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Journal of Geo-information Science >

2016 , Vol. 18 >Issue 7: 869 - 877

DOI: https://doi.org/10.3724/SP.J.1047.2016.00869

Orginal Article

Method of Automatic Shoulder Line Extraction in the Loess Hilly Area Based on Point Cloud Data

  • LI Min , 1, 2 ,
  • YANG Xin , 1, 2, * ,
  • CHEN Panpan 3 ,
  • XIONG Liyang 1, 2
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  • 1. Key Laboratory of Virtual Geographic Environment of Ministry of Education, Nanjing Normal University, Nanjing 210023, China
  • 2. Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China
  • 3. Institute of Geographical Sciences, Henan Academy of Sciences, Zhengzhou 450052, China
*Corresponding author: YANG Xin, E-mail:

Received date: 2015-11-30

  Request revised date: 2016-01-25

  Online published: 2016-07-15

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《地球信息科学学报》编辑部 所有
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Abstract

Shoulder line is one of the most distinguishing terrain structure lines in Loess Plateau. However, in the loess hilly area, the point cloud near the shoulder line is usually erased mistakenly while using the unified vegetation removal algorithm, which could result in the decrease of DEM accuracy in the terrain expression. Thus the shoulder line should be extracted firstly before removing the vegetation. This paper has proposed a novel shoulder line extraction method based on point cloud data using the multi-scale sampling and slope threshold segmentation. Firstly, a surface model was built based on the ground points selected by a proper filter window. Then, based on the constructed surface model, the slope was calculated and a significant difference near the shoulder line would emerge. Finally, the shoulder line was generated using the slope threshold segmentation. Through the multi-iterative experiments, the optimal filter sizes for each of the 8 sample areas were found, and a power function between the filter size and the point density was discovered. The correctness and reasonability of this correlation was verified in another 5 test areas. Then, the shoulder line of the whole area was generated by using this verified correlation. Using the overlay analysis over the manual identification result, the extracted shoulder line has an accuracy of 85% (within a 0.5 m buffer area). As a conclusion, this method could contribute to improve the accuracy of vegetation removal algorithm that uses the point cloud data for the loess hilly area.

Key words： point cloud; terrestrial 3D laser scanner; shoulder line; DEM; loess hilly area

Cite this article

LI Min , YANG Xin , CHEN Panpan , XIONG Liyang . Method of Automatic Shoulder Line Extraction in the Loess Hilly Area Based on Point Cloud Data[J]. Journal of Geo-information Science, 2016 , 18(7) : 869 -877 . DOI: 10.3724/SP.J.1047.2016.00869

1 引言

地面三维激光扫描技术已广泛应用于局部、精细地形的采集,具有数据精度高、密度大、周期短的特点[1-4]。获得的海量点云数据不仅记录了目标实体表面每一个点的三维信息,还包含了色彩信息和回光强度,能够精确地表达物体表面的位置和形态。然而,原始点云数据因为不仅有真实的地面点,还包含了如建筑物和植被等很多非地面点,所以给数字地形的制作带来了很多噪音。目前,去除点云地表噪音的方法主要有3种：基于点云的三维空间信息法[5-6]、点的回光强度法[7]以及点的几何信息和影像信息法[8-13]。这些方法逐渐应用于点云处理的商业软件中,如芬兰的Terrasolid公司的软件提供了基于不规则三角网（TIN）的渐进加密算法[14],奥地利Riegl公司的RiScan Pro软件提供了基于反射率算法[15]的滤波处理。它们均能够较好地实现地形的地面点和非地面点的自动分类,但在不同的地表形态下,去植被的效果差异明显。一般情况下,在地形变化起伏平缓的地区,效果较好;而对于具有陡变坡度的地区,则产生较大的误差甚至错误。针对该情况,李永强等提出双重滤波法,采用投影变换、粗滤波、地形点的区域增长和精滤波4个步骤对陡坡密集点云进行滤波处理[16]。该方法能有效地实现陡坡滤波,但是投影变换所使用的投影面与陡坡地形的空间形态有关,粗滤波在实际的操作过程中需要利用交互工具去除明显的非地面点,并且区域增长算法还会将少数非地形点误认为地形点。马鼎等提出基于激光回光强度衰减模型的植被滤波方法[17],能够克服坡度变化剧烈的不利影响,但是算法中的回光强度值因样区而异,因此现有方法的普适性还略显不足。
黄土高原丘陵沟壑区具有典型的沟沿线特征,即沟沿线以上坡面平缓（沟间地）,沟沿线以下沟坡明显变陡（沟坡地）,坡度变化差异显著（图1）。采用RiScan Pro软件进行自动去植被时,由于沟沿线上下很短的水平距离内的点云产生了很大的落差,其往往被当做噪声去除,大量坡面点云丢失,部分沟坡地的点云被去除,造成地形表达严重失真。图1中虽有些植被去除了（绿色框部分）,但是沟沿线附近大范围的地面点被误删（蓝色框部分）,造成地形表达的严重失真。因此,对该地形运用点云数据进行地形表面重建时,沟沿线成为去除植被前的重要分割线。此外,沟沿线是黄土地貌中一条重要的地形结构线,它将黄土地貌分为沟间地（正地形）和沟谷地（负地形）,而正地形和负地形在地形特征、土壤侵蚀特征和土地利用方式存在明显不同[18-19],在地貌学研究和水土保持工作中具有重要的作用。目前沟沿线已成为黄土地貌研究的热点之一[20-22],基于DEM进行沟沿线提取方法也日趋成熟,均极大地丰富了相关研究成果[23-27]。然而,随着越来越多的点云数据的获取和应用,面向点云数据的高精度沟沿线的准确提取略显不足。
Fig.1 Comparison of the point cloud before and after using RiScan Pro software to remove the vegetation automatically

图1 利用RiScan PRO软件进行自动去植被前后的对比

因此,本文针对黄土丘陵沟壑区自动去除植被所带来的地形失真问题,提出去除植被前沟沿线的提取方案,实行沟沿线上、下区域的分别处理,从而构建地形表达正确的数字高程模型;实现了利用原始点云的沟沿线自动提取,提高沟沿线提取精度,为基于沟沿线的地貌研究奠定基础。

2 研究区域与方法

2.1 研究区域

研究实验区位于陕西省榆林市靖边县麻地沟村,属于黄土丘陵沟壑区范围内的一条支沟（图2）。实验范围为该支沟及其集水区域,是一个完整小流域,包含沟间地和沟谷地。该区域属于黄土丘陵沟壑地貌,气候属温带半干旱大陆性季风气候,年均气温为7.8 ℃,年均降水量约为395 mm,光照充沛。点云区域为长约600 m的一条冲沟及其集水区域,实验区高差151 m。主沟为东西走向,沟的南北两侧发育大量切沟,北侧有3条较大的切沟,切沟下切侵蚀强烈,南侧切沟数量多,深度较浅,所有切沟的沟沿线明显。北侧坡面几乎没有浅沟,南侧坡面分布有较多的浅沟。沟两侧植被也有较大差别,北侧以灌丛为主,没有树木,南侧以草丛为主,有少量的树木。
Fig.2 The distribution map of point clouds data and the sample areas of Madigou

图2 麻地沟实验区点云数据及样区分布图

2.2 实验数据

数据为2014年8月在麻地沟实地测量获得。利用Rigle公司的VZ400三维激光扫描系统,共设置15个扫描站,测量面积约为0.23 km2,点云总数超6亿,点的平均密度约为2600个/m2。由于点云的数据量非常大,所以本文只以沟沿线附近的随机的小块区域且包含植被等噪声的点云数据作为研究单元。其中,8个点云样区（图2黑色方框,编号1-8）用于提取沟沿线,并探究提取沟沿线所用的网格大小与点云数据特征之间的关系;5个点云样区（图2黄色方框,编号t1-t5）用于验证二者之间关系的适用性。

2.3 沟沿线提取方法

在黄土丘陵沟壑区,沟沿线上部和下部的地形坡度区别很大,沟坡地坡度一般>35°,沟间地坡度一般<10°,最大差异可达25~35°[18],因此坡度变化是识别沟沿线的重要依据。而在原始点云中,又普遍存在大量植被噪音,需要去除一定的植被,构建地表模型,才能有效地提取沟沿线。基于此,本文提出一种多尺度格网采样和坡度分级的沟沿线自动提取方法,算法的具体流程如图3所示。
Fig.3 The schema of shoulder line extractionbased on point cloud

图3 基于点云的沟沿线提取流程图

（1）多尺度格网采样。由于实验区点云数据包含较多的低矮植被点（灌丛等）及少量树木点,因此利用一定的格网尺度,将点云划分到不同的格网内,选取每个格网的高程最低点,对原始点云进行采样。虽然这一过程可能会选出非地面点,但是实验证明,该方法选取到地面点的概率最大[28]。而格网尺度与点密度存在一定的联系,但是每个样区的点密度相差较大,所以需要对每个样区采用多个格网尺度来提取相应的沟沿线,不断测试每个样区的最佳格网尺度。
（2）插值地形表面。对采样的结果点进行插值,模拟地表起伏（图4）。对比反距离加权插值和最近邻点插值法,张婧认为克里金插值方法的结果明显优于其它2种结果,虽然与原始点云数据在细节上存在一定的差距,但能够基本实现对地形的完整形态进行描述[29],因此本文采用普通克里金插值方法对重采样的地面点进行插值。
Fig.4 Select the ground points and simulate the land surface map

图4 选取地面点进行地表面模拟示意图

（3）坡度计算与分级。对插值表面进行坡度计算,然后对坡度结果进行分级。目前已有多种坡度分级方法,可分为依据应用目的、基于坡度特征差异性和基于坡度数据的统计特征3类。自然裂点法属于第3种,是在获得地面坡度分布频数的基础上,以分布统计曲线的自然裂点为临界进行坡度分级的方法,能够根据坡度组合中的一些突变点进行分级,所以该方法能够很好地揭示地形类型分类与分布情况,从而有效地提取地貌类型界线[30]。本文采取自然裂点分级方法对插值模拟的地形表面的坡度进行二级划分,坡度较大的一级即为沟坡地,坡度较小的一级即为沟间地。
（4）提取最长公共边。坡度分割结果会在沟沿线上下分别形成一个大的缓坡面和陡坡面,这2个坡面的公共边即为沟沿线。同时,由于受植被点及其沟谷形态的影响,在2个大的坡面内产生较多的破碎多边形,在进行分割结果转矢量多边形的时候会有多条公共边,需要对破碎多边形进行消除,然后选取最长公共边作为提取的沟沿线（图5）,以样保证样区内提取沟沿线的拓扑正确性。
Fig.5 Illustration of the longest common side extraction

图5 提取最长公共边原理示意图

（5）判读沟沿线。对于提取出的沟沿线,将其与原始点云在三维可视软件中进行目视对比,若沟沿线基本符合真实位置,则输出沟沿线。若沟沿线位置偏离较多,则重新输入格网尺度,并重复步骤（1）-（4）。

3 结果分析

3.1 精度评价

（1）沟沿线套合
基于8个小样区,通过反复实验,确定了在格网采样中各自适宜的格网,并分别确定了位置最准确的一条沟沿线。图6为每个样区选取的最准确的沟沿线及其点云数据（三维视角）。其中,除样区3,自动提取的沟沿线与手工提取结果位置基本吻合,且自动提取的沟沿线精度更高,能展示出更丰富的细节信息。尤其是样区8,在沟沿线附近尽管有植被分布,但自动提取的沟沿线依然与手绘沟沿线吻合。
Fig.6 Point clouds of 8 test areas displayed in 3D

图6 8个样区的点云数据在三维显示

样区3范围内实际有两级沟沿线,在手绘沟沿线过程中,制图综合只选择了上部的沟沿线;而自动提取时,算法自动将样区内的两级沟沿线及转折线提取出来,虽然在沟沿线套合时,其精度和长度都有较大的偏差,但通过目视判断,上部的沟沿线吻合（图7）。
Fig.7 The hatch of two grades of shoulder lines in the test area 3

图7 样区3两级沟沿线剖面图

为了定量评价沟沿线的精度,使用手绘沟沿线缓冲区套合的方法,计算了8个样区自动提取沟沿线在一定距离的缓冲区内的长度与自身长度之比,表示自动提取沟沿线的偏移比率,以此作为精度评价的指标,结果如表1所示。大部分样区中,自动提取沟沿线分布在手动提取沟沿线的0.5 m缓冲范围内,与手动提取沟沿线较为匹配。只有样区4,由于沟坡地受植被点的影响较大,因此依据本方法自动提取的沟沿线有较长的一段并不属于真实的沟沿线,精度差异较大,但是目视判断自动提取沟沿线仍然与手动提取沟沿线有较多部分吻合。
Tab.1 Accuracy comparison of automatically and manually extracted shoulder lines

表1 自动提取沟沿线与手绘沟沿线精度对比

样区编号 0.1 m缓冲范围/（%） 0.5 m缓冲范围/（%） 1 m缓冲范围/（%）
1 82 100 100
2 42 92 100
3 68 90 100
4 37 70 73
5 43 100 100
6 21 76 88
7 7 53 99
8 43 99 100
（2）沟沿线长度对比分析
通过与手动提取的沟沿线相比,自动提取的沟沿线比手动提取的沟沿线长度普遍要长许多,二者的长度比在1-3之间（表2）。可见,虽然二者位置误差较小,但是长度误差较大。这是由于手动提取的沟沿线含有较大的制图综合过程,而自动提取的沟沿线反映了地形转折的更多细节,沟沿线曲率更大造成其长度明显更长。由图6的沟沿线套合的情况看,沟沿线本身越弯曲,自动提取的沟沿线越曲折,与手动提取的沟沿线长度相差也就越大,样区2、4、8长度比大于2,这是由于3个样区的实际沟沿线弯曲度较大,因而自动提取的沟沿线长度也更长。此外,样区3中,自动提取与手动提取比值明显大于其他样区,分析发现样区3存在2级沟沿线（而手动提取结果只有最上方一条）。
Tab.2 Length comparison of automatically and manually extracted shoulder lines (unit: m)

表2 自动与手动提取的沟沿线长度分析（m）

样区编号 沟沿线长度L1（自动） 沟沿线长度L2（手动） L1/L2
1 5.13 4.21 1.22
2 46.90 16.86 2.78
3 31.96 7.20 4.44
4 34.37 12.74 2.70
5 15.32 10.25 1.49
6 42.43 32.91 1.28
7 118.47 83.59 1.41
8 44.08 20.56 2.14

3.2 采样格网尺度对沟沿线提取的影响

在进行格网采样时,由于采样格网尺度选取的差别,选取的地面点不同,内插模拟的地表面也不相同,因而坡度分级时沟坡地和沟间地的临界处会有区别。为了确定采样的最佳格网,分析了不同格网下沟沿线的变化。
（1）多尺度采样格网下沟沿线的变化
以样区1为例,分别使用不同的格网尺度,在0.5的格网尺度下,沟沿线过于简略,部分沟沿线偏离其真实位置;在0.05格网尺度下,沟沿线表现出过多的细节（图8）。由此可见,若选择格网过大,选取的地面点较少,模拟的地表面及坡度分级过于简略,提取的沟沿线将会较远地偏离其真实的位置;相反,格网过小,会造成提取的沟沿线包含太多的细节,不够平滑,且易受沟沿线附近植被的影响,从而对提取的沟沿线造成干扰。因此,格网尺度对于自动提取精细的沟沿线尤为重要,选取合适的格网尺度是本方法的关键。
Fig.8 Shoulder lines extracted in multi-scale filter grids

图8 多尺度滤波格网下的沟沿线

（2）最佳采样格网尺度的自动判定
通过对所有样区的反复试验发现,格网尺度的选择和点密度有一定的关系。分析8个样区点云数据的点数、面积与密度,并经过多次尝试,最终确定各样区相对最佳的格网尺度（表3）。样区8在进行样区选取的时候,选中了过多的坡度较大的沟坡地,计算的密度较大,因此排除样区8的异常值。通过对其余7个样区建立采样格网尺度与点密度的关系（图9）可看出,选取的最佳格网尺度与点密度存在幂函数关系： y = 20.42 x - 0.68 ， 即格网尺度随着点密度的增大迅速减小,而后趋于平稳（图9）。
Fig.9 The relationship between optimal filter grid scale and point density

图9 最佳采样格网尺度与点密度的关系

Tab.3 The information statistics of 8 test areas and the testing best grid scales

表3 8个样区的信息统计及测试的最佳采样格网尺度

样区编号 点数/个 面积/m2 密度/(个/m2) 格网尺度/m
1 25 456 11.73 2170 0.10
2 74 954 76.34 982 0.15
3 80 365 31.98 2513 0.10
4 94 076 51.54 1825 0.15
5 110 384 34.11 3236 0.10
6 142 809 537.62 266 1.00
7 293 848 2173.08 135 0.50
8 310 510 112.36 2764 0.30
为了检验采样格网尺度与点密度关系的正确性,随机选取同一区域内的另外5个样区的沟沿线附近的点云数据。通过计算每个样区的点密度,依据上述采样格网尺度与点密度的关系,计算这5个样区提取沟沿线的格网尺度。然后,采用多尺度格网采样的方法测试出每个样区自动提取沟沿线的最佳格网尺度（表4）。对比结果表明,测试所得的格网尺度与利用上述关系计算的格网尺度较相近。说明在本样区的点云数据基础上,沟沿线的自动提取与采样的格网尺度存在明确的幂函数关系。因此,利用该关系,可对其他样区的采样格网尺度进行自动判定,以便对整个样区的完整沟沿线自动提取。
Tab.4 The optimal filter grid scale of each examination area

表4 5个测试样区最佳采样格网尺度

测试样区 点数/个 面积/m2 密度/（个/m2） 格网尺度（计算）/m 格网尺度（测试）/m
1 19 876 59.01 337 0.12 0.12
2 20 682 60.07 344 0.12 0.15
3 48 913 487.99 100 0.52 0.5
4 151 305 606.13 250 0.17 0.2
5 556 679 975.03 571 0.06 0.1

3.3 实验区完整沟沿线提取结果

由于采集的点云数据数以亿计,远远超出普通计算机的运算负载,因此对采集的点云数据进行分块,每块大小为50 m×70 m。通过计算每个分块内的点密度,确定自动提取沟沿线的最佳格网,提取出每块样区内的精细沟沿线,然后再进行拼接处理。由于2个相邻样区沟沿线端点间的距离大部分都小于0.2 m,因此使用拓扑容差可以实现大部分端点的自动连接,其余手动完成拼接,最后拼接成完整的无拓扑错误的沟沿线。图10为自动提取的完整沟沿线及其与5 m分辨率DEM提取的沟沿线的对比,其中5 m分辨率DEM仍采用坡度分割的方法进行沟沿线的提取。
Fig.10 Comparison of the shoulder lines extracted automatically, manually and with the 5 m DEM

图10 完整区域沟沿线的自动提取、手动提取及5 m分辨率DEM提取套合

从2条沟沿线的套合情况来看,利用本方法基于点云数据提取的沟沿线精度达到85%,而利用5 m DEM提取的沟沿线精度只有16%。相比于5 m分辨率DEM提取的沟沿线简略、不准确的缺点,利用点云自动提取的沟沿线能够准确地表达样区内的沟沿线细节。但在某些沟沿线不明显的区域,也会提取出细节过于丰富的沟沿线,需要人工进行判别。

4 结论

（1）沟沿线是黄土高原沟坡地和沟间地的重要分界线,本文在获取高精度的点云数据基础上,提出一个面向点云数据的沟沿线自动提取方法,在黄土丘陵沟壑区的实验显示,该方法提取的沟沿线位置精度达到85%,而且能反映沟沿线的细节信息,精度更高。其可用于点云数据去噪时,提取坡面和沟谷的分界线,为有效去除植被、构建精细地表提供方法基础。
（2）分析多个样区的点云数据密度与实验所采用的采样格网尺度联系,发现二者存在幂函数关系,即点密度越大采样格网越小、点密度越小采样格网越大。通过该区域另外5个样区的验证,结果显示点密度和采样格网尺度的这种指数关系较为普遍,为实现基于点云的高精度沟沿线的自动提取奠定基础。但是滤波格网与点密度的幂函数关系是否符合其他区域,还有待验证。
（3）在进行点云数据处理时,由于其运算量远远超过了普通计算机的计算负载能力。在提取全域范围内的沟沿线时,只能分块处理。今后,需进行该方法的并行化处理,以提高沟沿线提取效率。

The authors have declared that no competing interests exist.

References

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周毅,汤国安,习羽,等.引入改进Snake模型的黄土地形沟沿线连接算法[J].武汉大学学报·信息科学版,2013,38(1):82-85.提出了一种利用坡面汇流改进的Snake模型实现黄土地貌沟沿线 栅格点自动连接的新方法.该方法基于高分辨率DEM数据,利用正负地形边界处坡度转折特征,识别沟沿线点,进而用坡面汇流方向场改进了Snake模型中的 梯度矢量流场,指引分水线缓冲曲线向沟沿线点蠕移,达到有序连接沟沿线点从而实现正、负地形的自动分割的目的.对比实验结果表明,该方法所识别的黄土沟沿 线较好地逼近真实的地形特征.

[ Zhou Y., Tang G A., Xi ., et al.A shoulder-lines connection algorithm using improved Snake model[J]. Geomayics and Information Science of Wuhan University, 2013,38(1):82-85. ]

[26]
宋效东,汤国安,周毅,等.基于并行GVF Snake模型的黄土地貌沟沿线提取[J].中国矿业大学学报,2013,42(1):134-140.提出了一种改进的并行GVF Snake算法,用来提取大范围高分辨率黄土高原地区的沟沿线.该算法使用规则格网数字高程模型数据,基于全局梯度向量场提取各计算节点的沟沿线.结合沟沿线特殊的空间位置,提出初始轮廓线自动设定的方法.通过改善初始轮廓的自动设定,大大提高了沟沿线提取的准确性,同时也降低了GVF Snake模型的计算时间.在9节点的机群系统上对算法的性能和实验结果准确性进行了测试.在陕北黄土高原梁峁丘陵沟壑区的实验结果表明,本算法可准确地将初始轮廓线设置在有效逼近域内,大大提高了抗干扰性,能够实现黄土地貌沟沿线准确、有效的自动提取；同时,也可获得良好的并行加速比,并行效率较高.

[ Song X D., Tang G A., Zhou Y., et al.Extraction of loess landform shoulder line based on parallel GVF Snake modelp[J]. Journal of China University of Mining & Technology, 2013,42(1):134-140. ]

[27]
王轲,王琤,张青峰,等.地形开度和差值图像阈值分割原理相结合的黄土高原沟沿线提取法[J].测绘学报,2015,44(1):67-75.<p>鉴于地形正负开度对地貌的良好表达且具有分析尺度灵活性这一重要特性,本文提出一种借助地形正负开度及其差值图像阈值分割的黄土地貌沟沿线提取方法.首先,计算DEM的地形正负开度,对正负开度进行差值运算以得到开度差值图;然后,对开度差值图进行阈值处理以得到研究区正负地形空间分布特征;最后,借助数学形态学原理完成对二值化开度差值图正负地形边界&mdash;&mdash;沟沿线的自动提取.试验采用高分辨率DEM数据对陕西洛川塬部分地区进行沟沿线信息提取.结果表明,与其他提取技术方法相比,该方法不仅增强了地貌基本形态特征在沟沿线提取过程中的作用与影响,同时也在一定程度上实现了沟沿线提取的精确化和自动化.</p>

DOI

[ Wang K., Wang Z., Zhang Q ., et al.Loess shoulder line extraction based on openness threshold segmentation[J]. Acta Geodaetica et Cartographica Sinica, 2015,44(1):67-75. ]

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靳生洪,杨鸿海,王莲玉.基于格网化Lidar点云数据坡度滤波方法的研究[J].测绘与空间地理信息,2013,36(6):154-156.LIDAR数据是目前生产DEM/DSM最为理想的数据源,利用 机载激光雷达获取DEM/DSM数据是机载激光雷达最为直接的应用.本文提出了一种将LIDAR点云数据格网化与坡度滤波相结合的点云分类方法,该方法将 数据格网化的概念用于LIDAR点云数据的预处理,避免了LIDAR点云数据内插或者平滑造成的信息损失,并且引入坡度突变对格网化处理后的LIDAR点 云数据进行第二次地面点的选取,提高了LIDAR点云数据分类的效果.

DOI

[ Jin S ., Yang H ., Wang L Y.Research on slope filtering of point cloud data based on gridding LIDAR[J]. Geomatics & Spatial Information Technology, 2013,36(6):154-156. ]

[29]
张婧. 基于克里金算法的点云数据插值研究[D].西安:长安大学,2014:1-74.

[ Zhang J.Interpolation of point clouds data based on Kriging interpolation[D]. Xi'an: Chang'an University, 2014:1-74. ]

[30]
汤国安,宋佳.基于DEM坡度制图中坡度分集方法的比较研究[J].水土保持通报,2006,20(2):157-160,192.

[ Tang G ., Song J.Comparison of slope classification methods in slope mapping from DEMs[J]. Journal of Soil and Water Conservation, 2006,20(2):157-160,192. ]

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