The processing of high-density LiDAR point clouds presents significant computational challenges for DEM generation due to data redundancy and topographic feature degradation during simplification. To overcome this problem, this study proposes a Terrain-Feature Retention and Spatial Uniformity Balancing (TFRSUB) method that integrates three key innovations: (i) a Distance-Geometric Synergy Index (DGSI) combining orthogonal deviation distance and point sampling interval to mitigate boundary contraction artifacts; (ii) a Composite Terrain Factor (CTF) synthesizing multiple terrain parameters to characterize diverse topographic features; and (iii) a cluster-driven Gaussian Process Regression (GPR) framework using CTF for iterative feature point selection, optimizing the trade-off between topographic fidelity and point distribution homogeneity. Evaluated on eight high-resolution LiDAR terrain point clouds across six retention ratios, TFRSUB demonstrates significant accuracy improvements over seven state-of-the-art methods, achieving reductions of 9.22%-64.70% in DEM root mean square error, 7.80%-61.34% in mean absolute error, 16.43%-76.88% in slope error, and 28.12%-81.35% in mean curvature error. These results establish TFRSUB as an alternative solution for LiDAR point cloud simplification that maintains topographic fidelity while addressing computational storage challenges.

LiDAR-derived ground points have emerged as the primary data source for generating digital elevation models (DEMs). Typically, LiDAR data exhibits a random spatial distribution, suffers from sampling noise, and has an implicit representation of terrain breaklines, posing significant challenges for traditional spatial interpolators. In this paper, a terrain breakline-aware smoothing interpolation (TBASI) method is proposed to generate high-accuracy DEMs from LiDAR data. Specifically, a smoothing interpolation based on penalized least squares regression is developed to smooth out sampling errors inherent in LiDAR data, while avoiding overfitting. In the smoothing interpolation framework, a quadrilateral kernel function is presented to recover diverse terrain breaklines. Furthermore, an iterative interpolation strategy is designed to ensure the stability and robustness of the interpolated DEMs under complex topographical conditions. TBASI was benchmarked against five classical interpolation methods for producing DEMs using ten publicly available datasets with different terrain characteristics. The experimental results demonstrate that TBASI achieves superior accuracy compared to the conventional interpolation approaches on almost all samples. Of particular significance, TBASI is capable of accurately preserving critical terrain features such as ridges, valleys, and escarpments.

Blending satellite precipitation products (SPPs) with rain gauge observations through machine learning (ML)based methods offers a proficient means of achieving high-accuracy precipitation data. However, traditional ML methods often neglect the spatial heterogeneity of precipitation across the study area, and the unique strengths of individual ML models remain underutilized. To address these challenges, this paper proposes a stacking ensemble learning approach that accounts for spatial heterogeneity for blending SPPs with rain gauge data to produce highly accurate precipitation estimates. Specifically, the study area is segmented into several homogeneous zones to mitigate spatial heterogeneity, with each grid cell within these zones assigned a uniform identifier (ID). Furthermore, a stacking ensemble ML framework which takes the ID as an input feature is developed to merge SPPs and rain gauge observations. To evaluate the performance of our proposed method, we blended daily IMERG data and rain gauge observations spanning from 2016 to 2020 across the Chinese mainland, benchmarking it against seven ML methods and the original IMERG data. The experimental results provide several key insights: (i) Data-driven adaptive clustering emerges as an efficient tool for addressing the challenge of spatial heterogeneity in high-quality precipitation estimation. (ii) Across multiple temporal scales, the proposed method outperforms the classical ML-based methods. Notably, at the daily scale, it improves upon the classical approaches by at least 2.4 % in Mean Absolute Error (MAE), 0.76 % in Root Mean Square Error (RMSE), 1.4 % in Correlation Coefficient (CC), and 1.4 % in Kling-Gupta Efficiency (KGE). Furthermore, at the monthly and seasonal scales, it reduces MAE by at least 2.3 % and 2.8 %, respectively, and enhances KGE by at least 0.9 % and 1.1 %. (iii) The spatial distribution of precipitation estimated by the proposed method aligns more closely with rain gauge observations compared to the classical methods. (iv) The ID feature plays a crucial role in precipitation estimation, ranking first and second in terms of feature importance for 39.6 % and 33.9 % of days, respectively, over the five-year period. (v) The proposed method generates positive incremental values at 69 % of rain gauge stations, demonstrating greater added value compared to the classical methods. Overall, the proposed method can be regarded as an effective tool for generating high-accuracy daily precipitation products.

Complex landscapes, typically characterized by outliers, objects with diverse structures, vegetation on steep slopes, and terrain discontinuities, pose significant challenges to traditional filtering methods, especially when processing ultra-large-scale point clouds. To address these challenges, this paper proposes an efficient interpolation-based and terrain-adaptive hierarchical filtering method. Specifically, a hybrid algorithm combining a moving-window detector with robust surface fitting is developed to optimize the selection of initial ground seeds. Subsequently, a weighted finite-difference-based Thin Plate Spline (TPS) method is introduced to generate reference ground surfaces, thereby improving computational efficiency and mitigating the impact of misclassified object points. Finally, a terrain-adaptive filtering threshold incorporating different orders of terrain roughness is designed to accurately extract ground points near terrain discontinuities. To evaluate the proposed method, extensive experiments were conducted on the ISPRS benchmark samples and the ultra-large-scale OpenGF dataset. Results demonstrate that our method achieves an average Kappa coefficient of 92.3% across all 15 ISPRS samples, outperforming 24 state-of-the-art filtering methods published since 2010. On the OpenGF dataset, the proposed method surpasses five classical filters, reducing the average total error by 34.1%-77.4% and improving the average Kappa coefficient by 2.8%-21.7%. Overall, this framework provides a robust solution for filtering ultra-large-scale point clouds in complex landscapes.

High-accuracy digital elevation models (DEMs) serve as critical inputs for quantitative geomorphic analysis, yet precise surface reconstruction from irregularly distributed ground points continues to pose significant challenges. Conventional spatial interpolation methods with the surface-continuity assumption systematically distort abrupt terrain discontinuities, such as escarpments, fault scarps, and ridgelines. To address this limitation, we present a high-fidelity surface modeling (HFSM) method that explicitly incorporates 1-D Hausdorff measures of both elevation and normal discontinuities into a variational energy minimization formulation. By framing the reconstruction as a free-discontinuity problem, HFSM adaptively balances surface smoothness with discontinuity localization through parameter-controlled energy terms, enabling the preservation of critical terrain features. Extensive validation conducted across six distinct terrain types, each with different sampling densities ranging from 30% to 90%, showcases the outstanding performance of HFSM when compared to five benchmark approaches. On average, HFSM attains a reduction in DEM root mean squared error (RMSE) by 7.3%-43.1% and enhances the preservation of terrain feature lines by 2.7%-22.2%. These results position HFSM as an effective solution for high-quality DEM generation in morphologically complex terrains, particularly valuable for geomorphometric applications requiring precise representation of surface discontinuities.

Publicly available satellite precipitation products (SPPs) are essential inputs for hydrological models. However, the existing SPPs suffer from coarse resolutions and large uncertainties, which greatly hinder their widespread applications. Thus, to fully utilize the unique characteristics of each individual SPP, a spatial random forest (SRF)-based downscaling and merging (SRF-DM) method is proposed to fuse multiple SPPs and gauge observations in this paper. The proposed method incorporates spatial autocorrelation information between precipitation observations through a covariate. This covariate is estimated using ordinary kriging interpolation on spatial neighbors that have a high correlation with the target location. The proposed method was used to generate 1-km daily precipitation data using the datasets from five satellite precipitation products (IMERG, GSMaP, CHIRPS, MORPH, and PERSIANN) and gauge observations in the period from January 1, 2015 to December 31, 2019 over Sichuan province, China. The performance of SRF-DM was compared with the original SPPs, XGBoost-based downscaling and merging (XGB-DM), two double-layer machine learning (ML) methods, namely RF-RF and RF-artificial neural network (RF-ANN), and three single ML methods, namely RF, ANN, and RF-based Merging Procedure (RF-MEP). The experimental results demonstrate the following findings: (i) SRF-DM is more accurate than the original SPPs across different temporal scales (i.e., daily, monthly, and seasonal) in terms of statistical and categorical accuracy measures, (ii) SRF-DM outperforms the six ML-based methods in estimating high precipitation and capturing spatial precipitation patterns, (iii) the spatial autocorrelation between neighboring precipitation data is the most significant factor in both downscaling and merging, and (iv) the performance of SRF-DM is influenced by gauge density, but it still yields good results even with a limited number of gauges. On the whole, SRF-DM is considered an effective tool for generating daily precipitation products with high accuracy and resolution, which is primarily attributed to its satisfactory performance in regions with diverse precipitation patterns and topography.

Spatial heterogeneity and information redundancy of landslide influencing factors (LIFs) greatly impair the generalizability of landslide susceptibility mapping (LSM) models. To this end, this paper proposes a new LSM method that takes into account spatial heterogeneity and factor optimization. Firstly, a method based on frequency ratio, coupled with buffer-controlled sampling, is developed to extract non-landslides from the non-landslide area. Then, the study site is divided into several homogeneous areas using agglomerative clustering based on LIFs and spatial locations. Next, the LIFs are optimized in each region based on a combination of variance inflation factor, the Boruta algorithm, and geographical detector so as to avoid information redundancy and noise from both statistical and spatial perspectives. Finally, the random forest (RF) model with the optimized LIFs is used for LSM at the regional scale. Taking 686 landslides and 15 LIFs in Yibin city, China as an example, the proposed method was compared with four state-of-the-art models for LSM including regional RF, global RF with factor optimization, global RF using clustering attribute as one of its inputs, global RF without factor optimization, and global RF using a combination of factor optimization and clustering attribute. Results indicate that compared to the four classical models, the proposed method increases the Accuracy, Recall, Precision, F1 score, and the area under the receiver operating characteristic (AUC) curve by 1.6–5.2

Satellite remote-sensing precipitation products are currently the main source for obtaining large-scale and continuous precipitation observations.However,currently available satellite remote-sensing precipitation products have coarse spatial resolution and suffer from certain systematic biases.Thus,this paper aims to downscale the precipitation data and remove its inherent systematic biases. This paper proposes a two-stage Spatial Random Forest(SRF)method(SRF-SRF)by fully considering the influence of high-resolution environmental variables(including topography,NDVI,surface temperature,latitude,and longitude)on the precipitation and the spatial correlation of neighboring remotely sensed precipitation(stations).Taking the Global Precipitation Measurement Mission(GPM)monthly precipitation data of Sichuan Province from 2015-2019 as an example,its quality is enhanced with the help of SRF-SRF.The calculation results are compared with those of seven existing methods,including Geo-Weighted Regression(GWR),Back-Propagation Neural Network(BPNN),Random Forest(RF),Kriging interpolation of station precipitation(Kriging),Geographic Difference Analysis correction after downscaling by SRF(SRF-GDA),SRF correction after downscaling by bilinear interpolation(Bi-SRF),and annual precipitation downscaled by SRF.Subsequently,the results are scaled by month and corrected using SRF(SRFDis). Experimental analysis shows the following:(1)At the monthly scale,compared with the original GPM,the mean absolute error(MAE)of SRF-SRF is reduced by 19.51％,and the medium error(RMSE)is reduced by 16.35％.The accuracy is better than those of other methods.At the seasonal scale,SRF-SRF has the smallest error in winter and the largest error in summer,but its calculation accuracy is better than those of other methods.At the annual scale,the four SRF-based methods(including SRF-SRF,SRF-GDA,Bi-SRF,and SRFdis)outperform GWR,BPNN,and RF.The accuracy of SRF-SRF is higher than that of Bi-SRF and SRF-GDA.(2)The spatial-distribution continuity of SRF-SRF precipitation products is better,and the local precipitation details are significantly improved.(3)The spatial correlation of precipitation plays an important role in the improvement in GPM precipitation quality.(4)SRF-SRF based on the monthly scale is better than SRFdis based on the annual scale.This finding indicates that NDVI can be used for precipitation-quality enhancement at the monthly scale in Sichuan province. This paper proposes a two-stage satellite precipitation product-quality enhancement method that considers spatial correlation.The method takes into account the spatial autocorrelation between precipitation and combines downscaling and calibration while integrating environmental factors.Accordingly,the spatial resolution and accuracy of precipitation products improve.Experimental results show that the new method outperforms the other seven classical methods and is more applicable to the quality improvement of precipitation products in complex terrain.

The reliability of hourly PM2.5 data obtained from air quality monitoring stations is compromised as a result of the missing values, thereby impeding the thorough examination of crucial information. In this paper, we present a spatiotemporal (ST) stacking machine learning (ML) method with daily-cycle restrictions for reconstructing missing hourly PM2.5 records. First, the ST neighbors for the target station with missing values are selected at a daily scale. Subsequently, the non-null data within the ST neighbors undergo an iterative P-BSHADE interpolation process for re-interpolation. Next, a stacking ML model is constructed using the re-interpolation values and several environmental factors associated with PM2.5 as the predictors, while the observed PM2.5 is taken as the independent variable. Finally, the missing values are reconstructed by inputting the predictors into the trained stacking model. The study utilized hourly PM2.5 data in the Beijing-Tianjin-Hebei region as a case study to assess the effectiveness of the proposed method, using daily missing ratios of 10%, 30%, and 50%, respectively. The accuracy of the proposed method was then compared to four contemporary ST interpolation methods. The results indicate that the proposed method exhibits superior performance compared to the classical methods. Specifically, it achieves a reduction in the average root mean square error and mean absolute error by at least 40.6% and 40.1%, respectively. Additionally, the proposed method demonstrates the successful recovery of extreme values in the hourly PM2.5 records, in contrast to the classical methods which often exhibit a tendency to overestimate low values and underestimate high values. Overall, the proposed method presents a viable and efficient approach to recover missing values in the hourly PM2.5 records that demonstrate evident daily periodic patterns.

Satellite global digital elevation models (GDEMs) suffer from positive biases in urban areas due to building artifacts. While various machine learning (ML)-based methods have been proposed to remove these biases, their generalizability is limited by spatial heterogeneity and redundancy in prediction factors across different regions. Therefore, to investigate the spatial heterogeneity of prediction factors and address the problem of factor redundancy in ML-based model prediction, this paper proposes an explainable artificial intelligence framework (XAI) for correcting urban GDEMs using the SHapley additive explanation (SHAP)-random forest (RF) algorithm. The performance of the proposed model for correcting the 30-m COPDEM (COPDEM30) was demonstrated in New York City. The results were compared with the first global Forests-And-Buildings removed DEM (FABDEM) and three classical RF-based models without considering spatial heterogeneity and (or) factor optimization. The results indicate that each factor contributes differently to the correction of COPDEM30 across the regions, showing distinct regional characteristics and spatial heterogeneity. The constructed model is more applicable to regions with similar features to the training regions. In comparison to the three traditional RF-based models in areas with training points, the proposed method obtains the high accuracy. Specifically, while the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values of the classical RF models ranged between 2.601 m and 2.724 m, and 1.686 m and 1.785 m, respectively, the proposed method achieves an RMSE of 2.258 m and an MAE of 1.436 m. Moreover, the proposed method reduces the RMSE (MAE) of the original COPDEM30 from 7.652 m (4.858 m) to 3.797 m (2.404 m), when applied to an area without providing training points. In summary, the XAI framework based on SHAP-RF can effectively quantify the contribution of prediction factors on GDEM correction, both globally and locally, which is conducive to the construction and improvement of the prediction factor system for urban GDEM correction in different regions. It also provides a reference for improving the performance of ML-based spatial prediction in geosciences.

在数字高程模型(digital elevation model,DEM)建模过程中,经典空间插值方法均没有考虑断裂线附近的局部地形特征影响,使得断裂线局部区域高程被平滑,从而导致地形特征失真.为了解决该问题,构造了一种顾及断裂地形特征的定权方法,并以径向基函数(radial basis function,RBF)为插值算子,提出了加权径向基函数方法.首先通过捕捉每个采样点的结构张量,自适应计算采样点与待求点的距离,然后利用该距离对每个采样点赋予合适的权重,最后利用加权插值实现DEM建模.以10组国际摄影测量和遥感学会公共数据和1组山体滑坡区域的机载激光雷达点云数据为例,利用所提方法构建样区DEM,并将计算结果与标准RBF及传统插值算法(如反距离加权法、克里金法、约束不规则三角网法)进行比较.精度分析表明,不论采样点数为多少,所提方法计算精度均优于其他插值方法;对DEM山体阴影图分析表明,相较于传统插值方法,所提方法能较好地保持断裂线局部地形特征.

Light detection and ranging (LiDAR)-derived point cloud has become the standard spatial data for digital terrain model (DTM) construction; however, it suffers from huge data with much redundant information due to the oversampling. This often causes considerable inconvenience in the downstream data processing. To this end, an adaptive coarse-to-fine clustering and terrain feature-aware-based method is proposed to reduce data points in the context of terrain modeling in this paper. Firstly, a coarse-to-fine clustering method with the consideration of terrain complexity is developed to adaptively cluster LiDAR terrain points. Then, according to the geometric properties of terrain breaklines, a terrain feature-aware multi-strategy method is presented to pick representative points in the clusters. Finally, important boundary points including inflection point on the boundary curve and critical point on terrain features are further selected. The proposed method is compared with seven state-of-the-art point cloud simplification methods under six data reduction ratios on six plots with different terrain characteristics. Results indicate that the proposed method obtains a good balance between terrain-feature preservation and uniform distribution of data points. Compared to the state-of-the-art methods, the proposed method reduces the average root mean square errors (absolute errors) of the DTMs by 12.2%-51.7% (7.69%-83.8%) on the six plots. Moreover, the proposed method obtains the mean terrain slope and terrain roughness more reasonably approximate to the references. In short, the newly developed method can be considered as an alternative tool to select representative points from the huge remote-sensing-derived point cloud in the context of DTM production.

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Airborne LiDAR point cloud filtering is the key step in point cloud processing, and its computational accuracy significantly affects the granularities of subsequent applications. However, it is difficult for the existing filtering algorithms to effectively distinguish object points from ground points in complex areas. Thus, a multi-feature clustering-based hierarchical filtering method is proposed in this paper. The proposed method first performs multi-feature point cloud clustering based on the geometric and physical information of point clouds; then, a ground-cluster identification method was used to accurately capture ground points in the area with breaklines; finally, the ground reference surface was constructed through the initial ground points, and the multi-scale hierarchical filtering was employed to further identify missed ground points. The new method was used to handle the point clouds in four different areas, and the filtering results were comprehensively compared with six state-of-the-art filtering algorithms. Results show that the new method has the lowest average total error, the best filtering performance and the highest stability.

Due to the limitation of earth observation technology, the existing global Digital Elevation Model（DEM） datasets usually contain information of vegetation, buildings, and other non-ground objects. Especially in forested areas, the DEM data usually cannot describe the bare-earth surface precisely and show large systematic deviations. This study proposes a Back Propagation Neural Network（BPNN） model that takes into account the spatial autocorrelation of elevation to reduce the errors of bare-earth DEM in forested areas. This model first fits the optimal semivariogram to determine the spatial variation of elevation and takes the elevation points within the variation range from a target point as the optimal spatially autocorrelated neighborhood. Then, we train the BPNN model by using the terrain factors（i.e., slope, aspect, and terrain undulation）, vegetation factors（i.e., vegetation height and vegetation coverage）, and elevation points within the range of variation as the influencing factors, and using the elevation difference between DEM and Light Detection And Ranging（LiDAR） DEM as the predicted value. Finally, the trained model is used to correct the DEM in different forested areas. In order to verify the practicability and efficiency of the model, this paper takes the DEM products including SRTM1, AW3D30,and TanDEM-X（TDX） 90 of four types of forests（evergreen broad-leaved forest, evergreen coniferous forest,mixed forest, and deciduous broad-leaved forest） as the research objects, and trains the BPNN model respectively for each forest type. The correction result is compared with BPNN trained with all four types of forest data（BPNN-T）, BPNN trained without terrain factors（BPNN-W）, BPNN trained without spatial autocorrelation of elevation（BPNN-R）, and multiple linear regression model（MLR）. The results show that:（ⅰ） The BPNN model significantly improves the accuracy of DEM in the four forests, with the Mean Error（ME） close to 0-1 m and the Root Mean Square Errors（RMSE） reduced by 46%～70%;（ⅱ） The aspect has the largest influence on the DEM correction for TDX90 while has little influence on SRTM1 DEM correction. Before and after correction, the RMSE of each DEM increases with the increase of slope and relief;（ⅲ） The DEM error increases with the increase of vegetation height and vegetation coverage before correction, but this trend disappears after correction,indicating that BPNN effectively eliminates the impact of vegetation on bare ground DEM;（iv） BPNN has the highest prediction accuracy, followed by BPNN-T, MLR, and BPNN-W. And BPNN-R has the worst prediction accuracy. Therefore, the accuracy of DEM can be significantly improved by fully considering terrain factors and spatial autocorrelation of elevation for different forest types.

机载LiDAR点云是获取高质量数字高程模型(Digital Elevation Model,DEM)的主要数据源,而地表粗糙度作为DEM的主要派生产品,在地学研究中发挥了重要作用,但点云密度和插值方法对DEM及地表粗糙度精度影响程度并没有明确结论.为此,本文利用不同地形条件下的林区机载LiDAR点云为实验对象,将原始点云随机缩减为不同的采样密度,利用5种常用插值方法(克里金(Ordinary Kriging,OK),径向基函数(Radial Basis Function,RBF),不规则三角网(Triangulated Irregular Net-work,TIN),自然邻域(Natural Neighbor,NN)和反距离加权(Inverse Distance Weighting,IDW))构建各个测区不同采样密度条件下的DEM,并通过空间特征和统计特征两方面对DEM及其地表粗糙度精度分析.结果表明:①DEM插值算法的精度随点云密度缩减而降低,且数据量缩减至原始数据量的30％后,不同算法精度区别较为明显,其中,RBF和OK精度最优,IDW精度最低;②DEM误差与地表粗糙度存在正相关,随数据密度降低,OK、RBF、IDW所得粗糙度与DEM误差的相关系数均降低,与TIN和NN的相关系数先降低后在30％处升高;③从插值生成的DEM中提取地表粗糙度,其误差随数据密度缩减而增大,其中IDW所得粗糙度的精度在密度为90％和70％时最高,而数据密度缩减至50％后,RBF能够更准确地捕捉到地形变化.

To enhance the filtering accuracy in complex environments, a segmentation-based hierarchical interpolation filter using both geometric and radiometric features is proposed in this paper. Specifically, raw point cloud is first segmented using DBSCAN with both geometric and radiometric features. Then, initial ground seeds are selected from the set of segments with the consideration of terrain features. Finally, all ground points are detected using an enhanced multiresolution hierarchical filter based on three reference ground surfaces of different attributes coupled with slope-adaptive thresholds. Four plots with complex landscapes were adopted to evaluate the results of the proposed method, and its accuracy was compared with those of seven state-of-the-art filtering methods. Results demonstrate that the proposed method obviously outperforms the classical filtering methods, with the reduction of average type I, II, and total errors by at least 15.1%, 10.0%, and 19.4%, respectively, and the improvement of the kappa coefficient by at least 2.9%.

To remove vegetation bias (VB) from the global DEMs (GDEMs), an artificial neural network (ANN)-based method with the consideration of elevation spatial autocorrelation is developed in this paper. Three study sites with different forest types (evergreen, mixed evergreen-deciduous, and deciduous) are employed to evaluate the performance of the proposed model on three popular 30-m GDEMs, including SRTM1, AW3D30, and COPDEM30. Taking LiDAR DTM as the ground truth, the accuracy of the GDEMs before and after VB correction is assessed, as well as two existing GDEMs including MERIT and FABDEM. Results show that all the original GDEMs significantly overestimate the LiDAR DTM in the three forest types, with the largest biases of 21.5 m for SRTM1, 26.3 m for AW3D30, and 27.18 m for COPDEM30. Taking data randomly sampled from the corrected area as the training points, the proposed model reduces the mean errors (root mean square errors) of the three GDEMs by 98.8%-99.9% (55.1%-75.8%) in the three forests. When training data have the same forest type as the corrected GDEM but under different local situations, the proposed model lowers the GDEM errors by at least 76.9% (44.1%). Furthermore, our corrected GDEMs consistently outperform the existing GDEMs for the two cases.

Terrain surface roughness (TSR) is an important parameter in various geoscience applications. TSR can be easily estimated from digital elevation models (DEMs), which are generally derived from the interpolation of Light Detection and Ranging (LiDAR) point clouds. Thus, the quality of TSR is inevitably influenced by data density and interpolation method. However, to what extent the data density can be reduced and which method is more accurate than the others for quantifying TSR are still ambiguous. Thus, this paper evaluated the performance of five classical interpolation methods (ordinary kriging (OK), thin plate spline (TPS), natural neighbor (NN), Delaunay with linear interpolation (TIN) and inverse distance weighting (IDW)) for quantifying TSR under different airborne LiDAR data densities (90 %, 70 %, 50 %, 30 % and 10 % of the original data) in three study sites (samp1, samp2 and samp3) with different terrain characteristics. Results demonstrate that regardless of data density and study sites, TPS is consistently more accurate than the other methods for DEM production in terms of root mean square error (RMSE) and normalized median absolute deviation (NMAD), while IDW produces the worst results. Moreover, the reduction of data density to 50 % of the original data results in no obvious accuracy loss of DEMs for all the interpolation methods. For quantifying TSRs from DEMs, IDW shows the highest accuracy when data density is larger than 50 % in samp1 and samp2, and larger than 70 % in samp3, while TPS obtains the best results in the other densities; however, the surfaces of IDW are very coarse, which makes terrain details unrecognizable. Additionally, the DEM-based TSRs of all the interpolation methods can endure the reduction of LiDAR data to 50 % of the original samples without considerable accuracy decreases, especially for TPS. Overall, TPS can be considered as a promising method for LiDAR DEM production and TSR quantification.

é’ˆå¯¹çŽ°æœ‰æœºè½½æ¿€å ‰é›·è¾¾ï¼ˆLiDAR）点云滤波算法难以准确分离复杂地形中地面点与地物点问题，提出了一种基于点的多尺度形态学重建滤波方法PMMF（Point-based Multi-scale Morphological reconstruction Filter）。在初始尺度层次下，PMMFé€šè¿‡æž„å»ºä¸€ç§åŸºäºŽç‚¹çš„å½¢æ€å­¦é‡å»ºå¯¹åŽŸå§‹ç‚¹äº‘æ»¤æ³¢ï¼Œå³å ˆåœ¨æŽ©è†œç‚¹äº‘çº¦æŸä¸‹å€ŸåŠ©ké‚»åŸŸç»“æž„å ƒç´ å’Œé«˜ç¨‹ç¼“å†²åŒºåå¤è†¨èƒ€æ ‡è®°ç‚¹äº‘ï¼ŒèŽ·å–æ½œåœ¨åœ°é¢ç‚¹ï¼›ç„¶åŽé€šè¿‡è‡ªé€‚åº”å¡åº¦æ–¹æ³•å‰”é™¤æ½œåœ¨åœ°é¢ç‚¹ä¸­çš„éžåœ°é¢ç‚¹ï¼Œå ¶ä¸­ï¼Œå¡åº¦é˜ˆå€¼éšåœ°å½¢å¤æ‚åº¦è‡ªé€‚åº”å˜åŒ–ã€‚åœ¨ä¸Šå±‚æ»¤æ³¢ç»“æžœåŸºç¡€ä¸Šï¼ŒPMMFé€šè¿‡æå‡ç§å­ç‚¹é€‰æ‹©çš„ç½‘æ ¼å°ºåº¦é‡å¤ä¸Šå±‚æ»¤æ³¢è¿‡ç¨‹ï¼Œç›´è‡³ç»“æžœæ”¶æ•›ã€‚ä»¥å›½é™ æ‘„å½±æµ‹é‡ä¸Žé¥æ„Ÿå­¦ä¼šï¼ˆISPRS）发布的15ç»„åŸºå‡†æ•°æ®ä¸ºç ”ç©¶å¯¹è±¡ï¼Œå°†PMMF滤波结果与近5年（2016年—2020年）提出的15种滤波算法比较表明，PMMF有8ç»„æ•°æ®æ»¤æ³¢æ•ˆæžœå ä¼˜ï¼Œ15组数据平均总误差和Kappa系数分别为2.71%和91.08%。使用4种不同地形特征的高密度机载LiDAR点云数据进一步验证PMMF的滤波效果，并将计算结果与简单形态学滤波（SMRF）、布料模拟滤波（CSFï¼‰ã€æ¸è¿›åŠ å¯†ä¸‰è§’ç½‘æ»¤æ³¢ï¼ˆPTD）和多分辨率层次滤波（MHF）比较。结果表明，PMMF滤波性能最优，平均总误差为3.24%ï¼Œè¾ƒå ¶ä»–4种滤波方法分别减小了12.0%、59.1%、70.1%和53.2%。