEMs, especially the ones derived from remote sensing such as LiDAR or digital photogrammetry in non-open terrain.