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Journal of Geo-information Science >

2016 , Vol. 18 >Issue 9: 1249 - 1258

DOI: https://doi.org/10.3724/SP.J.1047.2016.01249

Orginal Article

Three-Dimensional Reconstruction of Large Multilayer Overpass Using Airborne LiDAR Data

  • WU Yang ,
  • CHENG Liang , * ,
  • CHEN Yanming ,
  • LI Manchun
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  • 1. Department of Geographic Information Science, Nanjing University, Nanjing 210023, China
  • 2. Jiangsu Provincial Key Laboratory of Geographic Information Science and Technology, Nanjing 210023, China
*Corresponding author: CHENG Liang, E-mail:

Received date: 2015-10-26

  Request revised date: 2016-04-18

  Online published: 2016-09-27

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Abstract

Three-dimensional (3D) model data of overpasses is significant for traffic navigation, landscape design, and many other applications. In this study, we explore the potential of using airborne light detection and ranging (LiDAR) data for the 3D reconstruction of large multilayer overpasses. To reduce the technical difficulty of this 3D reconstruction process, we propose a concept of “structure unit”. The “structure unit” represents a contiguous object with a consistent width, but does not include the bifurcation and/or intersection structures. A new technical framework, based on the structure units, is proposed to reconstruct the 3D models of large multi-layer overpass using the airborne LiDAR data. First, the overpass points are extracted from the raw LiDAR data by using a Reversed Iterative Mathematic Morphological (RIMM) method and inputting the area of overpass. Then, the hierarchal segmentation strategy, including the connectivity-based segmentation and the determination of structure units, is used to determinate the structure units from the overpass points. The central line of each structure is derived by the binarization and vectorization operations. And the obscured structures are detected and restored based on the central lines of the overpass. Finally, the complete 3D model of the overpass can be obtained by using the complete central line and the corresponding width value. Experiments were carried out to evaluate the validities of the proposed method on two different overpasses. The completeness rates of the 3D models of overpasses A and B are 92.77% and 94.58%, respectively. And the correctness rates of the 3D models of overpasses A and B are 98.84% and 98.97%, respectively. The experimental results indicate that the proposed method can provide satisfactory 3D models for large complex overpasses, and is capable to restore the occluded structures with high quality result.

Key words： LiDAR; overpass; three-dimensional reconstruction; structure unit

Cite this article

WU Yang , CHENG Liang , CHEN Yanming , LI Manchun . Three-Dimensional Reconstruction of Large Multilayer Overpass Using Airborne LiDAR Data[J]. Journal of Geo-information Science, 2016 , 18(9) : 1249 -1258 . DOI: 10.3724/SP.J.1047.2016.01249

1 引言

随着城市人口和车辆的急剧增加,交通需求日益增长。立交桥使城市交通从平面走向立体,避免了交叉路口的通行冲突,既可以保证车辆的行驶安全又能提高道路的通行能力,而且具备较强的交通管理功能。立交桥作为新型立体化的道路节点,成为现代城市地标式的建筑,也是城市景观设计和形象宣传中不可或缺的一部分。立交桥三维模型能够呈现完整的空间信息,在交通导航、景观设计、城市宣传等领域有重要的意义[1-3]。城市大型立交桥是较复杂的多层地物,随设计需求、所处地形和地物环境的不同,其形态结构差异较大,具有复杂的三维结构和空间拓扑关系。目前,立交桥的三维重建采用的手工建模方式效率较低,因此开展大型立交桥自动的识别和建模研究具有重要意义。
一些研究将遥感影像作为数据源,从中检测并提取立交桥信息。例如,文献[4]提出一种融合光学影像和合成孔径雷达影像的立体道路网络提取方法;文献[5]结合纹理信息和几何模型,在高分辨率全色IKONOS卫星影像中自动检测桥梁区域。此外,还有一些研究利用影像数据提取道路,常见的方法有数学形态学[6]、特征提取[7]、区域生长[8]等。但是,单纯依靠遥感影像对大型复杂立交桥进行自动提取和三维重建,尚存在较大的技术难度：（1）桥面提取难。由于纹理特征相似,立交桥桥面与道路路面难以区分;机动车辆、路灯、交通指示牌等目标对桥面的提取影响较大。（2）模型重建难。遥感影像无法直接获取三维信息,为立交桥的三维重建带了一定难度;利用影像信息不易恢复立交桥遮挡部分,难以保证重建模型的完整性。
激光雷达是近十几年来快速发展的一种新型的测量技术,广泛运用于地表探测[9]、特征检测[10]、数据匹配[11]、地物提取[12]、模型重建[13]等方面。其中,机载LiDAR平台能够获取高精度的三维点云,有助于大范围场景的目标提取和三维重建。文献[14]提出了一种利用机载LiDAR数据重建立交桥模型的方法,采用全约束三角网建模,并根据三角网信息检测和恢复遮挡结构,但在遮挡严重的情况下恢复效果有限。文献[15]融合激光雷达数据和遥感影像,利用遥感影像获取立交桥轮廓,并利用遮挡处点云进行曲面拟合,修复断裂桥面结构。文献[3]融合激光雷达数据和地形数据,提出了公路交汇处的自动建模方法,并通过道路的形状信息解决交汇处遮挡问题。文献[16]利用车载LiDAR数据检测并提取桥梁点云,对于航空点云提取立交桥很有启发。此外,部分研究利用LiDAR点云提取建筑物和道路并进行三维重建[17-18],对立交桥的建模研究有借鉴意义。然而,利用LiDAR数据对立交桥进行模型重建依然存在一些问题：现有研究对象较少涉及大型多层复杂立交桥,对于立交桥的遮挡结构检测及修复研究不多,且一些研究需要利用影像或地形等辅助数据。
大型立交桥通常包含主线桥面和各类匝道,为了降低自动三维重建的技术难度,本文提出了一个概念“结构单元”,其指无分叉或交汇结构且宽度保持一致的连续桥面。首先将立交桥分割为多个结构单元,然后对遮挡结构进行检测和修复,接着对结构单元进行重建,最后得到完整的立交桥三维模型。

2 研究方法

本文的立交桥模型重建流程分为5个步骤（图1）：（1）立交桥点云提取;（2）基于连通性的点云分割;（3）立交桥结构单元分割;（4）遮挡结构的检测和修复;（5）三维模型重建。
Fig.1 Flowchart of the reconstructed overpass model

图1 立交桥模型重建流程

2.1 立交桥点云提取

从原始LiDAR数据中提取立交桥点云。原始数据主要含有立交桥、建筑物、植被和地面4类点云。首先采用反向迭代数学形态学滤波方法[19]剔除植被和地面点云,然后设定面积阈值滤除面积较小的建筑物点云,以完成立交桥点云的提取。

2.2 基于连通性的点云分割

连通性分割是根据桥面的连通性对立交桥点云进行分割,分割后的连通桥面将进一步分割为结构单元。
2.2.1 三维格网构建
首先构建三维规则格网来容纳立交桥点云。
体元是一个标准的立方体,对每个LiDAR点,记录其所属体元的行 ( i ) 、列 ( j ) 和层 ( k ) 号,具体公式如式（1）所示。
i = int ( ( y - y min ) / Gridsize ) j = int ( ( x - x min ) / Gridsize ) k = int ( ( z - z min ) / Gridsize ) （1）
式中： ( x , y , z ) 代表体元内所含LiDAR点的坐标; ( x min , y min , z min ) 表示立交桥点云的最小坐标; Gridsize 为单一体元的大小。
2.2.2 基于连通性的点云分割
立交桥一般含有多个桥面,根据连通性将立交桥整体分割为若干互不连通的桥面。连通桥面的高程变化平缓,因此桥面连通的判断标准为：将体元内点的高程均值作为该体元的高程值,计算中心体元与其邻域体元的高程差值;若高差小于阈值,则认为两体元相互连通,体元内的点云属于同一连通桥面;否则,两体元不连通。
基于连通性的点云分割具体过程为：
（1）任选一个体元作为种子体元。如图2所示,种子体元位于3×3×3网格中心,按行、列、层的顺序遍历26个邻域体元,并判断是否符合连通性标准。若符合标准,将邻域体元与中心体元标记为同一类别。若不符合标准,则检索邻域内下一体元。
Fig.2 26 neighbors of a voxel

图2 体元26邻域

（2）通过步骤（1）,所有体元均被判断（内部无点数据为空体元,不进行判断）,按体元的分割结果对点云进行分类。至此,基于连通性的点云分割完成。

2.3 结构单元分割

连通桥面可能含有若干分叉或交汇的匝道,因此需要进一步将连通桥面分割为结构单元。中心线能够反映桥面连续的空间形态,故本文提出一种中心线垂线扫描方法来确定结构单元。首先,将三维桥面点云投影至二维水平面,构建二维规则格网将投影点云转换为面状要素;然后,通过二值化、细化、跟踪等矢量化操作,获得中心线。选择中心线的端点作为起始点,沿垂线方向以一定间隔迭代对桥面进行扫描,统计垂线方向有效网格（内含点数据）数量。在扫描的过程中,当桥面宽度不变时,有效网格数目稳定;当出现分叉或交汇结构时,有效网格数量出现突变,以突变处的扫描线作为检测桥面分叉或交汇结构的依据。根据扫描结果,分割连通桥面得到结构单元。本文将二维网格尺寸设置为1.0 m×1.0 m,约为立交桥点云平均点间距的2倍。
如图3所示,中心线含有3个端点 ( A , B , C ) ,存在2种分割情况：分叉结构（一条桥面分叉为多条匝道）;交汇结构（多条匝道交汇为一条桥面）。
Fig.3 Segmentation for detecting structure units

图3 结构单元分割

选择点 A 作为起始点,作垂线 A 1 。沿着 A 1 向中心线两侧扫描,当检测到空网格（内无点数据）,则达到桥面边缘并停止扫描。记录 A 1 方向上的有效网格数量 N A 1 。间隔一定距离选取下一节点,并作垂线 A 2 。依次选取节点,并记录每条垂线方向上的有效网格数量。 A k 表示第 k 次扫描线,与中线相交形成2个节点。此时,桥面出现分叉结构,停止扫描。
选择点 B 作为起始点。 B k 表示第 k 次扫描线, N B k 表示垂线 B k 方向上的有效网格数量。在扫描检测过程中,若 N B k + 1 大于 1.5 × N B k 且 N B k + 2 大于 1.5 × N B k ,则认为桥面出现交汇结构,停止扫描。如果以端点 C 作为起始点,则扫描分割过程与点 B 相似,不再重复说明。至此,中心线扫描完成,连通桥面分割得到3个结构单元。

2.4 立交桥遮挡检测与恢复

由于机载LiDAR俯视采集数据的特性,会出现下层桥面被上层桥面遮挡的现象,需对立交桥的遮挡结构进行检测并修复。
2.4.1 遮挡结构的检测
本文利用中心线端点处上下层桥面的高程差异对遮挡进行检测,具体思路为：选取中心线端点为圆心,作圆形缓冲区,若缓冲区内的点云属于同一桥面,则认为端点处不存在遮挡;若缓冲区内含有多层桥面点云且高程差值大于设定的阈值,则认为该处存在遮挡。
如图4所示,以中心线端点为圆心,作半径 r 的圆形缓冲区。缓冲区内含有桥面 B 的点云,统计 A 和 B 的点云高程均值 h A 和 h B ,计算高程差值 Δ h ,如式（2）所示。
Δ h = h B - h A （2）
若 Δ h 大于阈值则认为结构单元 A 被结构单元 B 所遮挡。遮挡形成2种结构：（1）断裂结构,桥面被结构单元 A 遮挡后形成结构单元 C 和 D ,这种结构可以通过结构单元匹配进行修复;（2）悬挂结构,桥面被结构单元 B 遮挡后只形成结构单元 A ,附近不存在可匹配的结构单元,这种结构称为悬挂结构。
Fig.4 Detection of obscured structures

图4 遮挡结构检测

2.4.2 断裂结构的恢复
（1）断裂结构单元的匹配
以图7为例对断裂结构单元匹配步骤进行说明,结构单元 A 1 ， A 2 ， B 1 ， B 2 （图5（a））,中心线 L A 1 ， L A 2 ， L B 1 ， LB ， （图5（b）,端点 E A 1 ， E A 2 ， E B 1 ， E B 2 （图5（b））,中心线点 P A 1 ， P A 2 ， P B 1 ， P B 2 （图5（c））。
Fig.5 Matching of fractured structures

图5 断裂结构单元匹配

① 搜索待匹配结构单元。以中心线的端点为圆心,设定合理的距离阈值（2-4倍的桥面宽度）,搜索范围内其他端点。
② 待匹配结构单元分组。待匹配结构单元被分为2组, L A 1 和 L A 2 一组; L B 1 和 L B 2 一组,分别位于上层桥面（图5（a）中绿色桥面）两侧。假设中心线分组后分别为 LA = { L A i , i = 1,2 , … , n } 和 LB = { L B j , j = 1,2 , … , m } 。
③ 形成匹配方案。从 LA 和 LB 中分别选取一条中心线,形成一个线对,共形成2种匹配方案（方案1： A 1 - B 1 , A 2 - B 2 ;方案2： A 1 - B 2 , A 2 - B 1 ） 。
④ 匹配方案筛选。计算每个线对端点的高程差值。若差值大于设定的阈值（2 m）,则认为该方案不合理。将筛选后的合理匹配方案记为集合 C = { C i , i = 1,2 , ⋯ , k } 。
⑤ 确定最优匹配方案。对匹配的结构单元利用式（3）拟合二维中心线。 LA 和 LB 对应的中心点分别为 PA = { P A i , i = 1,2 , … , n } 和 PB = { P B i , i = 1 , 2 , … , m } 。 采用最小二乘方法对中心线点进行曲线拟合。本文采用拟合系数 R 2 进行评价。计算每个方案所有线对的拟合系数,计算所有系数和为 R sum ,其中 R sum 值最大的方案即为最优匹配方案。
y = a x 2 + bx + c （3）
统计拟合曲线的总平方和 TSS 、残差平方 RSS 和以及拟合系数 R 2 。拟合系数 R 2 介于0-1之间,越接近1,拟合效果越好。 SST 、 SSR 、 R 2 计算公式如式（4）-（6）所示。
SST = ∑ i = 1 n ( y i - y ̅ ) （4）
SSR = ∑ i = 1 n ( y i ' - y i ) （5）
R 2 = 1 - SSR / SST （6）
图5（b）中端点 E A 1 、 E A 2 、 E B 1 和 E B 2 的高程值分别为15.11、16.25、15.21和15.88 m。任意2个端点的高程差值均小于设定的阈值,因此形成2种匹配方案。图5（d）、（e）分别为方案1、2的拟合结果, R sum 值分别为1.999和1.925。显然方案1是最优的匹配方案。
（2）断裂结构的修复
断裂结构的修复包括二维曲线拟合以及三维曲面高程插值等步骤。图6（a）为断裂的结构单元点云,通过矢量化等步骤得到二维中心线 （图6（b））,接着选取断裂区域的邻近点云并采用式（3）拟合得到修复曲线（图6（c））,得到完整的二维中心线（图6（d））,然后等间距对中心线进行重采样（图6（e））。本文采用式（7）并选择合适的区域 （图6（f））拟合得到曲面（图6（g））。断裂区域的二维采样点通过拟合得到的曲面进行高程插值（图6（h））,最终得到完整的三维中心线（图6（i））。
z = a x 2 + bxy + c y 2 + dx + ey + f （7）
Fig.6 Restoration of fractured structures

图6 断裂结构修复

2.4.3 悬挂结构的修复
遮挡可能产生悬挂结构,即在遮挡处仅形成单一的断裂桥面,无法通过断裂匹配的方式进行修复。现有研究采用的遮挡修复方法主要针对断裂结构,需要利用2个断裂的单体桥面信息进行修复,对于悬挂区域并不适用[14-15],因此本文提出利用桥面中心线的延伸合理性修复悬挂结构。如图7（a）、（b）所示,被遮挡的下层桥面1和3形成分叉（红框区域）,破坏了分叉结构的完整性,使桥面1不能正常分为2段结构单元,形成了悬挂结构。利用式（3）对桥面1拟合曲线,并向下方延伸与中心线2和3分别相交于 B 、 C 点。图7（c）中点 A 为悬挂节点, B 、 C 点位于中心线1的延长部分, B 1 、 C 1 点分别位于中心线2和3, B 1 、 C 1 的投影点是 B 、 C 点。根据式（7）对悬挂区域拟合曲面,根据拟合结果分别计算点 B 和 B 1 的高程差值 d B 、 点 C 和 C 1 的高程差值 d C ， 若 d B > d C 且 d C 小于高差阈值则认为桥面1与桥面3连通,若 d C > d B 且 d B 小于高差阈值,则认为桥面1与桥面2连通。根据连通结果对中心线1进行高程插值,得到完整的三维中心线。
Fig.7 Restoration of a suspended structure

图7 悬挂结构修复

2.5 三维模型重建

完成遮挡结构的修复后,进行三维模型重建。本文利用结构单元的三维中心线组成完整的桥面中心线。通过桥面三维中心线和桥面宽度信息（宽度由2.3节的中心线扫描操作获取）,重建获得完整的立交桥三维模型。

3 实验与分析

3.1 实验数据

本文实验区域为江苏省南京市秦淮区的赛虹立交桥（立交桥A）和双桥门立交桥（立交桥B）。立交桥A的大小约为520 m×450 m,立交桥B的大小约为580 m×600 m。立交桥A和B的原始数据（图8（a）、（c））分别含有82万个点和140万个点,平均点间距约为0.6 m,高程精度为20 cm,平面精度为50 cm。图8（b）、（d）为立交桥A和B的高分辨率航空影像,分辨率为10 cm,作为模型评价的参照数据。
Fig.8 Experimental data

图8 实验数据

3.2 实验结果

图9（a）、（e）为立交桥A和B重建模型与点云TIN底图的叠加效果图,可见重建模型的轮廓清晰,桥面层次分明。图9（b）、（f）为黑框区域对应的局部细节,图中的柱状结构为路灯,红色凸起为车辆,边缘的凸起为桥面护栏。图9（c）、（g）为立交桥A和B重建模型与原始点云的叠加效果图,可见模型与LiDAR点云吻合度较高。图9（d）、（h）表明立交桥的断裂（区域1、3）和悬挂（区域2、4）区域的修复效果较好,重建模型较为完整。
Fig.9 3D overpass model

图9 立交桥三维模型

3.3 模型评价

以手动提取航空影像的立交桥区域作为真实区域。图10（a）、（c）分别为立交桥重建模型投影在平面上的示意图,立交桥A和B模型分别分割为30和34个结构单元（按照结构单元着色）。图10（b）、（d）分别为立交桥A和B重建模型与真实区域的叠合结果;绿色区域表示正确区域;黑色区域表示模型的缺失区域;红色区域表示模型的错误区域。从立交桥模型的数量和面积2个方面进行评价。正确率和完整率的计算公式如式（8）-（9）所示。
Correctness = TP TP + FP （8）
Completeness = TP TP + FN （9）
式中：TP（True Positives）代表正确值;FN （False Negatives）代表遗漏值;FP（False Positives）代表错误值。基于数目的正确、错误、遗漏的判定如下：将结构单元作为一个判定单元,如果正确区域与结构单元的面积比值大于80%,则该结构单元重建正确;如果遗漏区域与结构单元的面积比值大于20%,则该结构单元遗漏;如果错误区域与结构单元的面积比值大于20%,则该结构单元重建错误。
Fig.10 Quality evaluation of 3D overpass model

图10 立交桥模型质量评价

根据表1的统计结果,从数量和面积2方面评价。立交桥A结构单元的数量正确率和完整率均为100%,面积正确率和完整率分别为92.77%和98.84%;立交桥B结构单元的数量正确率和完整率均为100%,面积正确率和完整率分别为94.58%和98.97%。可见立交桥A和B的重建模型均具有较高的完整率和正确率,重建模型的质量较高。
Tab.1 Correctness and completeness of the reconstructed model （quantity and area）

表1 立交桥模型正确率与完整率（数量和面积）

重建模型 正确 遗漏 错误 正确率/(%) 完整率/(%)
数量 面积/m2 数量 面积/m2 数量 面积/m2 数量 面积 数量 面积
立交桥A 30 44 657.46 0 3481.45 0 526.30 100 92.77 100 98.84
立交桥B 34 60 372.01 0 3457.44 0 624.75 100 94.58 100 98.97
从图10（b）、（d）中的细节放大区域可看出,遗漏区域（黑色）大都处于桥面边缘处,模型宽度稍小于桥面真实宽度;错误区域（红色）主要分布在立交桥的顶端。进一步分析可得：（1）由于点云的离散性,桥面点云的轮廓边缘参差不齐,因此重建模型区域与真实区域有一定偏差;（2）部分桥面与地面连通,高程与地面较为接近,因此在滤波处理中容易被识别为地面点云而被滤除。

4 结论

本文提出了一种利用机载LiDAR数据重建大型立交桥三维模型的方法,实验结果表明：
（1）本方法能够有效重建高质量的立交桥三维模型。从建模结果和模型质量可以看出本方法是稳健有效的,证明了利用航空LiDAR数据重建大型复杂立交桥三维模型的可行性。
（2）本文采用先分割后建模策略,通过引入“结构单元”概念,将复杂的立交桥整体分解为简单的桥面单元,降低了三维重建的技术难度和复杂度。
（3）本文提出的立交桥遮挡结构检测与修复技术,能够有效地恢复立交桥的断裂区域和悬挂区域,保证了重建模型的高完整性。
在后续研究中,将尝试其他类型的立交桥区域,借此提高方法的可靠性和适用性。同时还可以利用立交桥的设计参数信息,进一步优化重建模型的精度和质量。此外,下一步将融合多源空间数据对桥面超高现象开展研究。

The authors have declared that no competing interests exist.

References

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