- 无标题文档
查看论文信息

论文中文题名:

 基于无人机影像的矿区地表沉陷信息提取方法改进    

姓名:

 孙伟    

学号:

 20210061025    

保密级别:

 公开    

论文语种:

 chi    

学科代码:

 0816    

学科名称:

 工学 - 测绘科学与技术    

学生类型:

 硕士    

学位级别:

 工学硕士    

学位年度:

 2023    

培养单位:

 西安科技大学    

院系:

 测绘科学与技术学院    

专业:

 测绘科学与技术    

研究方向:

 矿区沉陷监测与评价    

第一导师姓名:

 汤伏全    

第一导师单位:

 西安科技大学    

论文提交日期:

 2023-06-16    

论文答辩日期:

 2023-06-04    

论文外文题名:

 Improvement of surface subsidence information extraction method in mining areas based on UAV images    

论文中文关键词:

 无人机影像 ; 水平位移 ; 开采沉陷 ; 植被去除 ; 误差改正    

论文外文关键词:

 UAV image ; Horizontal movement monitoring ; Coal mining subsidence ; Vegetation removal ; error correction    

论文中文摘要:

西部矿区高强度地下采煤引起的地表沉陷对煤矿安全生产和矿区生态环境造成了严重影响。为了快速、高效地获取地表沉陷变形信息,除了采用常规观测站方式进行观测外,近年来InSAR、激光扫描、摄影测量等技术也应用于矿区沉陷监测,但这些方法都存在一定的局限性。其中,利用无人机多次航拍影像构建沉陷区精细地形模型,通过模型叠加可获取地表沉陷信息。然而,在现有的数据处理流程中,很少考虑沉陷区水平位移的提取及高程模型叠加时地表水平位移对于下沉量的附加影响,尤其在地形起伏和植被覆盖区域以及存在航测系统性误差的情况下,往往导致叠加生成的沉陷模型噪声过大,制约了航测技术在矿区沉陷监测中的实际应用。本文针对上述问题及矿区开采沉陷监测的特点,通过现场实验和算法改进,利用低空无人机影像较高精度地提取了沉陷区地表形变信息。论文主要研究内容及结果如下:

(1) 根据开采沉陷原理制定了面向矿区沉陷监测的低空无人机航摄方案和数据处理流程。在分析无人机航测关键技术的基础上,根据影像分辨率要求与预计的沉陷边界确定合理的航飞高度与航线布设方案,分析了矿区沉陷监测中常规的航拍影像数据处理流程所存在的问题,并提出了相应的改进方案。

(2) 基于图像识别技术提出了一种结合影像地物矢量边界与影像特征信息的沉陷区水平位移提取方法。通过提取多期DSM模型中地物矢量边界的变化信息,粗提取地表水平位移的影响范围,再利用影像特征精确地提取地表水平位移信息。实验结果表明,这种融合地物矢量边界和影像特征的方法,将前者的效率优势与后者的精度优势相结合,能高效获取沉陷区水平位移信息。

(3) 针对航拍影像建模获取的初始沉陷模型开展植被去除和模型插值,显著削弱了了沉陷模型中的植被噪声影响,恢复了模型的完整性。在分析不同地物对沉陷模型影响的基础上,利用可见光波段差异植被指数剔除植被覆盖区的沉陷信息,根据开采沉陷原理结合高斯卷积核与数字高程模型插值算法,拟合生成完整的地表沉陷模型。经植被剔除后沉陷模型的噪声得到明显抑制。

(4) 利用非沉陷区下沉量应为零的先验条件,针对初始沉陷模型的系统性误差进行改正,提升了沉陷模型的精度。通过统计非沉陷区域的误差分布特征,分析沉陷模型中潜在的系统误差,利用反距离权重插值法施加误差改正。实测数据验证表明,系统误差改正后地表下沉误差明显变小。

(5) 依据图像仿射变换原理构建了考虑地表水平位移信息的沉陷模型叠加方法,显著削弱了复杂地形环境下因地表点水平位移引起的高程叠加误差。利用时序DOM影像提取的沉陷区水平位移信息,构建仿射变换矩阵进行仿射变换,实现地物间配准后再进行模型叠加,据此将同一平面坐标的高程叠加转变为同一地物点的高程叠加,实现了精准的地表沉陷信息提取。通过工程实例验证表明,经过水平位移校正获取的沉陷模型精度得到明显改善。因此,本文改进方法能够提升无人机航摄应用于矿区沉陷监测的实际精度和可靠性。

论文外文摘要:

Surface subsidence caused by high-intensity underground coal mining in western mining areas has caused serious impacts on coal mine safety production and mine ecological environment. In order to obtain surface subsidence deformation information quickly and efficiently, in addition to observation by conventional observation stations, InSAR, laser scanning, photogrammetry and other techniques have been applied to mine subsidence monitoring in recent years, but all these methods have certain limitations. Among them, the fine terrain model of the subsidence area is constructed by using multiple aerial images of UAVs, and the surface subsidence information can be obtained by model superposition. However, in the existing data processing process, the extraction of horizontal displacement of the subsidence area and the additional influence of the horizontal displacement of the surface on the subsidence amount when the elevation models are superimposed are seldom considered, especially in areas with undulating terrain and vegetation cover and in the presence of systematic errors in aerial survey, which often leads to excessive noise in the superimposed subsidence models and restricts the practical application of aerial survey technology in the subsidence monitoring of mining areas. In this paper, to address the above problems and the characteristics of mining subsidence monitoring, the 3D surface deformation information of the subsidence area is extracted with high accuracy by using low-altitude UAV images through field experiments and algorithm improvement. The main research contents and results of the paper are as follows

(1) A low-altitude UAV aerial photography scheme and data processing process for mine subsidence monitoring were developed based on the principle of mining subsidence. Based on the analysis of key UAV aerial survey technologies, a reasonable aerial flight height and route layout scheme are determined according to the image resolution requirements and the expected subsidence boundary, the problems of the conventional aerial image data processing process in mining subsidence monitoring are analyzed, and the corresponding improvement scheme is proposed.

(2) Based on image recognition technology, a method is proposed to extract horizontal displacement of subsidence area by combining image feature vector boundary and image feature information. By extracting the change information of the feature vector boundary in the multi-period DSM model, the influence range of the horizontal displacement of the ground surface is coarsely extracted, and then the image features are used to accurately extract the horizontal displacement information of the ground surface. The experimental results show that this method of fusing feature vector boundary and image features, which combines the efficiency advantage of the former with the accuracy advantage of the latter, can efficiently obtain the horizontal displacement information of the subsidence area.

(3) Vegetation removal and model interpolation were carried out for the initial subsidence model obtained from aerial image modeling, which significantly weakened the influence of vegetation noise in the subsidence model and restored the integrity of the model. Based on the analysis of the influence of different features on the subsidence model, the sinkhole information in the vegetation-covered area is removed by using the vegetation index of the visible band difference, and a complete surface subsidence model is fitted according to the principle of mining subsidence combined with Gaussian convolution kernel and digital elevation model interpolation algorithm. The noise of the subsidence model is significantly suppressed after vegetation rejection.

(4) The accuracy of the subsidence model was improved by correcting for the systematic errors in the initial subsidence model using the a priori condition that the subsidence in the non-sinkhole area should be zero. The potential systematic errors in the subsidence model were analyzed by counting the error distribution characteristics in the non-sinkhole area, and the error correction was applied by using the inverse distance weight interpolation method. The verification of the measured data shows that the surface subsidence error becomes significantly smaller after the systematic error correction.

(5) Based on the principle of image affine transformation, a subsidence model superposition method considering the horizontal displacement information of the ground surface is constructed, which significantly weakens the elevation superposition error caused by the horizontal displacement of the ground surface points in the complex terrain environment. The horizontal displacement information of the subsidence area extracted from the time-series DOM image is used to construct the affine transformation matrix for the affine transformation to realize the alignment between the features and then perform the model superposition, whereby the elevation superposition of the same plane coordinates is transformed into the elevation superposition of the same feature points to realize the accurate surface subsidence information extraction. The verification by engineering examples shows that the accuracy of the subsidence model obtained by horizontal displacement correction is significantly improved. Therefore, the method in this paper can improve the practical accuracy and reliability of UAV aerial photography applied to the subsidence monitoring in mining areas.

参考文献:

[1] 李佳洺, 余建辉, 张文忠. 中国采煤沉陷区空间格局与治理模式[J].自然资源学报, 2019, 034(004): 867-880.

[2] 973计划(2013CB227900)"西部煤炭高强度开采下地质灾害防治与环境保护基础研究"项目组. 西部煤炭高强度开采下地质灾害防治理论与方法研究进展[J]. 煤炭学报, 2017, 42(02): 267-275.

[3] 王燕. 煤炭开采对生态环境的影响及治理对策[J].煤炭科学技术, 2009, 37(12): 125-128.

[4] 王双明, 孙强, 乔军伟, 等.论煤炭绿色开采的地质保障[J]. 煤炭学报, 202045(01): 8-15.

[5] 何佳男.贴近摄影测量及关键技术研究[D]. 武汉: 武汉大学, 2019

[6] Zebker H A, Villasenor J. Decorrelation in interferometric radar echoes[J]. IEEE Transactions on geoscience and remote sensing, 1992, 30(5): 950-959.

[7] 邓喀中, 谭志祥, 姜岩.变形监测及沉陷工程学[M]. 徐州: 中国矿业大学出版社, 2014.

[8] 张继贤, 刘飞, 王坚. 轻小型无人机测绘遥感系统研究进展[J].遥感学报, 2021, 25(03): 708-724.

[9] 陈鹏飞. 无人机倾斜摄影测量开采沉陷监测方法研究[D]. 太原: 太原理工大学, 2018.

[10] Colomina I, Molina P. Unmanned aerial systems for photogrammetry and remote sensing: A review[J]. ISPRS Journal of photogrammetry and remote sensing 2014, 92: 79-97.

[11] Przybilla H J, Wester-Ebbinghaus W. Bildflug mitferngelenktem Kleinflugzeug. Bildmessung und Luftbildwesen[J]. Zeitschrift fuer Photogrammetrie und Fernerkundung, 1979.

[12] Ackermann F. Prospects of kinematic GPS for aerial triangulation[J]. ITC Journal, 1992, 4: 326-338.

[13] Cramer M, Stallmann D, Haala N. Direct georeferencing using GPS/inertial exterior orientations for photogrammetric applications[J]. International Archives of Photogrammetry and Remote Sensing 2000 33(B3/1; PART 3): 198-205.

[14] 袁修孝. POS辅助光束法区域网平差[J].测绘学报, 2008(03): 342-348.

[15] Colomina I, de la Tecnologia P M. Towards a new paradigm for high-resolution low-cost photogrammetryand remote sensing[C]//Proceedings of the International Society for Photogrammetry and Remote Sensing, (ISPRS) XXI Congress, Beijing, China. 2008: 3-11.

[16] Dubbini M, Curzio L, I Campedelli A. Digital elevation models from unmanned aerial vehicle surveys for archaeological interpretation of terrain anomalies: Case study of the Roman castrum of Burnum (Croatia)[J]. Journal of Archaeological Science: Reports 2016 8: 121-134.

[17] Rokhmana C A. The potential of UAV-based remote sensing for supporting precision agriculture in Indonesia[J]. Procedia Environmental Sciences, 2015, 24: 245-253.

[18] Yuan C, Zhang Y, Liu Z. A survey on technologies for automatic forest fire monitoring, detection, and fighting using unmanned aerial vehicles and remote sensing techniques[J]. Canadian journal of forest research, 2015, 45(7): 783-792.

[19] Kanun E, Alptekin A, Yakar M. Cultural heritage modelling using UAV photogrammetric methods: a case study of Kanlıdivane archeological site[J]. Advanced UAV, 2021, 1(1): 24-33.

[20] Chou T Y, Yeh M L, Chen Y C, et al. Disaster monitoring and management by the unmanned aerial vehicle technology[J]. 2010, 137-142.

[21] Gikas V. Three-dimensional laser scanning for geometry documentation and construction management of highway tunnels during excavation[J]. Sensors, 2012, 12(8): 11249-11270.

[22] Vezočnik R, Ambrožič T, Sterle O, et al. Use of terrestrial laser scanning technology for long term high precision deformation monitoring[J]. Sensors, 2009, 9(12): 9873-9895.

[23] Lindenbergh R, Uchanski L, Bucksch A, et al. Structural monitoring of tunnels using terrestrial laser scanning[J]. Reports on geodesy, 2009: 231-238.

[24] Altuntas C, Yildiz F, Scaioni M. Laser scanning and data integration for three-dimensional digital recording of complex historical structures: The case of Mevlana Museum[J]. ISPRS International Journal of Geo-Information, 2016, 5(2): 18: 1-16.

[25] 张舒, 吴侃, 王响雷, 等. 三维激光扫描技术在沉陷监测中应用问题探讨[J].煤炭科学技术, 2008(11): 92-95.

[26] 李强, 邓辉, 周毅. 三维激光扫描在矿区地面沉陷变形监测中的应用[J]. 中国地质灾害与防治学报, 2014, 25(01): 119-124.

[27] 郭文兵, 白二虎, 陈俊杰. 三维激光扫描监测开采沉陷的精度分析[J]. 煤炭科学技术2014, 42(11): 85-89.

[28] 冯婷婷,张键,冯鹏飞.三维激光扫描技术在开采沉陷监测中的应用[J]. 矿山测量, 2014, (05): 89-92.

[29] Zebker H A Goldstein R M. Topographic mapping from interferometric synthetic aperture radar observations[J]. Journal of Geophysical Research: Solid Earth, 1986, 91(B5): 4993-4999.

[30] Schlögel R Doubre C Malet J P et al. Landslide deformation monitoring with ALOS/PALSAR imagery: A D-InSAR geomorphological interpretation method[J]. Geomorphology, 2015, 231: 314-330.

[31] Gabriel A K, Goldstein R M. Cover Radar interferogram made from two passes of SIR-B over the Rocky Mountains in British Columbia, Canada[J]. International Journal of Remote Sensing, 1988, 9(5): 835-835.

[32] Massonnet D, Rossi M, Carmona C, et al. The displacement field of the Landers earthquake mapped by radar interferometry[J]. Nature, 1993, 364(6433): 138-142.

[33] Goldstein R M, Werner C L. Radar interferogram filtering for geophysical applications[J]. Geophysical research letters, 1998, 25(21): 4035-4038.

[34] Li Z W, Ding X L, Zheng D W, et al. Least squares-based filter for remote sensingimage noise reduction[J]. IEEE transactions on geoscience and remote sensing, 2008, 46(7): 2044-2049.

[35] Xu B, Li Z, Wang Q, et al. A refined strategy for removing composite errors of SAR interferogram[J]. IEEE Geoscience and Remote Sensing Letters, 2013, 11(1): 143-147.

[36] Feng G, Jónsson S, Klinger Y. Which fault segments ruptured in the 2008 Wenchuan earthquake and which did not? New evidence from near‐fault 3D surface displacements derived from SAR image offsets[J]. Bulletin of the Seismological Society of America, 2017, 107(3): 1185-1200.

[37] Ferretti A, Prati C, Rocca F. Permanent scatterers in SAR interferometry[J]. IEEE Transactions on geoscience and remote sensing, 2001, 39(1): 8-20.

[38] Zebker H A, Villasenor J. Decorrelation in interferometric radar echoes[J]. IEEE Transactions on geoscience and remote sensing, 1992, 30(5): 950-959.

[39] Ferretti A, Fumagalli A, Novali F, et al. A new algorithm for processing interferometric data-stacks: SqueeSAR[J]. IEEE transactions on geoscience and remote sensing, 2011, 49(9): 3460-3470.

[40] 王桂杰, 谢谟文, 邱骋等. D-InSAR 技术在大范围滑坡监测中的应用[J]. 岩土力学, 2010, 31(4): 1337-134.

[41] Jessica M. Wempen Michael K. McCarter. Comparison of L-band and X-band differential interferometric synthetic aperture radar for mine subsidence monitoring in central Utah[J]. International Journal of Mining Science and Technology, 2017, 27(01): 159-163.

[42] 袁枫.机载LiDAR数据处理与土地利用分类研究[D]. 徐州:中国矿业大学 (徐州), 2010.

[43] 李沛婷, 赵庆展, 陈洪. 回波强度约束下的无人机LiDAR点云K-means聚类滤波[J].地球信息科学学报, 2018, 20(04): 471-479.

[44] Leena Matikainen Matti Lehtom ki Eero Ahokas. Remote Sensing Methods for Power Line Corridor Surveys[J]. Journal of Photogrammetry and Remote Sensing, 2016, 119: 10-31.

[45] 林祥国, 张继贤. 架空输电线路机载激光雷达点云电力线三维重建[J].测绘学报, 2016, 45(03): 347-353.

[46] 韩立, 余代俊, 何延龙. LiDAR在四川某地电力选线项目中的应用[J].测绘与空间地理信息, 2014, 4: 86-88.

[47] 陈利明, 张巍, 于虹, 等. 无人机载LiDAR系统在电力线巡检中的应用[J]. 测绘通报, 2017, S1: 176-178.

[48] 张永庭, 徐友宁, 梁伟, 等.基于无人机载 Li DAR 的采煤沉陷监测技术方法——以宁东煤矿基地马连台煤矿为例[J].地质通报, 2018, 37(12): 2270-2277.

[49] 汤伏全, 芦家欣, 韦书平, 等. 基于无人机LiDAR的榆神矿区采煤沉陷建模方法改进[J]. 煤炭学报, 2020, 45(07): 2655-2666.

[50] Gasperini D, Allemand P, Delacourt C, et al. Potential and limitation of UAV for monitoring subsidence in municipal landfills[J]. International Journal of Environmental Technology and Management, 2014, 17(1): 1-13.

[51] A Pauliková et al. Use of low-cost UAV photogrammetry to analyze the accuracy of a digital elevation model in a case study[J]. Measurement 2016, 91: 276-287.

[52] 杨绪霆, 姚顽强, 郑俊良, 等. 无人机地形跟随在矿区沉陷监测中的应用[J]. 测绘通报, 2021, No.530(05): 111-115.

[53] 高冠杰, 侯恩科, 谢晓深, 等. 基于四旋翼无人机的宁夏羊场湾煤矿采煤沉陷量监测[J]. 地质通报, 2018, 037(012): 2264-2269.

[54] 侯恩科, 首召贵, 徐友宁, 等. 无人机遥感技术在采煤地面塌陷监测中的应用[J]. 煤田地质与勘探, 2017, 045(006): 102-110.

[55] 侯恩科, 张杰, 谢晓深, 等. 无人机遥感与卫星遥感在采煤地表裂缝识别中的对比[J]. 地质通报, 2019, 38(Z1): 443-448.

[56] Ignjatović Stupar D, Rošer J, Vulić M. Investigation of unmanned aerial vehicles-based photogrammetry for large mine subsidence monitoring[J]. Minerals, 2020, 10(2): 196: 1-14.

[57] Zhou D W, Qi L Z, Zhang D M, et al. Unmanned Aerial Vehicle (UAV) Photogrammetry Technology for Dynami Mining Subsidence Monitoring and Parameter Inversion: A Case Study in China[J]. IEEE Access, 2020, 8: 16372-16386.

[58] Nex F, Remondino F. UAV for 3D mapping applications: a review[J]. Applied geomatics, 2014, 6(1): 1-15.

[59] Ćwiąkała P, Gruszczyński W, Stoch T, et al. UAV applications for determination of land deformations caused by underground mining[J]. Remote Sensing, 2020, 12(11): 1733: 1-25.

[60] Burdziakowski P. Uav in todays photogrammetry–application areas and challenges[J]. International Multidisciplinary Scientific GeoConference: SGEM, 2018, 18(2.3): 241-248.

[61] Ren H, Zhao Y, Xiao W, et al. A review of UAV monitoring in mining areas: Current status and future perspectives[J]. International Journal of Coal Science & Technology, 2019, 6(3): 320-333.

[62] 毕凯, 李英成, 丁晓波, 等.轻小型无人机航摄技术现状及发展趋势[J]. 测绘通报, 2015, No.456(03): 27-31+48.

[63] 朱进, 丁亚洲, 陈攀杰, 等. 控制点布设对无人机影像空三精度的影响[J]. 测绘科学, 2016, 41(05): 116-120.

[64] Harris C, Stephens M. A combined corner and edge detector[C]//Alvey vision conference. 1988, 15(50): 147-151.

[65] Derpanis K G. The harris corner detector[J]. York University, 2004, 2: 1-2.

[66] Juan L, Gwun O. A comparison of sift, pca-sift and surf[J]. International Journal of Image Processing (IJIP), 2009, 3(4): 143-152.

[67] 何豫航, 岳俊. 基于CMVS/PMVS多视角密集匹配方法的研究与实现[J]. 测绘地理信息, 2013, 38(03): 20-23.

[68] 刘瑾, 季顺平. 基于深度学习的航空遥感影像密集匹配[J]. 测绘学报, 2019, 48(09): 1141-1150.

[69] 季顺平, 罗冲, 刘瑾. 基于深度学习的立体影像密集匹配方法综述[J]. 武汉大学学报(信息科学版), 2021, 46(02): 193-202.

[70] Jobson D J, Rahman Z, Woodell G A. Properties and performance of a center/surround retinex[J]. IEEE transactions on image processing, 1997, 6(3): 451-462.

[71] Rahman Z, Jobson D J, Woodell G A. Multi-scale retinex for color image enhancement[C]//Proceedings of 3rd IEEE international conference on image processing. IEEE, 1996, 3: 1003-1006.

[72] Jobson D J, Rahman Z, Woodell G A. A multiscale retinex for bridging the gap between color images and the human observation of scenes[J]. IEEE Transactions on Image processing, 1997, 6(7): 965-976.

[73] Bhateja V, Yadav A, Singh D, et al. Multi-scale Retinex with Chromacity Preservation (MSRCP)-Based Contrast Enhancement of Microscopy Images[C]//Smart Intelligent Computing and Applications, Volume 2: Proceedings of Fifth International Conference on Smart Computing and Informatics (SCI 2021). Singapore: Springer Nature Singapore, 2022: 313-321.

[74] 张春森, 李国君, 崔卫红. 一种基于矢量数据的遥感影像变化检测方法[J]. 武汉大学学报(信息科学版), 2021, 46(03): 309-317.

[75] Li X, Yeh A G O, Qian J, et al. A matching algorithm for detecting land use changes using case-based reasoning[J]. Photogrammetric Engineering & Remote Sensing, 2009, 75(11): 1319-1332.

[76] Burnett C, Blaschke T. A multi-scale segmentation/object relationship modelling methodology for landscape analysis[J]. Ecological modelling, 2003, 168(3): 233-249.

[77] 张法全, 王国富, 曾庆宁, 等. 利用重心原理的图像目标最小外接矩形快速算法[J].红外与激光工程, 2013, 42(05): 1382-1387.

[78] 徐胜荣, 包西洋. 平面图形的形心在旋转体体积计算中的应用[J]. 高等数学研究, 2020, 23(02): 22-24.

[79] 李春意, 车宇航, 王石岩. 煤矿开采地表沉陷盆地边界的再认识[J]. 中国安全生产科学技术, 2018, 14(12): 84-89.

[80] 刘义新, 戴华阳, 姜耀东. 厚松散层矿区地表移动盆地边界角确定方法[J]. 煤矿安全, 2012, 43(09): 47-49.

[81] 皮英冬. 缺少地面控制点的光学卫星遥感影像几何精处理质量控制方法[D]. 武汉:武汉大学, 2021.

[82] 周涛, 胡振琪, 韩佳政, 等. 基于无人机可见光影像的绿色植被提取[J]. 中国环境科学, 2021, 41(05): 2380-2390.

[83] Guindin-Garcia N, Gitelson A A, Arkebauer T J, et al. An evaluation of MODIS 8-and 16-day composite products for monitoring maize green leaf area index[J]. Agricultural and Forest Meteorology, 2012, 161: 15-25.

[84] Di Gennaro S F, Matese A. Evaluation of novel precision viticulture tool for canopy biomass estimation and missing plant detection based on 2.5 D and 3D approaches using RGB images acquired by UAV platform[J]. Plant Methods, 2020, 16(1): 1-12.

[85] Yuan H, Liu Z, Cai Y, et al. Research on vegetation information extraction from visible UAV remote sensing images[C]//2018 Fifth International Workshop on Earth Observation and Remote Sensing Applications (EORSA). IEEE, 2018: 1-5.

[86] 汪小钦, 王苗苗, 王绍强, 等. 基于可见光波段无人机遥感的植被信息提取[J]. 农业工程学报, 2015, 31(05): 152-159.

[87] Meyer G E, Neto J C. Verification of color vegetation indices for automated crop imaging applications[J]. Computers and electronics in agriculture, 2008, 63(2): 282-293.

[88] Bangare S L, Dubal A, Bangare P S, et al. Reviewing Otsu’s method for image thresholding[J]. International Journal of Applied Engineering Research, 2015, 10(9): 21777-21783.

[89] 杨勤科, Tim R, Mcvicar ,等. ANUDEM—专业化数字高程模型插值算法及其特点[J]. 干旱地区农业研究, 2006, 24(03): 36-41.

[90] Bartier P M, Keller C P. Multivariate interpolation to incorporate thematic surface data using inverse distance weighting (IDW)[J]. Computers & Geosciences, 1996, 22(7): 795-799.

[91] Oliver M A, Webster R. Kriging: a method of interpolation for geographical information systems[J]. International Journal of Geographical Information System, 1990, 4(3): 313-332.

[92] Boissonnat J D, Cazals F. Natural neighbor coordinates of points on a surface[J]. Computational Geometry, 2001, 19(2-3): 155-173.

[93] Habermann C, Kindermann F. Multidimensional spline interpolation: Theory and applications[J]. Computational Economics, 2007, 30: 153-169.

[94] 隋立春, 张熠斌, 张硕等. 基于渐进三角网的机载LiDAR点云数据滤波[J]. 武汉大学学报(信息科学版), 2011, 36(10): 1159-1163.

中图分类号:

 TD325/P237    

开放日期:

 2025-03-07    

无标题文档

   建议浏览器: 谷歌 火狐 360请用极速模式,双核浏览器请用极速模式