CN102930146A

CN102930146A - Method for quantitatively evaluating fidelity precision of digital elevation model

Info

Publication number: CN102930146A
Application number: CN2012103977419A
Authority: CN
Inventors: 张锦明; 游雄; 王光霞; 张威巍; 张寅宝
Original assignee: PLA Information Engineering University
Current assignee: PLA Information Engineering University
Priority date: 2012-10-18
Filing date: 2012-10-18
Publication date: 2013-02-13
Anticipated expiration: 2032-10-18
Also published as: CN102930146B

Abstract

The invention relates to a method for quantitatively evaluating the fidelity accuracy of a digital elevation model, which is used to solve the problem that in the quantitative evaluation, due to the lack of fidelity accuracy standards for the digital elevation model, the contour playback method can only be evaluated qualitatively. The method of the present invention makes full use of the regulations on the displacement of linear elements in the comprehensive specification of cartography, taking the water system and terrain reconstruction valley line as an example, calculating the error value and the maximum offset value in the offset between the two, and using the fuzzy mathematical method Establish the membership degree function of the fit offset of the water system and reconstruct the valley line, and finally determine the fit membership value of the single digital elevation model. This method can not only be used for quantitative evaluation of digital elevation model fidelity accuracy, but also can be used to determine the appropriate range of digital elevation model multi-scale conversion.

Description

A Method for Quantitatively Evaluating the Fidelity Accuracy of Digital Elevation Models

技术领域 technical field

本发明涉及一种定量评估数字高程模型保真精度的方法。 The invention relates to a method for quantitatively evaluating the fidelity accuracy of a digital elevation model. the

背景技术 Background technique

当前，数字高程模型（Digital Elevation Model，DEM）精度的研究主要集中在数值精度评估方面，常用的数值精度评估方法包括中误差法、传递函数法、协方差函数法、影像分析法（参见柯正谊，何建邦，池天河.数字地面模型[M].北京：中国科学技术出版社，1993.胡鹏，吴艳兰，胡海.数字高程模型精度评定的基本理论[J].地球信息科学，2003，(3)：64-70.唐新明，林宗坚，吴岚.基于等高线和高程点建立DEM的精度评价方法探讨[J].遥感信息，1999，(3)：7-10.ZHOU Xinghua,ZHAO Jixian,et al.Research on Interpolation and Accuracy Assessment ofDEM[J].Science of Surveying and Mapping，2005,30(5).汤国安，陶旸，王春.等高线套合差及在DEM质量评价中的应用研究[J].测绘通报,2007，(7)：65-67.），以及基于地形描述误差的综合判定方法（参见汤国安，龚健雅，陈正江，成燕辉，王占宏.数字高程模型地形描述精度量化模拟研究[J].测绘学报，2001，30(4)：361-365.王光霞，朱长青，史文中，等.数字高程模型地形描述精度的研究[J].测绘学报,2004，33(2)：168-173.）。 At present, the research on the accuracy of digital elevation model (Digital Elevation Model, DEM) mainly focuses on the evaluation of numerical accuracy. Commonly used numerical accuracy evaluation methods include medium error method, transfer function method, covariance function method, and image analysis method (see Ke Zhengyi, He Jianbang, Chi Tianhe. Digital Terrain Model [M]. Beijing: China Science and Technology Press, 1993. Hu Peng, Wu Yanlan, Hu Hai. Basic Theory of Digital Elevation Model Accuracy Evaluation [J]. Earth Information Science, 2003, (3 ): 64-70. Tang Xinming, Lin Zongjian, Wu Lan. Discussion on the accuracy evaluation method of DEM based on contour lines and elevation points [J]. Remote Sensing Information, 1999, (3): 7-10. ZHOU Xinghua, ZHAO Jixian, et al.Research on Interpolation and Accuracy Assessment ofDEM[J].Science of Surveying and Mapping, 2005,30(5). Tang Guoan, Tao Yang, Wang Chun. Interpolation difference of contour lines and its application in DEM quality assessment Research [J]. Surveying and Mapping Bulletin, 2007, (7): 65-67.), and a comprehensive judgment method based on terrain description errors (see Tang Guoan, Gong Jianya, Chen Zhengjiang, Cheng Yanhui, Wang Zhanhong. Digital elevation model terrain description accuracy Quantitative simulation research [J]. Journal of Surveying and Mapping, 2001, 30(4): 361-365. Wang Guangxia, Zhu Changqing, Shi Wenzhong, etc. Research on the accuracy of digital elevation model terrain description [J]. Journal of Surveying and Mapping, 2004, 33(2 ): 168-173.). the

保真度是判断DEM是否保持了实际三维空间或原始三维数据所具有的在相邻区域无冲突的三维特征和高程逻辑一致性的标准（参见申浩，荆鑫鑫.DEM高保真问题探析[J].测绘工程，2011，20(1)：30-32.），这恰恰是中误差法、传递函数法、协方差函数法和影像分析法等难以确定解决的问题，即无法确定DEM对原始地形的保真程度，因此基于“视觉精度”评估的等高线回放法成为DEM形态精度评估的主要方法，等高线回放法可以有效剔除局部粗差，较好地保证DEM数据的整体质量。但是等高线回放法工作量较大，且多为定性描述，缺乏定量描述指标，导致受人为因素影响较大。 Fidelity is the criterion for judging whether DEM maintains the 3D features and elevation logic consistency in adjacent areas without conflict in the actual 3D space or original 3D data (see Shen Hao, Jing Xinxin. Analysis of DEM high-fidelity problems[J] .Surveying and Mapping Engineering, 2011, 20(1): 30-32.), this is precisely the problem that is difficult to determine and solve with the medium error method, transfer function method, covariance function method and image analysis method, that is, it is impossible to determine the impact of DEM on the original terrain. Therefore, the contour playback method based on "visual accuracy" evaluation has become the main method for evaluating DEM shape accuracy. The contour playback method can effectively eliminate local gross errors and better ensure the overall quality of DEM data. However, the contour playback method has a large workload, and most of them are qualitative descriptions, lacking quantitative description indicators, resulting in a greater impact by human factors. the

许多学者提出了不同的定量评估指标，用以实现等高线回放的定量描述。汤国安等（参见汤国安，陶旸，王春.等高线套合差及在DEM质量评价中的应用研究[J].测绘通报,2007，(7)：65-67.）依据“1：1万DEM数据等高线回放检查时，同名等高线偏移不大于1/2等高距”的规定，运用等高线套合差指标定量评估DEM精度。江帆（参见江帆.DEM表面建模与精度评估方法研究[D].郑州:信息工程大学测绘学院,2006,6.）、朱长青等（(朱长青，王志伟，刘海砚.基于重构等高线的DEM精度评估模型[J].武汉大学学报(信息科学版)，2008，33(2)：153-156.）提出用原始等高线和重构等高线间的面积差与原始等高线长度之比（即重构误差），作为DEM精度评估指标。王志伟（王志伟.基于重构等高线的DEM误差模型研究及应用[D].郑州:信息工程大学测绘学院,2007,6.）在重构误差的基础上提出了等高线的最大重构偏移误差和平均最大重构偏移误差两个指标，利用这两个指标反映局部区域内DEM与实际地形的吻合程度。王光霞等（王光霞，边淑莉，张寅宝.用回放等高线评估DEM精度的研究[J].测绘科学技术学报，2010，27(1)：9-13.）同样在重构误差的基础上，增加重要地性线回放偏移误差指标反映原始等高线和重构等高线在地形特征表达上的差异。上述研究都对等高线回放法的定量评估做出了有益的探索。 Many scholars have proposed different quantitative evaluation indicators to realize the quantitative description of contour playback. Tang Guoan et al. (See Tang Guoan, Tao Yang, Wang Chun. Contour line fit difference and its application in DEM quality evaluation [J]. Surveying and Mapping Bulletin, 2007, (7): 65-67.) Based on " 1:10,000 DEM data contour playback inspection, the contour line offset of the same name is not greater than 1/2 contour distance" regulation, using the contour line fit difference index to quantitatively evaluate the DEM accuracy. Jiang Fan (see Jiang Fan. Research on DEM Surface Modeling and Accuracy Evaluation Method [D]. Zhengzhou: School of Surveying and Mapping, Information Engineering University, 2006, 6.), Zhu Changqing, etc. ((Zhu Changqing, Wang Zhiwei, Liu Haiyan. Based on reconstructed contour line DEM accuracy evaluation model [J]. Journal of Wuhan University (Information Science Edition), 2008, 33(2): 153-156.) It is proposed to use the area difference between the original contour line and the reconstructed contour line and the original contour line The ratio of length (that is, the reconstruction error) is used as the evaluation index of DEM accuracy. Wang Zhiwei (Wang Zhiwei. Research and Application of DEM Error Model Based on Reconstruction Contour [D]. Zhengzhou: School of Surveying and Mapping, Information Engineering University, 2007, 6.) On the basis of the reconstruction error, two indicators, the maximum reconstruction offset error and the average maximum reconstruction offset error of the contour line, are proposed, and these two indicators are used to reflect the degree of agreement between the DEM and the actual terrain in the local area. Wang Guangxia et al. (Wang Guangxia, Bian Shuli, Zhang Yinbao. Research on Evaluating DEM Accuracy with Playback Contours [J]. Journal of Surveying and Mapping Science and Technology, 2010, 27(1): 9-13.) Also on the basis of reconstruction error, increase The offset error index of playback of important geodetic lines reflects the difference in the expression of terrain features between the original contour and the reconstructed contour. The above studies have made useful explorations for the quantitative evaluation of the contour playback method.

无论是利用等高线套合差还是利用等高线重构误差等指标定量评估DEM保真程度，都必须解决两个关键问题。一是高保真重构等高线的生成，虽然基于DEM重构等高线的算法效率较高、健壮性较好，但是重构等高线的质量并不理想，尤其在平坦区或DEM尺寸较大时，歧义性和折线现象比较严重（王春，陶吻，贾敦新，朱雪坚.规则格网DEM地形描述形态精度研究[J].地理信息世界，2008，1：46-52.）。二是同名等高线的匹配，由于原始等高线和重构等高线之间并不是一对一的简单关系，而是一对多、多对一甚至多对多的复杂关系，同名等高线的匹配存在一定难度。这两个关键问题都可能需要大量的手工编辑操作，导致等高线回放法可操作性较差。 Whether it is to quantitatively evaluate the fidelity of DEM by using the contour line fit difference or the contour line reconstruction error and other indicators, two key problems must be solved. One is the generation of high-fidelity reconstructed contours. Although the algorithm based on DEM reconstructed contours has high efficiency and good robustness, the quality of reconstructed contours is not ideal, especially in flat areas or DEM dimensions. When it is larger, the ambiguity and broken line phenomenon are more serious (Wang Chun, Tao Wen, Jia Dunxin, Zhu Xuejian. Research on the Morphological Accuracy of Regular Grid DEM Terrain Description [J]. Geographic Information World, 2008, 1: 46-52.). The second is the matching of contour lines with the same name. Since the original contour line and the reconstructed contour line are not a one-to-one simple relationship, but a one-to-many, many-to-one or even many-to-many complex relationship, the same name, etc. There is a certain difficulty in matching the high line. Both of these key issues may require a large number of manual editing operations, resulting in poor operability of the contour playback method. the

更为重要的是，各种评估指标都没有形成系统的DEM保真精度评估标准，虽然可以评估同一实验区域、不同插值算法建立的DEM之间的差异，但无法确定DEM保真质量是否已经达到生产和应用的需求，进而无法确定DEM多尺度转换的适宜范围等关键性问题。 More importantly, various evaluation indicators have not formed a systematic DEM fidelity accuracy evaluation standard. Although the differences between DEMs established by different interpolation algorithms in the same experimental area can be evaluated, it is impossible to determine whether the DEM fidelity quality has reached Due to the requirements of production and application, key issues such as the appropriate range of DEM multi-scale conversion cannot be determined. the

发明内容 Contents of the invention

本发明的目的是提供一种利用水系和地形套合度定量评估数字高程模型保真精度的方法，用以解决定量评估中，由于缺少数字高程模型保真精度标准，等高线回放法只能定性评估的问题。 The purpose of the present invention is to provide a method for quantitatively evaluating the fidelity accuracy of digital elevation models by using water system and topographical fit, so as to solve the problem of quantitative evaluation. Due to the lack of digital elevation model fidelity accuracy standards, the contour playback method can only be qualitative assessment questions. the

为实现上述目的，本发明的方案是：一种定量评估数字高程模型保真精度的方法，步骤如下： To achieve the above object, the solution of the present invention is: a method for quantitatively evaluating digital elevation model fidelity accuracy, the steps are as follows:

1）对于一个实验区域，水系为基准要素，重构山谷线为比较要素，建立水系和重构山谷线套合偏移量隶属度函数f(ΔD)： 1) For an experimental area, the water system is the reference element, the reconstructed valley line is the comparison element, and the degree of membership function f(ΔD) of the coincidence offset between the water system and the reconstructed valley line is established:

f(ΔD)＝A*f_RMSE(ΔD)+B*f_Max(ΔD) f(ΔD)＝A*f _RMSE (ΔD)+B*f _Max (ΔD)

f_RMSE(ΔD)为偏移量中误差隶属度函数，f_Max(ΔD)为最大偏移量隶属度函数，A∈[0.1,0.3]，B∈[0.7,0.9]； f _RMSE (ΔD) is the membership function of the error in the offset, f _Max (ΔD) is the membership function of the maximum offset, A∈[0.1,0.3], B∈[0.7,0.9];

当DEM_s>2&&DEM_Δh>80时： When DEM _s >2&&DEM _Δh >80:

${f f}_{RMSE RMSE} ((ΔD ΔD)) = = \{\begin{matrix} 11 / / ((11 + + exp exp ((0.9902 0.9902 * * ((ΔD ΔD - - 5.6 5.6)))))) & {DEM DEM}_{size size} = = 12.5 12.5 \\ 11 / / ((11 + + exp exp ((0.2273 0.2273 * * ((ΔD ΔD - - 20.0 20.0)))))) & {DEM DEM}_{size size} = = 2525 \\ 11 / / ((11 + + exp exp ((0.1899 0.1899 * * ((ΔD ΔD - - 28.3 28.3)))))) & {DEM DEM}_{size size} = = 5050 \\ 11 / / ((11 + + exp exp ((0.1575 0.1575 * * ((ΔD ΔD - - 35.8 35.8)))))) & {DEM DEM}_{size size} = = 100100 \\ 11 / / ((11 + + exp exp ((0.0788 0.0788 * * ((ΔD ΔD - - 71.6 71.6)))))) & {DEM DEM}_{size size} = = 200200 \end{matrix}$

当DE_Ms≤2&&DEM_Δh≤80时： When DE _Ms ≤2&&DEM _Δh ≤80:

${f f}_{RMSE RMSE} ((ΔD ΔD)) = = \{\begin{matrix} 11 / / ((11 + + exp exp ((0.9902 0.9902 * * ((ΔD ΔD - - 11.2 11.2)))))) & {DEM DEM}_{size size} = = 12.5 12.5 \\ 11 / / ((11 + + exp exp ((0.2273 0.2273 * * ((ΔD ΔD - - 40.0 40.0)))))) & {DEM DEM}_{size size} = = 2525 \\ 11 / / ((11 + + exp exp ((0.1899 0.1899 * * ((ΔD ΔD - - 56.6 56.6)))))) & {DEM DEM}_{size size} = = 5050 \\ 11 / / ((11 + + exp exp ((0.1575 0.1575 * * ((ΔD ΔD - - 71.6 71.6)))))) & {DEM DEM}_{size size} = = 100100 \\ 11 / / ((11 + + exp exp ((0.0788 0.0788 * * ((ΔD ΔD - - 143.2 143.2)))))) & {DEM DEM}_{size size} = = 200200 \end{matrix}$

其中ΔD为实验区域的偏移量中误差值，DEM_size为数字高程模型尺度，DEM_s为实验区域的平均坡度，DEM_Δh为实验区域的高差； Where ΔD is the error value in the offset of the experimental area, DEM _size is the scale of the digital elevation model, DEM _s is the average slope of the experimental area, and DEM _Δh is the height difference of the experimental area;

当DEM_s>2&&DEM_Δh>80时： When DEM _s >2&&DEM _Δh >80:

${f f}_{Max Max} ((ΔD ΔD)) = = \{\begin{matrix} zmf zmf ((ΔD ΔD,, [\begin{matrix} 5.6 5.6 & 11.2 11.2 \end{matrix}])) & {DEM DEM}_{size size} = = 12.5 12.5 \\ zmf zmf ((ΔD ΔD,, [\begin{matrix} 2020 & 4040 \end{matrix}])) & {DEM DEM}_{size size} = = 2525 \\ zmf zmf ((ΔD ΔD,, [\begin{matrix} 28.3 28.3 & 56.6 56.6 \end{matrix}])) & {DEM DEM}_{size size} = = 5050 \\ zmf zmf ((ΔD ΔD,, [\begin{matrix} 35.8 35.8 & 71.6 71.6 \end{matrix}])) & {DEM DEM}_{size size} = = 100100 \\ zmf zmf ((ΔD ΔD,, [\begin{matrix} 71.6 71.6 & 143.2 143.2 \end{matrix}])) & {DEM DEM}_{size size} = = 200200 \end{matrix}$

当DEM_s≤2&&DEM_Δh≤80时： When DEM _s ≤2&&DEM _Δh ≤80:

${f f}_{Max Max} ((ΔD ΔD)) = = \{\begin{matrix} zmf zmf ((ΔD ΔD,, [\begin{matrix} 11.2 11.2 & 22.4 22.4 \end{matrix}])) & {DEM DEM}_{size size} = = 12.5 12.5 \\ zmf zmf ((ΔD ΔD,, [\begin{matrix} 4040 & 8080 \end{matrix}])) & {DEM DEM}_{size size} = = 2525 \\ zmf zmf ((ΔD ΔD,, [\begin{matrix} 56.6 56.6 & 113.2 113.2 \end{matrix}])) & {DEM DEM}_{size size} = = 5050 \\ zmf zmf ((ΔD ΔD,, [\begin{matrix} 71.6 71.6 & 143.2 143.2 \end{matrix}])) & {DEM DEM}_{size size} = = 100100 \\ zmf zmf ((ΔD ΔD,, [\begin{matrix} 143.2 143.2 & 286.4 286.4 \end{matrix}])) & {DEM DEM}_{size size} = = 200200 \end{matrix}$

其中zmf为z型隶属度函数，它是一种基于样条插值的函数，参数a、b分别定义了样条插值的起点和终点。 Among them, zmf is the z-type membership function, which is a function based on spline interpolation. The parameters a and b define the start and end points of spline interpolation respectively. the

2）计算f(ΔD)，确定给定实验区域的数字高程模型的保真程度。 2) Calculate f(ΔD) to determine the fidelity of the digital elevation model for a given experimental area. the

所述水系和重构山谷线套合偏移量隶属度函数是运用模糊数学建立的，建立水系和重构山谷线套合偏移量隶属度函数所遵循的准则包括：线状要素位移准则和尺度准则； The membership degree function of the fitting offset of the water system and the reconstructed valley line is established by using fuzzy mathematics. The criteria followed to establish the membership function of the fitting offset of the water system and the reconstructed valley line include: linear element displacement criteria and scale guidelines;

线状要素位移准则：当水系和地形特征线的偏移量中误差在0.3mm以内时，认为套合程度较好，即隶属度值达到0.8以上；当水系和地形特征线的偏移量中误差为0.4mm时，认为套合程度一般，即隶属度值在0.5左右；当水系和地形特征线的偏移量中误差大于0.4mm时，认为套合程度较差，即隶属度值在0.5以下； Displacement criteria for linear elements: When the error of the offset between the water system and the topographic feature line is within 0.3mm, it is considered that the matching degree is good, that is, the degree of membership is above 0.8; when the offset between the water system and the topographic feature line is within 0.3mm When the error is 0.4mm, it is considered that the degree of fit is average, that is, the degree of membership is about 0.5; when the error in the offset between the water system and the topographic feature line is greater than 0.4mm, the degree of fit is considered poor, that is, the value of the degree of membership is 0.5 the following;

尺度准则：依据线状要素的位移准则，并参照开方根规律，修正0.4mm的中误差阈值在不同比例尺地形图中对应的实地偏移量；当地形图比例尺为1：10000时，0.4mm的中误差阈值对应实地偏移量为5.6m；当地形图比例尺为1：50000时，0.4mm的中误差阈值对应实地偏移量为20m；当地形图比例尺为1：100000时，0.4mm的中误差阈值对应实地偏移量为28.3m；当地形图比例尺为1：250000时，0.4mm的中误差阈值对应实地偏移量为35.8m；当地形图比例尺为1：1000000时，0.4mm的中误差阈值对应实地偏移量为71.6m。 Scale criterion: According to the displacement criterion of linear elements and referring to the square root law, correct the offset of the medium error threshold of 0.4mm in different scale topographic maps; when the scale of the topographic map is 1:10000, 0.4mm The medium error threshold corresponds to a field offset of 5.6m; when the scale of the topographic map is 1:50000, the medium error threshold of 0.4mm corresponds to a field offset of 20m; when the scale of the topographic map is 1:100000, the 0.4mm The medium error threshold corresponds to a field offset of 28.3m; when the scale of the topographic map is 1:250000, the medium error threshold of 0.4mm corresponds to a field offset of 35.8m; when the scale of the topographic map is 1:1000000, the 0.4mm The medium error threshold corresponds to a field offset of 71.6m. the

建立水系和地形套合偏移量隶属度函数所遵循的准则还包括：平均坡度准则、最大套合偏移量准则和目视效果准则； The criteria followed to establish the membership degree function of water system and topographic alignment offset also include: average slope criterion, maximum alignment offset criterion and visual effect criterion;

平均坡度准则：实验区域平均坡度较小表明区域的等高线特征不明显，因此可以放宽线状要素位移准则；当平均坡度小于2°、高差小于80m时，重新修正0.4mm的中误差阈值在不同比例尺地形图中对应的实地偏移量；当地形图比例尺为1：10000时，0.4mm的中误差阈值对应实地偏移量为11.2m；当地形图比例尺为1：50000时，0.4mm的中误差阈值对应实地偏移量为40m；当地形图比例尺为1：100000时，0.4mm的中误差阈值对应实地偏移量为56.6m；当地形图比例尺为1：250000时，0.4mm的中误差阈值对应实地偏移量为71.6m；当地形图比例尺为1：1000000时，0.4mm的中误差阈值对应实地偏移量为143.2m； Average slope criterion: The small average slope of the experimental area indicates that the contour features of the area are not obvious, so the displacement criterion of linear elements can be relaxed; when the average slope is less than 2° and the height difference is less than 80m, the medium error threshold of 0.4mm should be re-corrected The corresponding field offset in different scale topographic maps; when the topographic map scale is 1:10000, the medium error threshold of 0.4mm corresponds to a field offset of 11.2m; when the topographic map scale is 1:50000, 0.4mm The medium error threshold corresponds to a field offset of 40m; when the scale of the topographic map is 1:100000, the medium error threshold of 0.4mm corresponds to a field offset of 56.6m; when the scale of the topographic map is 1:250000, 0.4mm The medium error threshold corresponds to a field offset of 71.6m; when the scale of the topographic map is 1:1000000, the medium error threshold of 0.4mm corresponds to a field offset of 143.2m;

最大套合偏移量准则：最大偏移量隶属度函数占水系和地形套合偏移量隶属度函数的比例为10％至30％； Maximum fit offset criterion: the maximum offset membership degree function accounts for 10% to 30% of the membership degree function of water system and topographic fit offset;

目视效果准则：同一实验地区不同尺度数字高程模型之间，如果目视观察效果类似，那么计算得到的偏移量隶属度值不存在较大地差别；不同实验地区同一尺度数字高程模型之间，如果目视观察效果类似，那么计算得到的偏移量隶属度值同样不存在较大地差别。 Visual effect criterion: If the visual observation effect is similar between different scale digital elevation models in the same experimental area, then there is no big difference in the calculated offset membership value; between the same scale digital elevation models in different experimental areas, If the visual observation effects are similar, then there is no big difference in the calculated offset membership degree values. the

本发明的方法充分利用制图综合规范中线状要素位移的规定，以水系和地形重构山谷线为例，计算两者之间的偏移量中误差值和最大偏移量值，运用模糊数学方法建立水系和重构山谷线套合偏移量隶属度函数，最终确定单一数字高程模型的套合隶属度值。该方法不仅可以用于数字高程模型的保真精度定量评估，而且可以用于确定数字高程模型多尺度转换的适宜范围。 The method of the present invention makes full use of the regulations on the displacement of linear elements in the comprehensive specification of cartography, taking the water system and terrain reconstruction valley line as an example, calculating the error value and the maximum offset value in the offset between the two, and using the fuzzy mathematical method Establish the membership degree function of the fit offset of the water system and reconstruct the valley line, and finally determine the fit membership value of the single digital elevation model. This method can not only be used for quantitative evaluation of digital elevation model fidelity accuracy, but also can be used to determine the appropriate range of digital elevation model multi-scale conversion. the

附图说明 Description of drawings

图1为本发明的水系和地形重构山谷线偏移图； Fig. 1 is the water system of the present invention and terrain reconstruction valley line offset figure;

图2为本发明的非平原地区的偏移量中误差隶属度函数示意图； Fig. 2 is a schematic diagram of the error membership function in the offset of the non-plain area of the present invention;

图3为本发明的非平原地区最大偏移量隶属度函数示意图； Fig. 3 is the non-plain region maximum offset membership degree function schematic diagram of the present invention;

图4a为本发明吉林永安实验区的依据DEM数据重构的山谷线图； Fig. 4 a is the valley line diagram reconstructed according to DEM data of Jilin Yong'an experimental zone of the present invention;

图4b为本发明河南登封实验区的依据DEM数据重构的山谷线图； Fig. 4 b is the valley line diagram reconstructed according to DEM data of Dengfeng Experimental Area, Henan Province of the present invention;

图4c为本发明福建马甲实验区的依据DEM数据重构的山谷线图； Fig. 4c is the valley line diagram reconstructed according to DEM data of Fujian vest experimental area of the present invention;

图4d为本发明甘肃张掖实验区的依据DEM数据重构的山谷线图； Fig. 4 d is the valley line diagram reconstructed according to DEM data of Zhangye Experimental Area, Gansu of the present invention;

图5为本发明同一实验地区不同尺度DEM和水系的套合结果； Fig. 5 is the fitting result of different scale DEM and water system in the same experimental area of the present invention;

图6为本发明同一实验地区不同尺度DEM和水系的套合结果目视效果比较； Fig. 6 is the comparison of the visual effects of the fitting results of different scale DEMs and water systems in the same experimental area of the present invention;

图7为本发明不同实验地区同一尺度DEM和水系的套合结果目视效果比较； Fig. 7 is the visual effect comparison of the fitting results of the same scale DEM and water system in different experimental areas of the present invention;

图8为本发明水系和地形套合实验结果示例。 Fig. 8 is an example of the results of the water system and topography fitting experiment of the present invention. the

具体实施方式 Detailed ways

下面结合附图对本发明做进一步详细的说明。 The present invention will be described in further detail below in conjunction with the accompanying drawings. the

如图1所示，其中A’、B’、C’、D’为重构等高线和重构山谷线的交叉点，A、B、C、D分别为A’、B’、C’、D’到水系线的相应最近点；本发明将以重构山谷线和重构等高线的交叉点为依据，计算各个交叉点到相应水系的垂直距离作为水系和地形套合的偏离量，如A’A、B’B、C’C、D’D。图1中共存在4个可供计算的水系和重构山谷线的交叉点，其中最大偏移量为42.56m，最小偏移量为3.66m，偏移量中误差为21.76m。 As shown in Figure 1, A', B', C', and D' are the intersection points of the reconstructed contour line and the reconstructed valley line, and A, B, C, and D are respectively A', B', and C' , D' to the corresponding closest point of the water system line; the present invention will be based on the intersection of the reconstructed valley line and the reconstructed contour line, and calculate the vertical distance from each intersection point to the corresponding water system as the deviation of the water system and terrain fit , such as A'A, B'B, C'C, D'D. In Figure 1, there are 4 intersection points of the river system and the reconstructed valley line that can be calculated, the maximum offset is 42.56m, the minimum offset is 3.66m, and the error in the offset is 21.76m. the

计算实验区域中水系和重构山谷线之间的偏移量，就可以实现水系和重构山谷线套合程度的定量量测。但是不同实验区域、不同尺度DEM得到的偏移量存在差异，此时判断某一实验区域中水系和地形套合程度和另一个实验区域的优劣是困难的，因此必须建立统一的判断模型。而运用模糊数学建立的水系和地形套合偏移量隶属度函数是较好地选择。 By calculating the offset between the water system and the reconstructed valley line in the experimental area, the quantitative measurement of the coincidence degree of the water system and the reconstructed valley line can be realized. However, there are differences in the offsets obtained by different experimental areas and different scales of DEM. At this time, it is difficult to judge the degree of water system and terrain fit in one experimental area and the pros and cons of another experimental area. Therefore, a unified judgment model must be established. And the membership degree function of the coincidence offset of water system and topography established by using fuzzy mathematics is a better choice. the

水系和重构山谷线套合偏移量隶属度函数必须遵循以下五个基本准则。 The membership function of the fit offset of the water system and the reconstructed valley line must follow the following five basic principles. the

准则一：线状要素位移准则 Criterion 1: Displacement Criterion for Linear Elements

制图综合规范明确规定“线状要素的平面位置除按制图综合原则进行的位移外，中误差必须控制在±0.3mm以内”。因此，当水系和地形特征线的偏移量中误差在0.3mm以内时，可以认为套合程度较好（即隶属度值达到0.8以上）；当水系和地形特征线的偏移量中误差为0.4mm时，可以认为套合程度一般（即隶属度值在0.5左右）；当水系和地形特征线的偏移量中误差大于0.4mm时，可以认为套合程度较差（即隶属度值在0.5以下）。 The Cartographic General Specification clearly stipulates that "the plane position of linear elements must be controlled within ±0.3mm, except for the displacement according to the cartographic general principle." Therefore, when the error in the offset between the water system and the topographic feature line is within 0.3mm, it can be considered that the degree of fit is good (that is, the degree of membership reaches above 0.8); when the error in the offset between the water system and the topographic feature line is 0.4mm, it can be considered that the degree of fit is average (that is, the value of the degree of membership is around 0.5); 0.5 or less). the

准则二：尺度准则 Criterion 2: Scale Criterion

建立偏移量隶属度函数时必须考虑DEM尺度因素的影响。国家测绘地理信息局于1998年规定了相应比例尺地形图建立的最适宜DEM尺度对应关系（表1）。因此，同样是准则一建立的判断准则，0.4mm的中误差阈值在不同尺度的DEM中代表不同的实地偏移量。 The influence of the DEM scale factor must be considered when establishing the membership function of the offset. In 1998, the National Bureau of Surveying, Mapping and Geographic Information stipulated the most suitable DEM scale correspondence for the establishment of corresponding scale topographic maps (Table 1). Therefore, it is also the judgment criterion established by criterion 1. The medium error threshold of 0.4mm represents different on-site offsets in DEMs of different scales. the

表1地形图比例尺、DEM尺度和实地偏移量之间关系 Table 1 Relationship among topographic map scale, DEM scale and field offset

在实际运用过程中，如果简单运用准则一判断水系和地形的套合程度，那么实验结果在不同DEM尺度时将导致严重的偏差，即随着DEM尺度的增大，水系和地形的实际套合偏移量的增大并非特别明显。以表1作为判断准则，将得到大尺度DEM的偏移量隶属度值好于小尺度的情况。 In the actual application process, if the criterion 1 is simply used to judge the matching degree of the water system and the terrain, then the experimental results will lead to serious deviations at different DEM scales, that is, as the DEM scale increases, the actual matching degree of the water system and the terrain The increase in offset is not particularly noticeable. Taking Table 1 as the judgment criterion, it will be obtained that the membership value of the offset of the large-scale DEM is better than that of the small-scale. the

从图5可以看出，DEM尺度为12.5m时，套合偏移中误差值为7.7649m，按照表1制定的准则，7.7649m的偏移量是非常巨大；而当DEM尺度为200m时，套合偏移中误差为36.9228m，此时用于判断它的标准是300m，无疑是非常精确地套合。但是从目视效果看，12.5m DEM的套合效果明显优于200m DEM的情况。这种悖离现象几乎在所有实验区域中普遍存在，因此准则二必须修改。 It can be seen from Fig. 5 that when the DEM scale is 12.5m, the error value in the coincidence migration is 7.7649m. According to the criteria formulated in Table 1, the offset of 7.7649m is very large; and when the DEM scale is 200m, The error in the fit offset is 36.9228m, and the standard used to judge it at this time is 300m, which is undoubtedly a very precise fit. But from the visual effect, the fitting effect of 12.5m DEM is obviously better than that of 200m DEM. This deviation is common in almost all experimental areas, so the second criterion must be modified. the

开方根规律法是德国Topfer提出的一种地图概括的数量处置方法，用于解决资料地图和新编地图由于比例尺的变换而产生的数量简化问题。他认为：资料地图与新编地图两种比例尺分母之比的开方根，便是新编地图应选取的地图要素的数量，即 The square root law method is a quantitative processing method of map generalization proposed by Germany Topfer, which is used to solve the quantitative simplification problem caused by the transformation of the scale of the data map and the new map. He believes that the square root of the ratio of the denominators of the two scales of the data map and the new map is the number of map elements that should be selected for the new map, that is,

$\frac{{N N}_{new new}}{{N N}_{orign origin}} = = \sqrt{\frac{{M m}_{orign origin}}{{M m}_{new new}}} - - - - - - ((11))$

其中N_new为新编图的地图要素数量，N_orign为资料图的地图要素数量，M_new为新编图比例尺分母，M_orign为资料图比例尺分母。 Among them, N _new is the number of map elements in the newly compiled map, N _orign is the number of map elements in the data map, M _new is the denominator of the scale of the newly compiled map, and M _orign is the denominator of the scale of the data map.

开方根规律法适用于解决地图要素数量的选取问题，研究对象主要是不同比例尺地图中的地图要素个数。假设地图要素均匀分布时，则不同比例尺地图要素之间的平均距离同样符合开方根规律法，即 The square root method is suitable for solving the problem of selecting the number of map elements, and the research object is mainly the number of map elements in maps of different scales. Assuming that the map elements are evenly distributed, the average distance between map elements of different scales also conforms to the square root law, that is

$\frac{{\overset{&OverBar; &OverBar;}{D D.}}_{orign origin}}{{\overset{&OverBar; &OverBar;}{D D.}}_{new new}} = = \sqrt{\frac{{M m}_{orign origin}}{{M m}_{new new}}} - - - - - - ((22))$

其中为新编图地图要素之间的平均距离，

Figure 47536DEST_PATH_GDA00002517240600075

为新编图地图要素之间的平均距离。 in is the average distance between newly compiled map elements,

is the average distance between newly edited map features.

考虑到新编图和资料图之间的范围差异，还应该在式（2）中增加改正因子C，即 Considering the range difference between the newly edited map and the data map, the correction factor C should also be added to formula (2), namely

$\frac{{\overset{&OverBar; &OverBar;}{D D.}}_{orign origin}}{{\overset{&OverBar; &OverBar;}{D D.}}_{new new}} = = \sqrt{C C * * \frac{{M m}_{orign origin}}{{M m}_{new new}}} - - - - - - ((33))$

其中C为范围改正因子。例如新编图为1：10万且资料图为1：5万时，则C取4。因此按照式（3）修改表1，如表2所示。 where C is the range correction factor. For example, when the newly edited map is 1:100,000 and the data map is 1:50,000, then C takes 4. Therefore, modify Table 1 according to formula (3), as shown in Table 2. the

表2地形图比例尺、DEM尺度和实地偏移量之间关系（按照开方根规律法修改） Table 2 The relationship between topographic map scale, DEM scale and field offset (modified according to the square root law method)

准则三：平均坡度准则 Criterion Three: Average Slope Criterion

建立偏移量隶属度函数时需要考虑实验区域平均坡度的影响。实验区域平均坡度较小意味着该区域的等高线特征不明显，在等高线特征不明显的区域研究水系和地形的套合程度没有太大的意义，多数情况下可以默认水系和地形套合程度较好。制图综合规范中规定“平原地貌”中可以将“线状要素的位移中误差放宽到±0.6mm以内”。因此平原地貌的“地形图比例尺、DEM尺度和0.4mm实地偏移量之间关系”如表3所示。 The influence of the average slope of the experimental area needs to be considered when establishing the membership function of the offset. The small average slope of the experimental area means that the contour features of the area are not obvious. It is not meaningful to study the degree of integration of water system and terrain in areas where the contour features are not obvious. In most cases, the water system and terrain can be set by default. The degree of fit is good. The comprehensive cartographic specification stipulates that "the error in the displacement of linear elements can be relaxed to within ±0.6mm" in the "plain landform". Therefore, the "relationship between topographic map scale, DEM scale and 0.4mm field offset" of the plain landform is shown in Table 3. the

表3地形图比例尺、DEM尺度和实地偏移量之间关系（平原地貌） Table 3 The relationship between topographic map scale, DEM scale and field offset (plain landform)

准则四：最大套合偏移量准则 Criterion 4: Maximum Fit Offset Criterion

建立偏移量隶属度函数时需要考虑最大套合偏移量的影响。偏移量中误差是从整体意义上水系和地形套合偏移量的离散程度，并没有考虑单个交叉点的影响。假设存在N个可供计算的交叉点，其中大多数偏移量较小，而某一交叉点的偏移量较大，则最终计算得到的中误差可能较小。此时将无法反映最大偏移量值的对套合精度的影响。因此，应该虑最大偏移量的影响，即在偏移量隶属度函数中占据20％的比率。 The influence of the maximum fit offset should be considered when establishing the offset membership function. The error in the offset is the degree of dispersion of the integration offset of the water system and terrain in the overall sense, and the influence of a single intersection is not considered. Assuming that there are N intersections available for calculation, most of which have small offsets, and a certain intersection has a large offset, the final calculated error may be small. At this time, the impact of the maximum offset value on the fitting accuracy cannot be reflected. Therefore, the influence of the maximum offset should be considered, that is, it occupies 20% of the offset membership function. the

准则五：目视效果准则 Criterion Five: Visual Effects Criterion

建立偏移量隶属度函数时需要考虑目视观察的效果。首先，同一实验地区不同尺度DEM之间，如果目视观察效果类似，则计算得到的偏移量隶属度值不应该存在较大的差别。如图6所示。其次，不同实验地区同一尺度DEM之间，如果目视观察效果类似，则计算得到的偏移量隶属度值也不应该存在较大的差别，如图7所示。 The effect of visual observation needs to be considered when establishing the membership function of the offset. First of all, if the visual observation effect is similar between DEMs of different scales in the same experimental area, there should not be a large difference in the calculated offset membership value. As shown in Figure 6. Secondly, if the visual observation effect is similar between DEMs of the same scale in different experimental areas, the calculated offset membership degree values should not have a large difference, as shown in Figure 7. the

上述五条准则中第一、二条必须严格遵守，第三、四、五条属于细微调节作用。因此参照上述五条准则，可以建立水系和重构山谷线偏移量隶属度函数，由偏移量中误差隶属度函数f_RMSE(ΔD)和最大偏移量隶属度函数f_Max(ΔD)组成： The first and second of the above five guidelines must be strictly followed, while the third, fourth, and fifth are fine-tuning functions. Therefore, referring to the above five criteria, the offset membership function of the water system and the reconstructed valley line can be established, which is composed of the error membership function f _RMSE (ΔD) in the offset and the maximum offset membership function f _Max (ΔD):

①偏移量中误差隶属度函数 ①The error membership function in the offset

当DEM_s>2&&DEM_Δh>80时（如图2所示，其中各条曲线从左到右依次为12.5m、25m、50m、100m、200mDEM的中误差隶属度函数图）： When DEM _s >2&&DEM _Δh >80 (as shown in Figure 2, each curve is the middle error membership function diagram of 12.5m, 25m, 50m, 100m, 200mDEM from left to right):

当DEM_s≤2&&DEM_Δh≤80时： When DEM _s ≤2&&DEM _Δh ≤80:

其中ΔD为每一实验区域的偏移量中误差值，DEM_size为DEM格网尺寸，DEM_s为每一实验区域的平均坡度，DEM_Δh为每一实验区域的高差。 Among them, ΔD is the error value in the offset of each experimental area, DEM _size is the DEM grid size, DEM _s is the average slope of each experimental area, and DEM _Δh is the height difference of each experimental area.

②最大偏移量隶属度函数 ②Maximum offset membership function

当DEM_s>2&&DEM_Δh>80时（如图3所示，其中各条曲线从左到右依次为12.5m、 25m、50m、100m、200mDEM的最大偏移量隶属度函数图）： When DEM _s >2&&DEM _Δh >80 (as shown in Figure 3, each curve is the maximum offset membership function diagram of 12.5m, 25m, 50m, 100m, 200mDEM from left to right):

当DEM_s≤2&&DEM_Δh≤80时： When DEM _s ≤2&&DEM _Δh ≤80:

确定偏移量中误差隶属度函数和最大偏移量中误差隶属度函数之后，就可以根据两个隶属度函数的比例关系确定偏移量隶属度函数，即： After determining the membership function of the error in the offset and the membership function of the error in the maximum offset, the membership function of the offset can be determined according to the proportional relationship between the two membership functions, namely:

f(ΔD)＝A*f_RMSE(ΔD)+B*f_Max(ΔD)（4） f(ΔD)＝A*f _RMSE (ΔD)+B*f _Max (ΔD) (4)

其中A∈[0.1，0.3]，B∈[0.7,0.9]。 where A ∈ [0.1, 0.3], B ∈ [0.7, 0.9]. the

以下以1：5万地形图数据为例，并结合附图对本发明的具体实施方式作进一步详细说明。 Taking the 1:50,000 topographic map data as an example, the specific implementation of the present invention will be further described in detail in conjunction with the accompanying drawings. the

第一步：数据准备 Step 1: Data Preparation

分别选取吉林永安、河南登封、福建马甲、甘肃张掖等四个地区25.6Km×25.6Km的1:5万地形图数据作为基础源数据，并计算相应的地形描述参数（表4），分别代表丘陵、低山、中山、和高山。 The 1:50,000 topographic map data of 25.6Km×25.6Km in Yongan, Henan, Dengfeng, Fujian, Majia, Fujian, and Zhangye, Gansu were respectively selected as the basic source data, and the corresponding terrain description parameters were calculated (Table 4), representing Hills, Low Mountains, Medium Mountains, and High Mountains. the

表4实验地区地形描述参数 Table 4 Terrain description parameters of the experimental area

（1.1）根据选择的实验区域，分别提取相应为水系线数据，作为基准数据；同时在实验区域中随机、均匀地选取实验样区用于套合精度的量测； (1.1) According to the selected experimental area, extract the corresponding water system line data as the benchmark data; at the same time, randomly and evenly select the experimental sample area in the experimental area for the measurement of the fitting accuracy;

（1.2）确定1：5万地形图建立的DEM的最佳尺度为25m； (1.2) Determine that the best scale of the DEM established by the 1:50,000 topographic map is 25m;

（1.3）使用DEM插值算法分别建立尺度分别为12.5m、25m、50m、100m、200m的DEM数据。 (1.3) Use DEM interpolation algorithm to establish DEM data with scales of 12.5m, 25m, 50m, 100m and 200m respectively. the

第二步：计算偏移量隶属度值 Step 2: Calculate the offset membership value

（2.1）提取多尺度DEM数据的重构山谷线信息，如图4a、4b、4c和4d所示； (2.1) Extract the reconstructed valley line information of multi-scale DEM data, as shown in Figures 4a, 4b, 4c and 4d;

（2.2）基于实验样区，寻找可用于比较的水系线和重构山谷线的匹配点，计算相应的偏移量； (2.2) Based on the experimental sample area, find the matching points of the water system line and the reconstructed valley line that can be used for comparison, and calculate the corresponding offset;

（2.3）分别计算水系和重构山谷线套合偏移量隶属度值。 (2.3) Calculate the degree of membership of the coincidence offset of the water system and the reconstructed valley line respectively. the

第三步：分析单一DEM的套合精度，并确定多尺度转换的适宜范围 Step 3: Analyze the fitting accuracy of a single DEM and determine the appropriate range for multi-scale conversion

（3.1）所有实验区域中，基于多尺度DEM数据计算得到套合精度隶属度值具有不同的表现。如图8所示，25m和50m DEM计算得到的套合精度最佳，12.5m DEM计算得到的套合精度最差。表明以1：5万等高线数据为基准建立的多尺度DEM数据中，25m和50m DEM对原始数据中隐含高程信息的再现最合适，再次验证了基于1：5万等高线数据建立DEM的最佳尺度为25m是合理的。同时表明基于25m DEM进行尺度下推变换时，下推1个等级是完全合理的，下推2-3个等级则需要斟酌，因为100m和200m DEM计算得到套合精度中存在地形表达的逻辑错误（即水系跨越山脊线、水系跨越山顶、水系跨越鞍部等三种，其最大偏移量值为9999.0）；但是基于25m DEM进行尺度上推变换时，实验表明没有任何意义，即套合精度计算结果极差，说明1：5万等高线数据中隐含的高程信息并不能通过不同DEM插值算法（即使是稳定性、鲁棒性都较好的插值算法）得到补充，唯一的方法是增加新的高程信息，否则利用任何插值算法提高DEM精度都是徒劳的。 (3.1) In all experimental areas, the fitting accuracy membership degree values calculated based on multi-scale DEM data have different performances. As shown in Figure 8, the fitting accuracy calculated by 25m and 50m DEM is the best, and the fitting accuracy calculated by 12.5m DEM is the worst. It shows that among the multi-scale DEM data established based on the 1:50,000 contour data, 25m and 50m DEM are most suitable for reproducing the hidden elevation information in the original data, and it is verified again that the 1:50,000 contour data It is reasonable that the optimal scale of DEM is 25m. At the same time, it shows that when the scale is pushed down based on the 25m DEM, it is completely reasonable to push down 1 level, and it needs to be considered when pushing down 2-3 levels, because there is a logical error in the accuracy of the terrain expression calculated by the 100m and 200m DEM (That is, the water system crosses the ridge line, the water system crosses the mountain top, and the water system crosses the saddle, etc., and the maximum offset value is 9999.0); however, when the scale is pushed up and transformed based on the 25m DEM, the experiment shows that it does not make any sense, that is, the accuracy calculation The results are extremely poor, indicating that the elevation information implied in the 1:50,000 contour data cannot be supplemented by different DEM interpolation algorithms (even interpolation algorithms with better stability and robustness). The only way is to increase new elevation information, otherwise it is futile to use any interpolation algorithm to improve DEM accuracy. the

（3.2）实验区域的平均坡度越平坦，DEM尺度变换越“平缓”；表5中吉林永安的各尺度DEM数据计算得到的套合隶属度值整体上优于其他实验区域，表明地形平均坡度越是平坦的区域，在进行多尺度变换时差异越小，越能够实现DEM尺度的“平缓”变换；但是在地形平均坡度较大的区域，在进行多尺度变换的过程中差异变大，尺度上推由于没有更多的高程信息而不能满足要求，尺度下推则存在一个有限范围，即1-2个尺度。从DEM尺度变换时的最小高程、最大高程、平均坡度等地形特征因子的变化中也能窥见一斑。DEM尺度和地形特征因子的变化关系一般表现为：随着DEM尺度的增加，最小高程变大、最大高程变小、平均坡度变小，整个区域逐渐区域坦化，这种变化规律在地形较为复杂的区域是较为激烈的，而在地形较为简单的区域则比较平缓，反映到等高线信息的变化中也是如此，最终表现套合程度上同样如此。 (3.2) The flatter the average slope of the experimental area, the more "smooth" the DEM scale transformation; in Table 5, the composite membership value calculated from the DEM data of various scales in Yong'an, Jilin is generally better than that of other experimental areas, indicating that the average slope of the terrain is more "smooth". It is a flat area, the smaller the difference when performing multi-scale transformation, the more "smooth" transformation of DEM scale can be realized; Pushing cannot meet the requirements because there is no more elevation information, and scaling down has a limited range, that is, 1-2 scales. It can also be seen from the changes of terrain characteristic factors such as minimum elevation, maximum elevation, and average slope during DEM scale transformation. The change relationship between DEM scale and terrain feature factors is generally manifested as: with the increase of DEM scale, the minimum elevation becomes larger, the maximum elevation becomes smaller, the average slope becomes smaller, and the entire area gradually becomes flatter. This change rule is more complex in the terrain The area is relatively intense, while the area with relatively simple terrain is relatively gentle, which is also reflected in the changes of contour information, and the same is true for the degree of final performance. the

表5各实验区域多尺度DEM中水系和地形套合隶属度值 Table 5 The membership degree value of water system and topography in the multi-scale DEM of each experimental area

本发明的优点在于： The advantages of the present invention are:

（1）本发明基于制图综合规范原理，运用模糊隶属度函数，实现了利用水系和地形套合程度定量化评估DEM地形保真精度。 (1) The present invention is based on the principle of cartographic comprehensive specification, and uses the fuzzy membership function to realize the quantitative evaluation of DEM terrain fidelity accuracy by using the degree of water system and terrain fit. the

（2）本发明不仅可以用于单一DEM数据的地形保真精度定量量测，而且可以用于确定多尺度DEM转换的适宜范围，保证了多尺度DEM的适用范围；而且根据水系基准数据的选择的不同，可以用于评估不同综合算法建立的DEM综合精度。 (2) The present invention can not only be used for quantitative measurement of terrain fidelity accuracy of single DEM data, but also can be used to determine the suitable range of multi-scale DEM conversion, ensuring the applicable range of multi-scale DEM; and according to the selection of water system reference data can be used to evaluate the synthesis accuracy of DEMs established by different synthesis algorithms. the

Claims

1. A method for quantitatively evaluating digital elevation model fidelity accuracy, characterized in that the steps are as follows:

1) For an experimental area, the water system is the reference element, the reconstructed valley line is the comparison element, and the degree of membership function f(ΔD) of the coincidence offset between the water system and the reconstructed valley line is established:

f(ΔD)＝A*f _RMSE (ΔD)+B*f _Max (ΔD)

f _RMSE (ΔD) is the membership function of the error in the offset, f _Max (ΔD) is the membership function of the maximum offset, A∈[0.1,0.3], B∈[0.7,0.9];

When DEM _s >2&&DEM _Δh >80:

{f f}_{RMSE RMSE} ((ΔD ΔD)) = = \{\begin{matrix} 11 / / ((11 + + exp exp ((0.9902 0.9902 * * ((ΔD ΔD - - 5.6 5.6)))))) & {DEM DEM}_{size size} = = 12.5 12.5 \\ 11 / / ((11 + + exp exp ((0.2273 0.2273 * * ((ΔD ΔD - - 20.0 20.0)))))) & {DEM DEM}_{size size} = = 2525 \\ 11 / / ((11 + + exp exp ((0.1899 0.1899 * * ((ΔD ΔD - - 28.3 28.3)))))) & {DEM DEM}_{size size} = = 5050 \\ 11 / / ((11 + + exp exp ((0.1575 0.1575 * * ((ΔD ΔD - - 35.8 35.8)))))) & {DEM DEM}_{size size} = = 100100 \\ 11 / / ((11 + + exp exp ((0.0788 0.0788 * * ((ΔD ΔD - - 71.6 71.6)))))) & {DEM DEM}_{size size} = = 200200 \end{matrix}

When DEM _s ≤2&&DEM _Δh ≤80:

{f f}_{RMSE RMSE} ((ΔD ΔD)) = = \{\begin{matrix} 11 / / ((11 + + exp exp ((0.9902 0.9902 * * ((ΔD ΔD - - 11.2 11.2)))))) & {DEM DEM}_{size size} = = 12.5 12.5 \\ 11 / / ((11 + + exp exp ((0.2273 0.2273 * * ((ΔD ΔD - - 40.0 40.0)))))) & {DEM DEM}_{size size} = = 2525 \\ 11 / / ((11 + + exp exp ((0.1899 0.1899 * * ((ΔD ΔD - - 56.6 56.6)))))) & {DEM DEM}_{size size} = = 5050 \\ 11 / / ((11 + + exp exp ((0.1575 0.1575 * * ((ΔD ΔD - - 71.6 71.6)))))) & {DEM DEM}_{size size} = = 100100 \\ 11 / / ((11 + + exp exp ((0.0788 0.0788 * * ((ΔD ΔD - - 143.2 143.2)))))) & {DEM DEM}_{size size} = = 200200 \end{matrix}

Where ΔD is the error value in the offset of the experimental area, DEM _size is the scale of the digital elevation model, DEM _s is the average slope of the experimental area, and DEM _Δh is the height difference of the experimental area;

When DEM _s >2&&DEM _Δh >80:

{f f}_{Max Max} ((ΔD ΔD)) = = \{\begin{matrix} zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 5.6 5.6 & 11.2 11.2 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 12.5 12.5 \\ zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 2020 & 4040 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 2525 \\ zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 28.3 28.3 & 56.6 56.6 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 5050 \\ zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 35.8 35.8 & 71.6 71.6 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 100100 \\ zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 71.6 71.6 & 143.2 143.2 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 200200 \end{matrix}

When DEM _s ≤2&&DEM _Δh ≤80:

{f f}_{Max Max} ((ΔD ΔD)) = = \{\begin{matrix} zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 11.2 11.2 & 22.4 22.4 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 12.5 12.5 \\ zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 4040 & 8080 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 2525 \\ zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 56.6 56.6 & 113.2 113.2 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 5050 \\ zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 71.6 71.6 & 143.2 143.2 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 100100 \\ zmf zmf (\begin{matrix} ΔD ΔD,, [\begin{matrix} 143.2 143.2 & 286.4 286.4 \end{matrix}] \end{matrix}) & {DEM DEM}_{size size} = = 200200 \end{matrix}

Among them, zmf is the z-type membership function, which is a function based on spline interpolation. The parameters a and b define the start and end points of spline interpolation respectively.

2) Calculate f(ΔD) to determine the fidelity of the digital elevation model for a given experimental area.

2. The method according to claim 1, characterized in that, the membership function of the fitting offset of the water system and the reconstructed valley line is established by using fuzzy mathematics, and the fitting offset of the water system and the reconstructed valley line is established The criteria followed by the membership function include: linear element displacement criteria and scale criteria;

Displacement criteria for linear elements: When the error of the offset between the water system and the topographic feature line is within 0.3mm, it is considered that the matching degree is good, that is, the degree of membership is above 0.8; when the offset between the water system and the topographic feature line is within 0.3mm When the error is 0.4mm, it is considered that the degree of fit is average, that is, the degree of membership is about 0.5; when the error in the offset between the water system and the topographic feature line is greater than 0.4mm, the degree of fit is considered poor, that is, the value of the degree of membership is 0.5 the following;

Scale criterion: According to the displacement criterion of linear elements and referring to the square root law, correct the offset of the medium error threshold of 0.4mm in different scale topographic maps; when the scale of the topographic map is 1:10000, 0.4mm The medium error threshold corresponds to a field offset of 5.6m; when the scale of the topographic map is 1:50000, the medium error threshold of 0.4mm corresponds to a field offset of 20m; when the scale of the topographic map is 1:100000, the 0.4mm The medium error threshold corresponds to a field offset of 28.3m; when the scale of the topographic map is 1:250000, the medium error threshold of 0.4mm corresponds to a field offset of 35.8m; when the scale of the topographic map is 1:1000000, the 0.4mm The medium error threshold corresponds to a field offset of 71.6m.

3. The method according to claim 2, characterized in that, the criteria to be followed in establishing the membership function of the water system and topographic fit offset also include: the average slope criterion, the maximum fit offset criterion and the visual effect criterion ;

Average slope criterion: The small average slope of the experimental area indicates that the contour features of the area are not obvious, so the displacement criterion of linear elements can be relaxed; when the average slope is less than 2° and the height difference is less than 80m, the medium error threshold of 0.4mm should be re-corrected The corresponding field offset in different scale topographic maps; when the topographic map scale is 1:10000, the medium error threshold of 0.4mm corresponds to a field offset of 11.2m; when the topographic map scale is 1:50000, 0.4mm The medium error threshold corresponds to a field offset of 40m; when the scale of the topographic map is 1:100000, the medium error threshold of 0.4mm corresponds to a field offset of 56.6m; when the scale of the topographic map is 1:250000, the 0.4mm The medium error threshold corresponds to a field offset of 71.6m; when the scale of the topographic map is 1:1000000, the medium error threshold of 0.4mm corresponds to a field offset of 143.2m;

Criteria for maximum coincidence offset: the maximum offset membership function accounts for 10% to 30% of the membership function of water system and terrain coincidence offset;

Visual effect criterion: If the visual observation effect is similar between different scale digital elevation models in the same experimental area, then there is no big difference in the calculated offset membership value; between the same scale digital elevation models in different experimental areas, If the visual observation effects are similar, then there is no big difference in the calculated offset membership degree values.