Hierarchical moving curved fitting filtering method based

1007-4619 (2009) 05-827-13 Journal of Remote Sensing 遥感学报

Received: 2008-06-18; Accepted: 2008-12-08 Foundation: National Natural Science Foundation of China (No. 40801128). First author biography: SU Wei (1979— ), Ph. D lecturer, in College of Information and Electrical Engineering, China Agriculture University. She has

published 14 academic articles, including 3 SCI indexed, 6 EI indexed. She majors in the application of remote sensing and LIDAR. E-mail: [email protected]

Corresponding author: ZHAO Dongling, E-mail: [email protected]

Hierarchical moving curved fitting filtering method based on LIDAR data

SU Wei1, SUN Zhong-ping2, ZHAO Dong-ling1, SUN Chong-li1, ZHANG Chao1, YANG Jian-yu1

1. College of Information and Electrical Engineering, China Agriculture University, Beijing 100083, China; 2. Centre for Satellite Environmental Application, Ministry of Environmental Protection of the People’s Republic of China,

Beijing 100029, China

Abstract: LIDAR data is accurate 3D data of terrain acquired from airborne laser detection and ranging system. Compared with hardware technique, data post-processing technique of LIDAR data is weak and time consumed. In this situation, a HMCFA (Hierarchical Moving Curved Fitting Algorithm) filtering method of LIDAR data is reported in this paper. Firstly, block grid searching and indexing mechanism is set up to label discrete LIDAR cloud points. Secondly, quadratic polynomial is set up to fit land terrain with different window size. At last, adaptive threshold is used to distinguish ground points and non-ground points. Accuracy assessment results indicate that the filter error is less than 1m, which can be used in application. Key words: Light Detection and Ranging (LIDAR), Hierarchical Moving Curved Fitting Algorithm (HMCFA), filtering, quadratic polynomial, adaptive threshold CLC number: TP751.1 Document code: A

1 INTRODUCTION

LIDAR (Light Detection and Ranging) is an active imaging technique which integrating techniques including Global Posi-tioning System (GPS), Inertial Measurement Unit (IMU), laser scanner, digital camera, etc. (Liu & Zhang, 2003; Luo et al., 2006). As laser can penetrate into dense vegetation, LIDAR system can acquire high resolution digital surface information in the area covered by vegetation. This character of LIDAR data is very important for terrain recovery in urban area. The reason for this fact is that traditional aerial surveying can not measure the terrain elevation covered by buildings, vegetations, etc. Fortunately, LIDAR can echo more than one time on an object so that the terrain elevation can be measured even if in dense vegetation areas (Zhou, 2003). For these advantages of LIDAR data, a new filtering algorithm named HMCFA of LIDAR data is developed in this paper, and the study area is Kuala Lumpur City Centre (KLCC), Malaysia, where topog-raphic relief is obvious.

There are 4 types of LIDAR data filtering algorithm (Sithole & Vosselman, 2004; Sithole & Vosselman, 1997): morphology filtering method, adaptive filtering method, filtering method based on slope change and hierarchical filtering method. (1) Morphology filtering method: the ground points and non-ground points are distinguished by the probability of LIDAR cloud points belonging to ground points. Hug and Wehr

(1997) developed a moving window morphology-based filter method to do LIDAR data filtering, and the disadvantage of their method is that the topographic type is not fully considered. Tao et al. (2008) developed a filtering method with restraint conditions, in order to solve the problem of excessive opening operation of gray value leading to lost detail information of terrain. (2) Adaptive filtering algorithm (Axelsson, 1999): starting from the lowest line of scanned line and connecting this line with next ground points by MDL (Minimum Description Length) rule. And MDL rule is used to define the fluctuation state of filtered area. The disadvantage of this method lies in the TIN (Triangulated Irregular Network) data, which loss a part of filtering accuracy compared with those LIDAR filtering meth-ods using LIDAR data. (3) Filtering based on slope change (Vosselman, 2000; Vosselman & Maas, 2001; Vosselman, 2002). The judgment of ground point and non-ground point is based on the height differences and derived slope parameter of two neighboring LIDAR cloud points. In some degree, this filtering method is closely related to the erosion operator used in mathematical morphology. So the probability that the higher point is classified as ground point will decrease if the distance between the two points increases. The disadvantage of this method lies in the poor filtering accuracy in sparse LIDAR cloud point areas. (4) Hierarchical filtering method. Zhang (2002) developed a moving curved fitting filtering algorithm based on raw discrete LIDAR data, and two fitting curve (in-

828 Journal of Remote Sensing 遥感学报 2009, 13(5)

cluding plane surface and curving surface) were used. Lin (2004) and Huang (2006) developed a Coarse to Fine Terrain Algorithm (CFTRA). Block grid is used to sort raw discrete LIDAR data in their algorithm and DEM (Digital Elevation Model) is acquired at the same time of LIDAR data filtering. Li and Li (2007) developed hierarchical filtering algorithm, and there were three steps in their operation. Firstly, normalizing raw LIDAR cloud points and producing DSM (Digital Surface Model); secondly, filtering on DSM in line of blocks and ac-quiring initial DTM in this step; at last, finishing DTM smooth using gradient threshold operation. Liu et al. (2008) produced digital surface model using all LIDAR data in a studied forest area firstly, and fitting the surface curve step by step through iterative computation. Secondly, extracting the data less than selected threshold and producing modified surface model at last. Liang et al. (2007) developed hierarchical self-adapting mor-phology filtering method applied in urban area. They used 3 kinds of LIDAR data set with different spatial resolution and different terrain characteristics in their experiments, in order to dissolve some problems such as the district of window size and misjudgment of coarse error. Borrowing ideas from mentioned above filtering method of LIDAR data, we develop a new fil-tering algorithm named HMCFA (Hierarchical Moving Curved Fitting Algorithm) in this study, aiming to increase the filtering accuracy of LIDAR data in urban area.

2 STUDY AREA AND DATA SOURCE

The study area is an urban area (Kuala Lumpur City Centre, from 101°40′46″E to 01°43′25″E, 3°08′00″N to 03°10′39″N) located midway along the west coast of Peninsular Malaysia, at the confluence of the Klang and Gombak rivers, covering approximately 25km2. This region is characterized by rolling topography and flourishing vegetation. The benchmark build-ing Twin Tower is located in this study area, and the peak of which reaches 420m, and the elevation of buildings around which ranges from 100m to 150m. High trees range from 20m to 30m.

Fig. 1 QuickBird Pan-Sharpened image (0.6m, acquired on 11 February, 2004) of Study Area (Kuala Lumpur City Centre, Malaysia) S1 is Shrub, G is Grassland, W is Water, R is Road, B is Building, V is

Vacant land, and S2 is Shadow

LIDAR data is a series of discrete 3D points of terrain ac-quired from airborne laser detection and ranging system, which includes two kinds of attribute such as elevation and intensity of objects. And there are 4 kinds of LIDAR data format: raster grid, TIN, profiles and Volumetric Pixel (Liang et al., 2005). The LIDAR data used in this study is captured by CET LTD. and Malaysia remote sensing center (Malaysian: MACRES). This LIDAR data is produced in 2002 with ASCII data format, and other parameters of LIDAR data is listed in Table 1. Auxil-iary QuickBird high resolution imagery is used to get land cover information through visual interpretation, developing prior knowledge of land cover information in study area. Due to the huge data size, the raw LIDAR data is segmented into sev-eral 1024m×1024m blocks during the filtering operation proc-ess.

Table 1 The parameters of captured LIDAR data

Parameters Value

Platform British Nor Mad airborne

Sensor First Class Infrared Laser

LIDAR system OPTECH System

Captured time 2002

Data controlling Investigation in field work, airborne GPS and Inner Measure Unit

DEM resample interval 1m

Cloud point precision 15cm (vertical), 30cm (horizontal)

Data format ASCII

3 HMCFA FILTER ALGORITHM

3.1 Principles of HMCFA filtering algorithm

The discriminate of ground point and non-ground point is based on the elevation different of considered point with fitting curve, and the considered point will be referred as a non-ground point if it is higher than a threshold, otherwise ground point. The filtering operation includes two main steps. Firstly, search-ing for the minimum point within a certain window size and acquiring 16 this kinds of minimum points when extending to 4×4 neighboring windows with the same window size. These 16 minimum points are used to develop quadratic polynomial and coarse surface model is acquired after surface fitting. Sec-ondly, enlarging the window size and acquiring more detailed terrain model after multiple iteration. The principle of acquiring detailed terrain model through several iterations lies in that higher LIDAR cloud points are filtered with a small window size and next high points are filtered with a large window size then.

3.2 Description and analysis of algorithm

There are 5 steps in HMCFA filtering process. (1) Searching the lowest LIDAR point in a certain window

size, such as 3×3, 5×5, 7×7, 9×9, then extending to 4×4 window

SU Wei et al.: Hierarchical moving curved fitting filtering method based on LIDAR data 829

and finding the lowest point within each window correspond-ingly. In order to keep the completeness of window size, the window will be backspaced in the boundary of image.

(2) Using these 16 minimal values compued from step (1) to create a quadratic polynomial curve fitting equation, we can solve 6 unknown parameters and acquire the expression of ground surface fitting.

(3) Classifying ground points and non-ground points coarsely by setting adaptive threshold.

(4) Enlarging the window size, iterating step (1) to step (3), acquiring more accurate surface model step by step.

(5) Selecting appropriate interpolation method to estimate the elevation of non-ground points, and getting the detailed digital terrain model of study area.

The flowchart of HMCFA filtering process is as Fig. 2. The named Hierarchical Moving Curve Fitting means iterate filter-ing using different window size in order to filter non-ground LIDAR cloud points step by step. The setting value of block size is related to the size of all buildings in study area. The real ground points will be filtered if the window size is too large, then the detailed surface information will loss unfortunately; otherwise, the building point will be judged as ground point and preserved in the followed data interpolation if filtering window size is too small, which will result in the severe skewness of terrain recovery.

3.3 Searching and indexing mechanism of block grid

Labeling raw discrete LIDAR cloud points using block grid, hierarchical filtering is externalized by different window sizes. Block grid searching and indexing mechanism is as Fig. 3. The window size is determined by the building size adaptively, which is set larger if the inner building size is larger; otherwise, smaller.

3.4 Constructing fitting curve

There are 16 minimal LIDAR cloud points resulting from 4×4 filtering window used to construct quadratic polynomial fitting curve(Vosselman & maas, 2001), which is as followed equation: 2 2

1 2 3 4 5 6Z A A X A Y A XY A X A Y= + + + + + (1)

Generally speaking, the number of known points should be greater than or equal to the number of parameters waiting for calculation. If the number of known points is equal to the num-ber of parameters, the result of this equation is unique; however, this unique solution is not always proximate to real surface, which is decided by all selected known points and there will be an obvious error of fitting curve if there is a point which has a huge error. In order to solve this problem, the least-square tech-nique is adopted and redundancy observation of survey is used to resolve fitting curve parameters. Using this method, we can get a group of parameter with the least error, in other words, the best solution.

Fig. 2 Flowchart of HMCFA filtering algorithm

Fig. 3 Searching mechanism of grid (a) Raw discrete LIDAR cloud points; (b) Indexed data of block grid


3.5 Confirmation of adaptive threshold

As mentioned above, the judgment of ground points and non-ground points is done by the elevation difference between studied points and fitting curve. The point whose elevation difference is less than a threshold will be classified as ground point; otherwise, non-ground points. The confirmation of threshold is decided by rolling terrain, which is larger if the terrain is more rolling, vice verse smaller. In named adaptive threshold is computed as followed: max minThreshold ( ) ScaleH H= − × (2)

where, Hmax and Hmin are the maximal elevation value and the minimal elevation value, respectively. The value of Scale is as small as possible, experiment results indicate that this value can be set equal to 0.1 generally.

3.6 Elevation estimation of non-ground points

The elevation of non-ground points is null after filtering, which need to be interpolated in order to solve the problem of rare known points. There are two kinds of interpolation meth-ods used in this study, IDW (Inverse Distance Weighting) method and NN (Nearest Neighbor) method. In IDW interpola-tion method, every point affects the interpolation result locally and this effort decreases with increasing distance. Therefore, one principle of IDW method is setting a higher weight for those nearer points compared with those farer points. NN in-terpolation method is called voronoi polygon method, and only the nearest simple points are used in elevation estimation of non-ground points. In line with the position of LIDAR cloud point, the whole area is segmented in to a lot of subreigons and there is only one point in every segmented region.

4 RESULTS AND ANALYSIS

In order to assess the accuracy of this hierarchical moving curved fitting algorithm (HMCFA), we select three typical study areas to do LIDAR data filtering experiment and fol-lowed accuracy assessment. Three framed areas marked in Fig. 1 are the position and scope of these three study areas, and Region 1 is dense building area, Region 2 is building and vege-tation overlapped area, Region 3 is dense vegetation area. Tak-ing Region 2 as an example, iterative filtering process is illus-trated. Fig. 4 (a) is the surface model of raw discrete LIDAR data, Fig. 4 (b) is the first iterated result and Fig. 4 (c) is the second iterated result. Resulting from these two interpolated results, we can conclude that the interpolate results are ap-proaching to the real surface of terrain step by step.

In order to represent the validity of this HMCFA filtering algorithm, we select 16 quads in these 3 types of test areas to do filtering accuracy assessment. These 16 quads distribute in dense building area (six quads), dense vegetation area (five quads), building and vegetation overlapped hybrid area (five quads). The difference of mean value and standard deviation

between original LIDAR data and filtered continuous DTM are used to validate filtering algorithm accuracy. And the accuracy is higher if the difference is less. The accuracy assessment re-sults of these three framed areas are described as follows.

4.1 Dense building area

The accuracy assessment of filtering in dense building area is done in the position of road, vacant land and grassland, and the detailed assessment result is listed in Table 2. Judging from the elevation difference between DTM and DSM, we can con-clude that the filtering result is ideal and the absolute value of the highest error is less than 0.5m. The least error is less than 0.3m where distributed large area of vacant land. On the con-trary, the filtering accuracy in dense building area is poorer, where there are less LIDAR points distributed.

4.2 Dense vegetation area

The error analysis is only selected on the road, incommodi-ous forest gaps for dense vegetation area. Table 3 is the accu-

Table 2 Accuracy assessment result in dense building area

Statistical value Test site

DSM of raw LIDAR data/m

Filtered results

(DTM)/m

(DTM−DSM) /m

Road 1 42.00 42.50 0.50

Road 2 42.14 41.75 −0.39

Road 3 37.00 37.39 0.39

Road 4 35.77 36.08 0.31

Vacant land 35.77 36.08 0.31

Mean value

Grassland 64.02 64.02 0

Road 1 0 0.15 0.15

Road 2 0.14 0.43 0.29

Road 3 0 0.05 0.05

Road 4 0.43 0.06 −0.37 Vacant land 0 0 0

Standard deviation

Grassland 0.14 0.14 0

Table 3 Accuracy assessment result in dense vegetation area



Filtered results

(DTM)/m

(DTM−DSM) /m

Road 1 42.66 41.84 −0.82

Road 2 46.09 45.00 −1.09

Road 3 59.00 59.00 0

Road 4 39.00 39.64 0.64

Mean value

Gaps of forest 35.52 36.04 0.52

Road 1 0.76 0.37 −0.39

Road 2 0.29 0 −0.29

Road 3 0 0 0

Road 4 0 0.12 0.12

Standard deviation

Gaps of forest 0.50 0.20 −0.30

SU Wei et al.: Hierarchical moving curved fitting filtering method based on LIDAR data 831

Fig. 4 3D view of original LIDAR data and filtered result after two iterative operations

(a) Original LIDAR data; (b) The first interpolated result; (c) The second interpolated result

racy assessment result in dense vegetation area. The absolute difference of DTM-DSM ranges from 0m to 1m, this filtering accuracy is lower in dense vegetation areas compared with dense building distributed areas. One reason of this result is that there are less LIDAR return pulse distributed in these areas.

4.3 Hybrid area

There are several kinds of land cover types distributed in hybrid area: high buildings, trees, roads, vacant lands, and wa-ter, etc. And Table 4 is the accuracy assessment results in this hybrid area. Indicating from the difference results of DTM-DSM, we can see that the filtering results are the most perfect. The maximum error is 0.5m and the error is 0m in most vacant land area.

Table 4 Accuracy assessment result in hybrid area



Filtered results

(DTM)/m

(DTM−DSM) /m

Vacant land 1 31.20 31.00 −0.2

Vacant land 2 31.10 31.00 −0.1

Vacant land 3 42.00 42.00 0

Road 1 30.53 30.00 −0.53

Mean value

Road 2 30.44 30.00 −0.44

Vacant land 1 0 0 0

Vacant land 2 0 0 0

Vacant land 3 0 0 0

Road 1 0.18 0 −0.18

Standard deviation

Road 2 0.24 0 −0.24


5 DISCUSSION AND CONCLUSIONS

Taking Kuala Lumpur City Centre, Malaysia, as study area, the HMCFA method of LIDAR data is developed in this study, which is in allusion to the low filtering accuracy of discrete distribute LIDAR cloud points. Accuracy assessment of LIDAR data filtering is done in 16 quads which are distributed in dense building area, dense vegetation area and hybrid areas. And these 16 quads are selected in vacant land, road, and square, etc., where there is no objects covered. The difference of mean and standard deviation between DSM and DTM are used to illustrate the filtering accuracy quantificationally. Accuracy assessment results indicate that all filtering error is less than 1m and is higher in hybrid area for the reason of there are more LIDAR points distributed in terrain surface and have real sur-face elevation value. The filtering accuracy assessment in dense vegetation areas are poorer, however, which can be controlled less than 1m. This filtering accuracy meets the demand of ap-plication and can be extended to other areas.

The innovation of this filtering algorithm lies in: (1) Hierarchical moving curve fitting filtering algorithm

with different window size are used to determine ground points and non-ground points, which can describe the actual fluctuant condition of ground surface and make filtered results equal to their actual elevation.

(2) The adaptive threshold is used to judge ground points and non-ground points, which increase filtering accuracy. The deficiency of this method lies in that there is less laser returned in dense vegetation area where is sheltered from branches of leaves, which result in a low filtering accuracy in this kind of areas. In the future research, we can increase the accuracy of this algorithm with the help of survey data resulting from field work.

REFERENCES

Axelsson P. 1999. Processing of laser scanner data-algorithms and applications. ISPRS Journal of Photogrammetry and Remote Sensing, 54: 138—147

Huang M Z. 2004. A Knowledge-Based Approach to Urban-feature Classification Using Aerial Imagery with Airborne LiDAR Data. China Taiwan, National Sun Yat-sen University

Hug C and Wehr A. 1997. Detecting and identifying topographic ob-jects in imaging laser altimeter data. International Archives of Photogrammetry and Remote Sensing, 32: 19—26

Li R L and Li T. 2007. Method to extract DTM from LIDAR data.

Railway Investigation and Surveying, 5: 53—54, 57 Liang X L, Zhang J X and Li H T. 2007. An Adaptive Morphological

Filter for LIDAR Data Filtering in Urban Area. Journal of Remote

Sensing, 11(2): 276—281 Liang X L, Zhang J X, Li H T and Yan P. 2005. Representations of

LIDAR Data in Different Applications. Remote Sensing Informa-

tion, 6: 60—64 Lin C Y. 2004. The Study of DEM Generation from Airborne Laser

Scanning Data. Institute of Civil Engineering and Disaster Pre-

vention Technology National Kaohsiung University of Applied Sciences

Liu J N and Zhang X H. 2003. Progress of airborne laser scanning altimetry. Geomatics and Information Science of Wuhan Univer-sity, 28(2): 132—137

Liu Q J, Yoichi Numata and Shinichi Kaneta. 2008. Processing of Air-

borne Laser Scanned Data for Altimetry in Forest Area. Journal of Remote Sensing, 12(1): 104—110

Luo Z Q, Zhang H R, Wu Q, Li C, Chen S, Ding X Q and Wang X. 2006. The airborne LIDAR technology. Land and Resources In-formation, 2(25): 20—25

Sithole G and Vosselman G. 2004. Experimental comparison of filter

algorithms for bare-earth extraction from airborne laser scanning point clouds. ISPRS Journal of Photogrammetry & Remote Sens-ing, 59(1—2): 85—101

Sithole G and Vosselman G. 2005. Filtering of airborne laser scanner data based on segmented point clouds. Laser Scanning

Tao J H, Su L and Li S K. 2008. A detailed protected method of ex-

tracting digital terrain model from airborne laser point cloud in urban areas. Journal of Remote Sensing, 12(2): 233—238

Vosselman G. 2000. Slope based filtering of laser altimetry data. Inter-

national Archives of Photogrammetry and Remote Sensing, 33(B3): 935—942

Vosselman G. 2002. Fusion of laser scanning data, maps, and aerial

photographs for building reconstruction. IEEE International Geo-science and Remote Sensing Symposium and the 24th Canadian Symposium on Remote Sensing, Toronto

Vosselman G and Maas H G. 2001. Adjustment and filtering of raw laser altimetry data. Proceedings of OEEPE Workshop on Air-borne Laserscanning and Interferometric SAR for Detailed Digital

Elevation Models, Stockholm, Sweden Zhang X H. 2002. Airborne Laser Scanning Altimetry Data Filtering

and Features Extraction, Wuhan University Zhou F C. 2005. An Adaptive Point Cloud Filtering Algorithm for DEM

Generation from Airborne Lidar Data. China Taiwan, National Cheng Kung University

苏伟等: 多级移动曲面拟合 LIDAR数据滤波算法 833

收稿日期: 2008-06-18; 修订日期: 2008-12-08 基金项目: 国家自然科学基金(编号: 40801128)。

第一作者简介: 苏伟(1979— ), 女, 山东滕州人, 博士, 中国农业大学信息与电气工程学院讲师, 已发表论文 14篇, 其中 SCI检索 3篇,

EI检索 6篇, 主要从事遥感数字图像处理及遥感应用方面的研究, E-mail: [email protected]。

通讯作者: 赵冬玲, E-mail: [email protected]。

多级移动曲面拟合 LIDAR数据滤波算法

苏伟1, 孙中平2, 赵冬玲1, 孙崇利1, 张超1, 杨建宇1 1. 中国农业大学信息与电气工程学院, 北京 100083;

2. 环境保护部卫星环境应用中心, 北京 100029

摘要: 为提高城市区 LIDAR数据滤波精度, 提出了一种多级移动曲面拟合滤波方法。建立区块网格搜寻及索引机制完成对离散 LIDAR 点云的标示; 通过建立二次多项式完成参考曲面的拟合, 不同窗口大小获得

不同层次的拟合曲面; 设置自适应阈值, 完成地面点与非地面点的判断。精度评价结果表明, 该滤波算法误差在 1m以内, 能够满足实际应用的需求。

关键词: 多级移动曲面拟合, LIDAR数据, 滤波, 二次多项式, 自适应阈值

中图分类号: TP751.1 文献标识码: A

1 引言

激光雷达(light detection and ranging, LIDAR)是激光探测及测距的简称(刘经南 & 张小红, 2003)。该系统集成了定位与导航系统 (global positioning system, GPS)、惯性测量装置(inertial measurement unit, IMU)、激光扫描仪、数码相机等光谱成像设备(罗志清等, 2006), 是一种主动式技术。激光所具有的穿透能力使激光雷达系统可以获取植被覆盖区内

较高精度的地形表面数据, 这对于城市区 LIDAR数据滤波十分重要, 因为传统的航测方法在量测时因为建筑物、植被的遮蔽导致只能观测到道路、空地

部分的地面点 , 而激光雷达具有多重反射的特性 , 即使在树木涵盖的区域仍然可以量测到地面点(周富晨, 2005)。基于 LIDAR数据的这些优势, 我们选择地形起伏较大的马来西亚首都吉隆坡市城市中心

区(Kuala Lumpur city centre, KLCC)为研究区, 进行城市区 LIDAR数据滤波算法研究。

LIDAR数据滤波算法大致可以分为 4类(Sithole & Vosselman, 1997, 2004): (1) 形态学滤波算法, Hug和Wehr运用形态学滤波, 通过不断的迭代, 基于每一个激光雷达脚点属于地面点的概率来区分地面点

与非地面点(Hug & Wehr, 1997), 使用的是移动窗口

形态学滤波算法, 不足之处是对地形的考虑不是很完整; 陶金花等(2008)针对形态学灰度值运算过度过滤导致地形细节丢失的问题, 提出了一种带有约束条件的滤波方法, 根据地形起伏程度设定阈值, 通过阈值控制运算结果。(2) 自适应滤波算法(Axelsson, 1999), 基本思想是: 从所有扫描点的最低的一行开始 , 这一行同下面的地面点通过 MDL(minimum description length)建立关联, 该算法使用的数据类型是不规则三角网, 相对于使用原始 LIDAR点云数据滤波精度有所损失。(3) 基于坡度变化的滤波算法(Vosselman, 2000; Vosselman & Maas, 2001; Vosselman, 2002), 通过定义两点之间的可接受高差作为两点之间距离函数进行基于坡度变化的滤波算

法研究, 根据相邻两点的高差以及衍生的坡度参数判断各点的地面点与非地面点的归属, 高程较大的激光点云属于地面点的可能性较小, 该算法的不足之处是由于过滤条件过于宽松导致在点密度稀疏的

区域数据滤波效果较差。(4) 多级多层次滤波算法。张小红(2002)提出了移动曲面拟合法滤波算法, 直接基于离散的激光点云数据进行数据滤波, 设计的算法有平面法和曲面法两种。林承毅和黄明哲提出

了由粗到精的 LIDAR 数据滤波算法(Lin, 2004; Huang, 2004), 采用区块网格对原始 LIDAR 点云数


据进行二维空间排序, 在将地物点过滤的同时产生DEM(digital elevation model)。李瑞林和李涛(2007)提出的多层次滤波算法共分 3 个步骤: 首先对原始LIDAR 数据进行规则化处理 , 生成 DSM(digital surface model); 然后对 DSM按单元进行一些操作 , 得到初始 DTM; 最后利用梯度阈值操作 , 进行DTM 平滑。刘琪等则以森林为研究对象 , 利用全部数据生成地表的数字表面模型后反复运算并逐

渐逼近 , 提取小于阈值的数据生成修正的表面模型 , 从而达到数据滤波并完成地形恢复目的 (Liu 等, 2008)。梁欣廉等(2007)发展了一种应用于城市区域的分层自适应形态学滤波方法, 采用三个不同分辨率、不同地形/地物特点的数据集进行实验, 并解决了窗口尺寸限制、粗差误判等问题。本文在综

合借鉴上述算法优点的基础上, 发展 HMCFA (hi-erarchical moving curved fitting algorithm)多级移动曲面拟合滤波算法, 提高城市区 LIDAR数据滤波的精度。

2 研究区概况及数据源

研究试验区为马来西亚首都吉隆坡市城市中心区 , 地理范围为 101°40′46″— 101°43′25″E, 03°08′00″—03°10′39″N, 覆盖面积大约 25km2, 位置如图 1。吉隆坡是马来西亚的首都, 位于西马来半岛的中部地区, Klang 河流和 Gombak河流在此交汇。吉隆坡市距西海岸线约 35km, 是该国最大的城市, 区内交通发达。马来西亚的地标建筑 Twin Tower双子塔位于该研究区内, 最高点塔顶约 420m, 周围建筑物高度在 100—150m 之间; 市区内高大绿化树木的高度在 20—30m之间。

图 1 马来西亚吉隆坡市城市中心区(KLCC) (区域 1是建筑物密集区, 区域 2是建筑物与植被相间分布的混

合区, 区域 3是植被密集区)

LIDAR数据是分布于地物表面的一系列三维坐标点, 在形式上呈离散分布, 属性包括所获取点的高程值和反映地物表面对激光信号响应的强度信息, 数据的表现形式有规则格网(raster grid)、不规则三角网(triangular irregular network, TIN)、剖面(profiles)和体元(volumetric pixel)(梁欣廉等, 2005)。研究使用的 LIDAR数据由马来西亚 CET公司获取、马来西亚国家遥感中心(MACRES)提供的原始激光雷达脚点资料。数据获取的具体参数如表 1。以相同地理范围内的 QuickBird 高空间分辨率遥感影像为辅助数据 , 进行研究区内地物分布的目视判断 , 建立研究区内地物分布的先验知识。为了客观评价

和验证本研究所提出的数据滤波算法的有效性, 我们选择了 3个典型区域(图 1中矩形框标出的区域)进行算法有效性的验证, 分别是: 建筑物密集区、植被密集区和两者的混合区域。由于数据资料比较庞大, 滤波算法运行过程中将原始 LIDAR 数据分割成1024m×1024m的小区分别进行处理与运算。

表 1 激光雷达数据的相关获取参数

参数类型参数值

所搭载的飞机 British Nor Mad

传感器类型 First Class Infrared Laser

激光雷达系统 OPTECH System

数据获取时间 2002年

数据控制源地面调查、机载 GPS和内部测量装置

DEM采样间隔 1m

点云精度

垂直方向 15cm, 水平方向是 30cm, 有明显的地面定标标志

数据存储格式 ASCII

3 HMCFA滤波算法

3.1 算法原理

所分析 LIDAR 数据点是地面点还是非地面点的判断标准是: 寻求一定尺寸的窗口内的最低点后, 扩展到 4×4 个同样大小的相邻窗口, 这样就得到 16个最低点, 建立二次多项式, 通过表面拟合运算得到粗的地面模型; 然后再将窗口尺寸扩大, 通过多次迭代得到较为精细的地面模型。迭代过程能够获

得较为精细的地面高程模型的原理是: 较大窗口内的最低点属于地面的概率要高于较小窗口内的最低

点的概率, 在利用小尺寸窗口过滤掉较高地物点的基础上, 逐渐细化, 最终完成非地面点的滤除。

3.2 算法描述与分析

HMCFA 多级移动曲面拟合滤波算法有 5 个


步骤: (1) 在一定大小的窗口范围内, 比如 5×5、7×7、

9×9 的窗口大小, 搜寻高程的最低点; 然后依次类推 4×4 个这样大小的窗口, 分别找出相应窗口内的最低点, 在边界处退格处理, 前提是要保持窗口大小的完整性;

(2) 通过步骤(1)的运算得到 16个地面点的高程值, 建立二次多项式曲面方程式, 进行参考曲面的拟合, 求解 6 个参数值的大小, 得到拟合地形表面的表达式;

(3) 设置自适应阈值 , 进行地面点和非地面点的粗分类;

(4) 扩大其计算窗口, 重复(1)—(3)步, 通过多次迭代获得较为准确的地面模型;

(5) 选择合理的插值方法 , 估算非地面点处的高程值, 得到研究区内的地形恢复结果。

算法的具体流程如图 2, 所谓的多级移动曲面拟合滤波, 主要是指使用不同大小窗口的区块进行多次滤波, 逐渐将地物点滤除。在滤波的过程中区块大小的设定跟研究区内的最大建筑的尺寸有关系, 如果滤波的尺寸过大, 则会使一些真实的地面点滤除掉 , 这样就损失了一些详细的地表信息 ; 反之 , 如果滤波的尺寸过小, 较大尺寸建筑物中心的高程点则会被判断为真实的地面点而保留下来, 这样会使地形的恢复严重失真。

3.3 区块网格搜寻及索引

采用区块网格对原始 LIDAR 点云数据进行标示, 算法中的多级滤波体现在使用不同大小的滤波窗口迭代实现, 区块网格搜寻机制示意图如图 3。搜索区块中小窗口尺寸的大小根据研究区内建筑物大

小情况自适应的确定, 建筑物尺寸较大时该值就设置的大一些, 否则就小一些; 较大窗口的尺寸是小窗口的 4 倍, 所覆盖的面积是 4×4 个小尺寸处理窗口的面积。

3.4 建立拟合曲面

基于 4×4 个窗口内滤波得到的 16 个最小LIDAR 点云高程值, 构建二次多项式曲面方程, 进行参考曲面的拟合(Vosselman & Maas, 2001), 其方程式为:

2 21 2 3 4 5 6Z A A X A Y A XY A X A Y= + + + + + (1)

一般来说, 方程式中有几个待求参数, 最少需要几个参考点。若参考点数目与待求参数个数相同, 所求得的解就是唯一解, 但是这个唯一解并不一定代表最接近真实地表的点, 这要由所选择的参考点

图 2 HMCFA滤波算法工作流程图

而定, 如果参考点内有一点误差较大, 则所求出的拟合曲面也会有较大的误差。鉴于这个原因, 本研究采用最小二乘法, 利用测量上的多余观测的观念求解拟合曲面参数。利用这种方法可获得误差平方

最小的一组参数解, 即最优解。

3.5 自适应阈值的确定

地面点与非地面点的判断通过所考察点同拟合

曲面的高差情况进行判断, 高差在一定阈值范围内的点判断为地面点, 否则为非地面点。阈值的确定则根据研究区内的地形起伏情况而定, 起伏较大的区域需要较大的阈值 , 反之 , 则需要较小的阈值 , 即所谓自适应阈值, 计算方法如式(2)。 max minThreshold ( ) ScaleH H= − × (2) 式中, Hmax和 Hmin为计算窗口内的最大高程值和最

小高程值; Scale 值则尽可能小, 实际滤波操作中可以由用户自定义输入, 经多次试验结果表明: 该值


图 3 区块网格搜寻机制示意图 (a) 原始 LIDAR点云数据; (b) 区块网格索引数据

设为 0.1 时就能描述考察窗口内的地面高差情况, 该值设置过小或者过大将会导致过度滤波和滤波不

足的情况。

3.6 非地面点高程插值预测

非地面点(即地物点)被滤除后, 该位置上留下数据空洞, 需要进行内插计算, 以得到与原始扫描资料相同点密度的真实地表 LIDAR点云数据, 这样就可以解决制作高精度 DEM 时搜寻范围内参考点

密度不足的问题。该研究中数据空洞处的高程插值

采用两种方法进行: IDW(inverse distance weighting)反距离加权法和 NN(nearest neighbor)最近距离法。IDW 插值法认为每个采样点都有局部影响, 这种影响随距离增加而减弱, 因此该插值法一个原则就是给予距离近的点的权重大于距离远的点的权重; NN插值法又称泰森多边形法, 是一种极端边界内插方法, 只用最近的单个点进行区域插值, 泰森多边形按数据点位置将区域分割成子区域, 每个子区域包含一个数据点, 各子区域到其内数据点的距离小于任何到其他数据点的距离, 并用其内数据点进行赋值。

4 试验结果与分析

为客观验证本研究所提出的多级拟合曲面滤波

算法的滤波精度, 我们选择 3 个各具特征的试验区

进行数据滤波试验及精度验证。图 1 中 3 个矩形框所标示的就是这 3 个试验区的地理范围及位置, 其中, 区域 2为混合试验区, 高大建筑物、较高植被、道路、空地和广场相间分布。以区域 2 混合试验区为例, 说明多级拟合曲面滤波过程中逐步迭代的运算结果。图 4(a)为混合试验区原始的 LIDAR点云数据表面处理结果, 图 4(b) 为第一次迭代后得到的处理结果 , 图 4(c)为第二次迭代后得到的处理结果 , 从两次迭代结果可以看出滤波结果逐渐接近真实的

地表信息。为了定量说明该滤波算法的有效性, 分别选择

这 3种类型试验区的 16个样方进行滤波结果的精度验证: 建筑物密集区(6个样方)、植被密集区(5个样方)、建筑物与植被同时存在的混合试验区(5 个样方)。以每个样方内离散分布的原始 LIDAR 点云高程值与滤波后连续分布的 DTM 高程值之间的均值

与标准差的差值作为评价依据, 差值越小说明滤波精度越高, 下面分别对这 3 种类型的试验区进行滤波结果的精度评价分析。

4.1 建筑物密集试验区

建筑物密集区的滤波精度验证是选择在道路、

空地、草地进行的, 表 2 为建筑物密集区滤波精度评价结果。从 DTM-DSM 的差值结果, 滤波效果还是比较理想的, 最高误差的绝对值在 0.5m左右。其中, 有大片空地分布的地方滤波效果最理想, DTM- DSM差值的绝对值在 0—0.3m之间; 建筑物排列密集、道路较窄的地方, 地面上的 LIDAR点云分布较少, 滤波处理精度差一些。

表 2 建筑物密集区滤波精度评价结果

统计值

检验位置

原始 LIDAR数据高程/m

滤波结果(DTM)/m

(DTM−DSM) /m

道路 1 42.00 42.50 0.5

道路 2 42.14 41.75 −0.39

道路 3 37.00 37.39 0.39

道路 4 35.77 36.08 0.31

空地 35.77 36.08 0.31

均值

草地 64.02 64.02 0

道路 1 0 0.15 0.15

道路 2 0.14 0.43 0.29

道路 3 0 0.05 0.05

道路 4 0.43 0.06 −0.37

空地 0 0 0

方差

草地 0.14 0.14 0


图 4 原始 LIDAR点云数据及两次迭代滤波结果三维显示图

(a) 原始激光雷达数据; (b) 第一次迭代滤波结果; (c) 第二次迭代滤波结果

4.2 植被密集试验区

植被密集试验区的误差分析只能选择在道路、

狭窄的林间空隙地进行, 表 3 为植被密集区滤波精度评价结果。相对于建筑物密集区来讲, 植被密集区的滤波效果较差一些, DTM−DSM 差值的绝对值

在 0—1m 之间, 主要原因是植被甚密导致激光回波较少。

4.3 混合试验区

混合试验区内地物类型比较多, 高大建筑物、较高的城市绿化树、道路、空地、水体等, 精度验

证可以选择在大片的空地和道路路面上。表 4 为混合试验区精度评价结果, 该试验区内有大片的无地物覆盖区域分布, 从 DTM−DSM 的差值结果看出该区域滤波的效果最好, 最大误差在 0.5m 左右, 大片空地分布的区域几乎没有误差。

5 结论与讨论

本文以马来西亚吉隆坡市城市中心区(KLCC)的 LIDAR 数据为例, 针对 LIDAR 数据离散分布的特点和滤波精度低的问题, 发展了 HMCFA 多级移


表 3 植被密集区滤波精度评价结果统计

值

检验位置


滤波结果(DTM)/m

(DTM−DSM)/m

道路 1 42.66 41.84 −0.82

道路 2 46.09 45.00 −1.09

道路 3 59.00 59.00 0

道路 4 39.00 39.64 0.64

均值

林间地 35.52 36.04 0.52

道路 1 0.76 0.37 −0.39

道路 2 0.29 0.00 −0.29

道路 3 0 0 0

道路 4 0.00 0.12 0.12

方差

林间地 0.50 0.20 −0.3

表 4 混合试验区滤波精度评价结果

统计

值

检验位置


滤波结果(DTM) /m

(DTM−DSM) /m

空地 1 31.20 31.00 −0.2

空地 2 31.10 31.00 −0.1

空地 3 42.00 42.00 0

道路 1 30.53 30.00 −0.53

均值

道路 2 30.44 30.00 −0.44

空地 1 0 0 0

空地 2 0 0 0

空地 3 0 0 0

道路 1 0.18 0 −0.18

方差

道路 2 0.24 0 −0.24

动曲面拟合滤波算法进行研究区内的地形滤波算法

研究。精度评价基于 3个地形类型区的 16个样方进行, 样方选择在空地、道路、广场等具有原始激光雷达地面高程真值的无地物覆被区域。通过样方内

离散分布的原始 LIDAR 点云高程值与连续分布的DTM 高程值的均值与标准差的差值定量说明滤波

精度。精度评价结果表明: 研究区内滤波误差在 1m以内, 其中, 建筑物密集区和建筑物与植被相间分布的混合区内精度相对高一些, 控制在 0.5m 以内, 这是因为这两种试验区内无地物覆被区域面积比例

较大, 因而具有地面高程真值的原始激光雷达点云数据较多 ; 植被密集区的滤波结果精度稍差一些 , 但基本能够控制在滤波误差小于 1m的精度范围内。这样的滤波精度能够满足实际应用的要求, 具有一定的推广性。

该算法的创新点在于: (1) 滤波过程中 , 基于不同窗口大小的多级移

动曲面进行地面点与非地面点的判断, 能够客观的描述地物的实际起伏状况, 使滤波结果更接近于实

际地面高程; (2) 以自适应的阈值作为地面点与非地面点的

判断标准, 提高了 LIDAR数据的滤波精度。本研究不足之处在于, 植被茂密地区由于树木

枝叶的阻挡导致激光脉冲回波很少, 因此数据滤波的精度较低, 在将来的研究中可以在有实际地面测量数据的支持下进一步改进算法, 提高 LIDAR数据滤波的精度。

REFERENCES

Axelsson P. 1999. Processing of laser scanner data-algorithms and

applications. ISPRS Journal of Photogrammetry and Remote

Sensing, 54: 138—147

Huang M Z. 2004. A Knowledge-Based Approach to Urban-feature

Classification Using Aerial Imagery with Airborne LiDAR

Data. China Taiwan, National Sun Yat-sen University

Hug C and Wehr A. 1997. Detecting and identifying topographic

objects in imaging laser altimeter data. International Archives

of Photogrammetry and Remote Sensing, 32: 19—26

Li R L and Li T. 2007. Method to extract DTM from LIDAR data.

Railway Investigation and Surveying, (5): 53—54, 57.

Liang X L, Zhang J X and Li H T. 2007. An Adaptive Morphologi-

cal Filter for LIDAR Data Filtering in Urban Area. Journal of

Remote Sensing, 11(2): 276—281

Liang X L, Zhang J X, Li H T and Yan P. 2005. Representations of

LIDAR Data in Different Applications. Remote Sensing In-

formation, 6: 60—64

Lin C Y. 2004. The Study of DEM Generation from Airborne Laser

Scanning Data. Institute of Civil Engineering and Disaster

Prevention Technology National Kaohsiung University of Ap-

plied Sciences

Liu J N and Zhang X H. 2003. Progress of airborne laser scanning

altimetry. Geomatics and Information Science of Wuhan Uni-

versity, 28(2): 132—137

Liu Q J, Yoichi Numata and Shinichi Kaneta. 2008. Processing of

Airborne Laser Scanned Data for Altimetry in Forest Area.

Journal of Remote Sensing, 12(1): 104—110

Luo Z Q, Zhang H R, Wu Q, Li C, Chen S, Ding X Q and Wang X.

2006. The airborne LIDAR technology. Land and Resources

Information, 2(25): 20—25

Sithole G and Vosselman G. 2004. Experimental comparison of

filter algorithms for bare-earth extraction from airborne laser

scanning point clouds. ISPRS Journal of Photogrammetry &

Remote Sensing, 59(1—2): 85—101


Sithole G and Vosselman G. 2005. Filtering of airborne laser scan-

ner data based on segmented point clouds. Laser Scanning

Tao J H, Su L and Li S K. 2008. A detailed protected method of

extracting digital terrain model from airborne laser point cloud

in urban areas. Journal of Remote Sensing, 12(2): 233—238

Vosselman G. 2000. Slope based filtering of laser altimetry data.

International Archives of Photogrammetry and Remote Sens-

ing, 33(B3): 935—942

Vosselman G. 2002. Fusion of laser scanning data, maps, and aerial

photographs for building reconstruction. IEEE International

Geoscience and Remote Sensing Symposium and the 24th

Canadian Symposium on Remote Sensing, Toronto

Vosselman G and Maas H G. 2001. Adjustment and filtering of raw

laser altimetry data. Proceedings of OEEPE Workshop on

Airborne Laserscanning and Interferometric SAR for Detailed

Digital Elevation Models, Stockholm, Sweden

Zhang X H. 2002. Airborne Laser Scanning Altimetry Data Filter-

ing and Features Extraction, Wuhan University

Zhou F C. 2005. An Adaptive Point Cloud Filtering Algorithm for

DEM Generation from Airborne Lidar Data. China Taiwan,

National Cheng Kung University

附中文参考文献李瑞林, 李涛. 2007. 一种从 LIDAR取 DTM的方法. 铁道勘察,

(5): 53—54, 57

梁欣廉 , 张继贤 , 李海涛 , 闫平 . 2005. 激光雷达应用中的几种

数据表达方式. 遥感信息, 6: 60—64

梁欣廉, 张继贤, 李海涛. 2007. 一种应用于城市区域的自适应

形态学滤波方法. 遥感学报, 11(2): 276—281

刘经南, 张小红. 2003. 激光扫描测高技术的发展与现状. 武汉

大学学报(信息科学版), 28(2): 132—137

刘琪, 沼田洋, 金田真一. 2008. 航空激光雷达用于森林测量的

数据处理方法研究. 遥感学报, 12(1): 104—110

罗志清, 张惠荣, 吴强, 李琛, 陈申, 丁秀泉, 王溪. 2006. 机载

激光雷达技术. 国土资源信息化, 2(25): 20—25

陶金花, 苏林, 李树楷. 2008. 一种保护细节的从机载激光点云

中提取城区 DTM的方法. 遥感学报, 12(2): 233—238

张小红 . 2002. 机载激光扫描测高数据滤波及地物提取 . 武汉:

武汉大学

周富晨. 2005. 适应性点云过滤演算法与空载光达资料产生数值

高程模型之研究 . 中国台湾 : 国立成功大学测量及空间资

讯学系

Documents

Hierarchical moving curved fitting filtering method based