A Low-resolution Slope Compensation Method Involving Slope Change Rate
-
摘要: 为解决月球、火星等行星表面缺乏高分辨率DEM（Digital Elevation Model）而造成的坡度低估问题，提出一种坡度变化率因子参与建模的低分辨率坡度补偿方法。方法对现有坡度补偿模型进行改进，在补偿模型中引入了坡度变化率参数，以提升坡度补偿的精度；利用月球和火星数据进行方法验证，选取覆盖多种地形的月球和火星低分辨率DEM，利用改进的方法进行坡度补偿，并利用高分辨率DEM生成的坡度做验证。实验结果表明：补偿后坡度较补偿前能更好地表征月球和火星表面的地形特征，且考虑坡度变化率的改进方法比传统的线性补偿方法更加有效。基于此方法，给出了适用于月球多地形的整体坡度补偿模型参数以及分级补偿模型参数，并对覆盖“天问一号”着陆点50 km×50 km的低分辨率火星坡度数据进行了补偿及分析应用。Abstract: To solve the problem of slope reduction caused by the lack of high-resolution Digital Elevation Model ( DEM ) on the surface of moon, Mars and other planets, we propose a low-resolution slope compensation method involving slope change rate factors. It is an improvement on the existing linear compensation method by incorporating slope change rate into the compensation model to obtain better accuracy for slope compensation. In this paper, lunar and Martian data are used to verify the method. Several lunar and Martian low-resolution DEMs covering a variety of terrains are selected and compensated using the improved method. Then they are validated using slopes generated from the high-resolution DEMs. The results show that after applying the proposed compensation function, the compensated slopes can represent the terrain features of the lunar and Martian surface better compared to the original low-resolution slopes. Meanwhile, the proposed method considering the slope change rate is more effective than the traditional linear compensation method. Based on the improved method, the overall and hierarchical compensation models suitable for various lunar landforms are established and the low-resolution Martian slope data covering 50*50 km of the Tianwen-1 landing site are compensated and analyzed.
-
Key words:
- Digital Elevation Model /
- slope compensation /
- deep space exploration /
- Moon /
- Mars
Highlights● An improved method for low-resolution slope compensation is proposed. By incorporating the change rate information of low-resolution slope to the compensation model, the compensation results of low-resolution slope are closer to the reference value of high-resolution slope. ● The model suitable for the low-resolution slope compensation of the entire lunar surface are supplied and the graded compensation models are supplemented. ● The low-resolution slope data covering 50 km×50 km of the Tianwen-1 landing site is compensated and topographic analysis is performed. -
图 9 HiRISE坡度以及HRSC-MOLA坡度补偿前后对比
Fig. 9 HiRISE slope and HRSC-MOLA slope before and after compensation
表 1 月球数据拟合结果
Table 1 Fitting results of lunar data
影像
编号线性补偿结果$Z=a\times X+b$ 引入坡度变化率的补偿结果$Z=a\times X+b\times {X}^{\text{'} }+c$ 系数a 系数b 系数a 系数b 系数c 1 1.048 1.641 1.040 0.079 1.388 2 1.081 1.298 1.064 0.073 1.099 3 1.103 1.498 1.049 0.096 1.214 4 1.054 2.659 1.054 0.111 2.031 5 0.916 8.831 0.933 0.136 6.628 6 1.063 1.845 1.063 0.086 1.423 7 1.168 0.606 1.143 0.129 0.120 8 1.184 1.427 1.175 0.049 1.242 9 1.137 1.285 1.108 0.116 0.889 10 1.080 3.906 1.087 0.096 2.528 11 1.240 0.708 1.212 0.109 0.328 12 1.122 1.051 1.078 0.119 0.734 13 1.128 0.653 1.111 0.126 0.306 14 1.131 0.958 1.111 0.080 0.735 
下载: 导出CSV
表 2 火星数据拟合结果
Table 2 Fitting results of Martian data
影像
编号线性补偿结果 $Z=a\times X+b$ 引入坡度变化率的补偿结果$Z=a\times X+b\times {X}^{\text{'} }+c$ 系数a 系数b 系数a 系数b 系数c a 0.646 5.150 0.594 0.175 5.010 b 0.878 3.414 0.779 0.243 3.128 c 0.886 2.857 0.729 0.384 2.508 d 0.491 3.759 0.345 0.329 3.614 e 0.699 2.186 0.612 0.325 2.018 f 0.801 2.513 0.717 0.338 2.237
下载: 导出CSV
表 3 月球补偿实验精度评价
Table 3 Evaluation of lunar data experiments
影像
编号未补偿坡度/（°） 线性补偿结果 $Z=a\times X+b$ 引入坡度变化率的补偿结果$Z=a\times X+b\times{X}^{\text{'} }+c$ MAE RMSE MAE 补偿幅度/% RMSE MAE 补偿幅度/% RMSE 1 2.000 2.377 0.855 57.3 1.272 0.842 57.9 1.232 2 1.585 1.867 0.680 57.1 0.970 0.665 58.0 0.934 3 1.762 2.223 0.863 51.0 1.305 0.808 54.1 1.221 4 3.295 4.059 1.681 49.0 2.337 1.617 50.9 2.246 5 7.285 9.163 3.932 46.0 5.488 3.644 50.0 5.092 6 2.375 2.809 1.094 53.9 1.517 1.062 55.3 1.461 7 2.070 3.180 1.288 37.8 2.019 1.187 42.7 1.853 8 3.453 4.240 1.576 54.4 2.187 1.569 54.6 2.174 9 1.716 2.260 0.846 50.7 1.328 0.771 55.1 1.206 10 5.247 6.630 2.969 43.4 3.993 2.827 46.1 3.806 11 2.345 3.436 1.228 47.6 2.059 1.201 48.8 1.971 12 1.361 1.840 0.713 47.6 1.184 0.661 51.4 1.093 13 2.713 3.492 1.129 58.4 1.715 1.078 60.3 1.605 14 1.626 2.220 0.760 53.3 1.289 0.743 54.3 1.248
下载: 导出CSV
表 4 火星实验精度评价
Table 4 Evaluation of Martian data experiments
影像
编号未补偿坡度/（°） 线性补偿结果$ Z=a \times X+b $ 引入坡度变化率的补偿结果$ Z=a \times X+b \times {X}^{\text{'}}+c $ MAE RMSE MAE 补偿幅度/% RMSE MAE 补偿幅度/% RMSE a 4.772 5.013 1.164 75.6 1.511 1.162 75.7 1.501 b 3.101 3.616 1.437 53.7 1.858 1.381 55.5 1.791 c 2.602 3.071 1.284 50.7 1.638 1.212 53.4 1.544 d 3.273 3.547 1.016 69.0 1.311 0.995 69.6 1.279 e 1.856 2.156 0.772 58.4 1.075 0.751 59.5 1.046 f 2.049 2.402 0.899 56.1 1.232 0.812 60.4 1.104
下载: 导出CSV
表 5 月球多地形整体补偿模型精度评价
Table 5 Evaluation of compensation model for global moon
项目 MAE RMSE 补偿后坡度值–目标坡度值 1.363 4.881
下载: 导出CSV
表 6 分级坡度拟合和检验结果
Table 6 Fitting and validating results of graded lunar slopes
分级标准/（°） 数据量 引入坡度变化率的坡度分级模型 整体补偿模型 系数a 系数b 系数c MAE RMSE MAE RMSE 0~3 8 294 895 1.188 0.144 0.626 0.686 1.111 0.690 1.116 3~6 2 946 604 1.139 0.161 0.670 1.083 1.742 1.069 1.758 6~9 3 083 811 1.109 0.157 0.852 1.338 2.084 1.321 2.095 9~12 4 367 343 1.133 0.133 0.761 1.729 2.557 1.730 2.557 12~15 2 744 330 1.145 0.096 0.937 2.480 3.401 2.472 3.413 15~20 1 226 338 1.135 0.083 1.194 2.700 3.510 2.708 3.536 20~30 120 588 1.197 0.071 1.408 2.787 3.706 2.924 3.821 >30 6 277 0.860 0.045 15.228 4.238 5.399 5.194 6.754
下载: 导出CSV
表 7 补偿前后对比分析
Table 7 Comparison analysis before and after compensation
项目 补偿前 补偿后 MAE RMSE MAE 补偿幅度 RMSE HRSC-MOLA融合数据&HiRISE数据（DTEEC_069876_2055_069942） 2.846 3.179 0.796 72.0% 1.409 HRSC-MOLA融合数据&HiRISE数据（DTEEC_069665_2055_069731） 3.313 3.405 0.624 81.2% 0.916
下载: 导出CSV
-
[1] 杨旭艳,董治宝,杨勤科,等. 基于DEM的地球与火星格状沙丘对比分析[J]. 中国沙漠,2021,41(6):1-11.YANG X Y,DONG Z B,YANG Q K,et al. Comparison of networked dunes in the Earth and the Mars based on DEM[J]. Journal of Desert Research,2021,41(6):1-11. [2] GARRIDO S, MORENO L, MARTIN F, et al. Fast Marching subjected to a Vector Field-path planning method for Mars rovers[J]. Expert Systems with Applications. 2017, 78: 334-346. [3] MORAD S, KALITA H, THANGAVELAOTHAM J. Planning and navigation of climbing robots in low-gravity environments[C]//IEEE Aerospace Conference Proceedings. [S. l. ]: IEEE, 2018. [4] ROSA D D,BUSSEY B,CAHILL J T,et al. Characterization of potential landing sites for the European space agency's lunar lander project[J]. Planetary and Space Science,2012,74(1):224-246. doi: 10.1016/j.pss.2012.08.002 [5] KIM J R,LIN S Y,MULLER J P,et al. Multi-resolution digital terrain models and their potential for Mars landing site assessments[J]. Planetary and Space Science,2013,85:89-105. doi: 10.1016/j.pss.2013.06.001 [6] 汤国安,赵牡丹,李天文,等. DEM提取黄土高原地面坡度的不确定性[J]. 地理学报,2003,58(6):824-830. doi: 10.3321/j.issn:0375-5444.2003.06.004TANG G A,ZHAO M D,LI T W,et al. Modeling slope uncertainty derived from DEMs in loess plateau[J]. Acta Geographica Sinica,2003,58(6):824-830. doi: 10.3321/j.issn:0375-5444.2003.06.004 [7] ROBINSON M S, BRYLOW S M, TSCHIMMEL M, et al. Lunar Reconnaissance Orbiter Camera （LROC） instrument overview[J]. Space Science Reviews 2010, 150（1-4）: 81-124. [8] MCEWEN A S,ELIASON E M,BERGSTORM J W,et al. Mars reconnaissance orbiter's High Resolution Imaging Science Experiment (HiRISE)[J]. Journal of Geophysical Research-Planets,2007,112(E5):E05S02. [9] 邸凯昌,刘斌,辛鑫,等. 月球轨道器影像摄影测量制图进展及应用[J]. 测绘学报,2019,48(12):1562-1574.DI K C,LIU B,XIN X,et al. Advances and applications of lunar photogrammetric mapping using orbital images[J]. Acta Geodaetica of Cartographica Sinica,2019,48(12):1562-1574. [10] 邸凯昌,刘斌,刘召芹. 火星遥感制图技术回顾与展望[J]. 航天器工程,2018,27(1):15.DI K C,LIU B,LIU Z Q. Review and prospect of Mars mapping technique using remote sensing data[J]. Spacecraft Engineering,2018,27(1):15. [11] YANG Q K, DAVID J, LI R, et al. Re-scaling lower resolution slope by histogram matching[M]. Springer: Berlin Heidelberg, 2008. [12] 汤国安,刘学军,房亮,等. DEM及数字地形分析中尺度问题研究综述[J]. 武汉大学学报(信息科学版),2006(12):1059-1066.TANG G A,LIU X J,FANG L,et al. A Review on the scale issue in DEMs and digital terrain analysis[J]. Geomatics and Information Science of Wuhan University,2006(12):1059-1066. [13] 王英,龚家国,贾仰文,等. 基于不同分辨率 DEM 提取坡度值的转换关系研究[J]. 水利水电技术,2019,50(8):45-51.WANG Y,GONG J,JIA Y,et al. Study on conversion relationship of slope information extracted from different resolution DEM[J]. Water Resources and Hydropower Engineering,2019,50(8):45-51. [14] ZHANG X,DRAKE N A,AND J W,et al. Comparison of slope estimates from low resolution DEMs:scaling issues and a fractal method for their solution[J]. Earth Surface Processes and Landforms,1999,24(9):763-779. doi: 10.1002/(SICI)1096-9837(199908)24:9<763::AID-ESP9>3.0.CO;2-J [15] 陈燕,齐清文,汤国安. 黄土高原坡度转换图谱研究[J]. 干旱地区农业研究,2004(3):180-185. doi: 10.3321/j.issn:1000-7601.2004.03.040CHEN Y,QI Q W,TANG G A. Research on slope-conversion-atlas in Loess Plateau[J]. Agricultural Research in the Arid Areas,2004(3):180-185. doi: 10.3321/j.issn:1000-7601.2004.03.040 [16] WANG Y R, WU B. Improved large-scale slope analysis on Mars based on correlation of slopes derived with different baselines[C]// PRSM 2017. [S. l. ]: ISPRS-International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2017. [17] WU B,LI F,HU H,et al. Topographic and geomorphological mapping and analysis of the Chang'E-4 landing site on the far side of the Moon[J]. Photogrammetric Engineering and Remote Sensing,2020,86(4):247-258. doi: 10.14358/PERS.86.4.247 [18] 何振芳,赵牡丹,韩羽. 不同地貌类型坡度提取算法的比较[J]. 水土保持通报,2008,28(6):130-133.HE Z F,ZHAO M D,HAN Y. Comparison of extracting slope algorithms in different types of landscape[J]. Bulletin of Soil and Water Conservation,2008,28(6):130-133. [19] BOUREAU Y L, PONCE J, LECUN Y. A Theoretical analysis of feature pooling in visual recognition[M]. Omnipress: Madison WI USA, 2010. [20] 段瑞玲,李庆祥,李玉和. 图像边缘检测方法研究综述[J]. 光学技术,2005,31(3):415-419. doi: 10.3321/j.issn:1002-1582.2005.03.028DUAN R L,LI Q X,LI Y H. Summary of image edge detection[J]. Optical Technique,2005,31(3):415-419. doi: 10.3321/j.issn:1002-1582.2005.03.028 [21] 姚佩雯. 基于火星遥感影像的“天问一号”着陆区及非极区的尘暴时空分布研究[D]. 青岛: 山东大学, 2021.YAO P W. Spatiotemporal distribution of dust dorm activity in Tianwen-1 landing area and Mars non-polar region based on Mars remote sensing images[D]. Qingdao: Shangdong University, 2021. [22] 王越,王彪,王汛,等. 火星探测任务着陆区选址和地质分析[J]. 深空探测学报(中英文),2020,7(4):371-383.WANG Y,WANG B,WANG X,et al. Analysis and selection of landing areas for Mars mission[J]. Journal of Deep Space Exploration,2020,7(4):371-383. -
计量
- 文章访问数: 37
- 被引次数: 0
