﻿ ﻿ 附加约束条件的光束法区域网平差在四拼数码航空相机平台检校中的应用
 文章快速检索 高级检索

1. 中测新图(北京)遥感技术有限责任公司，北京 100039； 2. 中国测绘科学研究院，北京 100830

The Application of Bundle Block Adjustment with Constraint Conditions in Platform Calibration of Four-Head Aerial Digital Camera
XU Bin1LI Yingcheng1,2,LIU Xiaolong1,2 ZHU Xiange1,QI Yanqing1
1. China TopRS Technology Company Limited，Beijing 100039，China； 2. Chinese Academy of Surveying and Mapping，Beijing 100830，China
First author: XU Bin(1982—), male, PhD candidate, engineer, majors in aerial photogrammetry. E-mail： magic_x@163.com
Abstract: A method of bundle block adjustment with constraint conditions aimed at the four-head aerial digital camera is presented. The exterior orientation parameters of camera and relative positions of sub-cameras are calculated to derive platform calibration parameters. Experimental results verify that the precision of platform calibration parameters calculated with this method is high, the quality of virtual images is good, and the aerial triangulation precision satisfies the large scale and medium scale specifications of surveying.
Key words: TOPDC-4     aerial digital camera     bundle block adjustment     platform calibration

1 引言

TOPDC-4(以下简称四拼相机)基于这种原理，通过在平台上安装4个数码相机的方式，来获取具有大范围地面覆盖度的拼接影像。四拼相机的平台检校[6]就是准确获取相机与虚拟投影面之间相对位置关系的过程，根据平台检校参数可以从子影像生成高精度的虚拟影像。

2 现有平台检校原理分析

2.1 平台检校基本原理

 图 1 TOPDC-4外观及其安装方式 Fig. 1 TOPDC-4 and the configuration of sub-cameras

 图 2 影像拼接示意图 Fig. 2 Illustration of mosaic images

2.2 虚拟影像的拼接误差分析

 图 3 hg 与Δh/hg对dx′与dy′的影响 Fig. 3 Influences in dx′ and dy′ as a function of hg and Δh/hg

2.3 十字重叠区方式平台检校及其存在的问题

2.4 传统光束法原理及其在平台检校中的问题

 影像编号 子相机编号 X Y Z 相机距离 备注 437 1 2 443.949 3 440.260 0 974.830 8 0.885 2 1、2相机 2 2 444.376 5 439.951 6 974.119 5 1.009 3 2、4相机 3 2 443.933 3 439.858 9 975.081 0 0.473 0 1、3相机 4 2 444.598 5 439.908 7 975.103 1 0.667 4 3、4相机 438 1 2 450.569 7 234.565 5 975.601 0 0.929 1 1、2相机 2 2 451.024 5 234.234 3 974.861 6 0.917 2 2、4相机 3 2 450.511 3 234.182 9 975.787 6 0.429 7 1、3相机 4 2 451.178 8 234.248 0 975.765 6 0.671 0 3、4相机 439 1 2 453.662 6 26.004 3 978.711 1 0.874 9 1、2相机 2 2 454.121 3 25.763 9 978.006 0 0.880 4 2、4相机 3 2 453.655 8 25.650 5 978.879 7 0.392 0 1、3相机 4 2 454.283 5 25.682 3 978.867 5 0.628 6 3、4相机

3 附加约束条件的光束法原理

3.1 模型建立

3.1.1 线元素的约束

 图 4 4个子影像与虚拟影像的投影关系 Fig. 4 Projection relationship between sub-image and virtual image

 图 5 4个子影像的摄影中心与虚拟影像摄影中心的关系 Fig. 5 Relationship between the projection centers of sub-images and the projection center of virtual image

 图 6 摄影中心竖直方向位移引起的像点误差 Fig. 6 Image point error caused by vertical shift of projection center

P为A点到摄影中心在地面 投影M的距离，四拼相机视场角约为96°×74°，则沿长边方向P的最大值为1.11H，沿宽边方向P的最大值为0.75H。当f=47 mm，H=700 m时，摄影中心竖直方向10 mm的误差在长边方向引起的像点误差约为0.52 um，在宽边方向引起的像点误差约为0.35 um，四角的像点误差最大值约为0.63 um，即最大像点误差不足0.1像素，且越靠近影像中心误差值越小。因此，子相机摄影中心到M的偏差对拼接影像的结果影响非常小，可以忽略不计[9]，可以认为4个摄影中心在O-XYZ中的Z坐标相等，即Dz1=Dz2=Dz3=Dz4=0。

3.1.2 角元素的约束

3.2公式推导

 图 7 子影像与虚拟影像夹角差异大引起的像元采样不平衡 Fig. 7 Unbalanced resample caused by the differences between sub-images and virtual image

4 试验结果与分析

4.1 单相机检校及线元素的确定

 Camera Da Db 1 0.054 684 -0.056 077 2 -0.055 214 -0.051 725 3 0.054 610 0.047 328 4 -0.054 080 0.060 475

4.2 计算平台检校参数

 Camera φ ω κ 1 -22 18 0 2 22 18 180 3 -22 -18 0 4 22 -18 180

 Camera φ ω κ 1 -22.003 572 17.820 681 0.122 107 2 22.081 682 17.836 309 179.827 715 3 -21.963 220 -17.720 887 0.107 504 4 21.940 784 -17.902 666 179.891 631

4.3 平台检校参数验证

 mx/m my/m mz /m 平面点数 高程点数 高程相对精度 定向点 0.035 0.052 0.066 24 24 1/10 606 检查点 0.059 0.065 0.106 70 70 1/6604
 图 8 地面控制点及检查点分布情况 Fig. 8 Distribution of ground control points and check points

5 结 论

 [1] MADANI M, DRSTEL C, HEIPKE C, et al. DMC Practical Experience and Accuracy Assessment[C]//Proceedings of IAPRS.Istanbul:IAPRS, 2004: 396-401. [2] KARSTEN J. Geometric Handling of Large Size Digital Airborne Frame Camera Images[J]. Optical 3D Measurement Techniques, 2007(8): 164-171. [3] YOUNG J L, ALPER Y, OLGA M S. In-flight Camera Platform Geometric Calibration of the Aerial Multi-Head Camera System[C]// Proceedings of the Aerospace and Electronics Conference.[S.l.]:IEEE, 2010: 136-139. [4] LI Jian, LIU Xianlin, WAN Youchuan, et al. Generation of SWDC-4 Aerial Digital Camera Virtual Image[J]. Geomatics and Information Science of Wuhan University, 2008, 33(5): 450-453. (李健,刘先林,万幼川,等. SWDC-4数码航空相机虚拟影像生成[J]. 武汉大学学报:信息科学版,2008,33(5): 450-453.) [5] LI Junjie, GUAN Yanling, YANG Mengmeng, et al. Development of Digital Airborne Camera[J]. Science of Surveying and Mapping, 2013, 38(1): 54-56. (李军杰,关艳玲,杨蒙蒙,等. 数字航测相机的研究进展[J]. 测绘科学,2013,38(1): 54-56.) [6] WOLFGANG Z, CHRISTOPH D, KARSTEN J. Geometric Calibration of the DMC: Method and Result[C]//Proceedings of IAPRS.Denver:IAPRS, 2002: 324-333. [7] LIANG T, CHRISTOPH D, KARSTEN J, et al. Geometric Accuracy Potential of the Digital Modular Camera[C]// Proceedings of ISPRS.Amsterdam:ISPRS, 2000. [8] ZHU Xiange, LI Yingcheng, LIU Xiaolong, et al. Analysis of Two Platform Calibration Methods of Multi-head Camera[J]. Remote Sensing Information, 2012, 27(4): 71-74. (朱祥娥,李英成,刘晓龙,等. 大幅面拼接航摄仪的两种平台检校方法分析[J]. 遥感信息,2012,27(4): 71-74) [9] HELMUT H , MICHAEL K , WOLFGANG Z . Calibration of the Digital Modular Camera[C]//Proceedings of FIG XXII International Congress. Washington :FIG,2002. [10] LI Jian, LIU Xianlin, LIU Fengde,et al. Mosaic Model of SWDC-4 Large Format Aerial Digital Camera and Accuracy Analysis of Stereo Mapping[J]. Science of Surveying and Mapping, 2008, 33(2): 104-106. (李健,刘先林,刘凤德,等. SWDC-4大面阵数码航空相机拼接模型与立体测图精度分析[J]. 测绘科学,2008,33(2): 104-106.) [11] CHEN Zhen, LI Jun, SU Guozhong. Technique of Digital Camera Image Joint[J]. Urban Geotechnical Investigation & Surveying,2006(5): 44-46. (陈镇,李军,苏国中. 数码相机影像拼接技术[J]. 城市勘测,2006(5): 44-46.) [12] LIU Fengying, WANG Dong. The Self-stablized and Dual-combined Camera Image Mosaic Technology[J]. Bulletin of Surveying and Mapping, 2012(1): 56-58. (刘凤英,王冬. 自稳定双拼相机影像拼接技术[J]. 测绘通报,2012(1): 56-58.) [13] Standardization Administration of the People’s Republic of China. GB/T 27920.1-2011. Specifications for Digital Aerial Photography-Part 1: Frame Digital Aerial Photography[S].Beijing:China Zhijian Publishing House,2011. (中国国家标准化管理委员会.GB/T 27920.1-2011.数字航空摄影规范第1部分:框幅式数字航空摄影[S] .北京:中国质检出版社,2011.) [14] WU Wenjing. Image Joining and Processing Technology Study of SWDC Aerial Digital Camera[D].Jiaozuo:Henan Polytechnic University, 2008. (吴文静. SWDC航空数码相机的影像拼接与处理技术研究[D]. 焦作:河南理工大学,2008.) [15] WANG Zhizhuo. Principle of Photogrammetry[M]. Wuhan:Wuhan University Press, 2007: 134-138. (王之卓. 摄影测量原理[M]. 武汉:武汉大学出版社,2007: 134-138.) [16] CHRISTOPH D, KARSTEN J, DIRK S. DMC-Photogrammetric Accuracy-Calibration Aspects and Generation of Synthetic DMC Images[J]. Optical 3-D Measurement Techniques VI, 2003(1): 74-82. [17] WU Dun. Geometric Aspects of Large Size Digital Frame Cameras and Their Use for Photogrammetric Data Acquisition[D]. Hannover: Leibniz University, 2007. [18] ZHANG Zuxun. Aspects on Aerial Digital Cameras[J]. Engineering of Surveying and Mapping, 2004, 13(4): 1-4. (张祖勋. 航空数码相机及其有关问题[J]. 测绘工程,2004,13(4): 1-4)) [19] WANG Hui, WU Yundong, ZHANG Yongsheng. Modeling and Analyzing of Geometric Joint Error for CCD Matrix Images of Digital Aerial Camera[J]. Journal of Institute p> of Surveying and Mapping, 2003, 20(4): 257-262. (王慧,吴云东,张永生. 面阵CCD数字航测相机影像几何拼接误差模型与分析[J]. 测绘学院学报,2003,20(4): 257-262.) [20] ZHENG Shunyi, HUANG Rongyong, GUO Baoyun, et al. Stereo-camera Calibration with Restrictive Constraints[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(6): 877-885. (郑顺义,黄荣永,郭宝云,等. 附加约束条件的立体相机标定方法[J]. 测绘学报,2012,41(6): 877-885.) [21] LIN Zongjian, CUI Hongxia, SUN Jie, et al. Research on the Digital Camera Distortion Calibration[J]. Geomatics and Information Science of Wuhan University, 2005, 30(2): 122-125. (林宗坚,崔红霞,孙杰,等. 数码相机的畸变差检测研究[J]. 武汉大学学报:信息科学版,2005,30(2): 122-125.) [22] ZHANG Jianxia, WANG Liuzhao, LIU Xianlin, et al. Camera Calibration for Digital Air Survey[J]. Bulletin of Surveying and Mapping, 2005(11):41-42. (张建霞,王留召,刘先林,等. 数字航空摄影测量的相机检校[J]. 测绘通报,2005(11):41-42.) [23] Standardization Administration of the People’s Republic of China.GB/T 23236-2009.Specifications for Aerotriangulation of Digital Aerophotogrammetry[S]. Beijing:China Zhijian Publishing House,2009. (中国国家标准化管理委员会.GB/T 23236-2009.数字航空摄影测量空中三角测量规范[S]. 北京:中国质检出版社,2009.)
http://dx.doi.org/10.13485/j.cnki.11-2089.2014.
0010

0

#### 文章信息

XU Bin，LI Yingcheng，LIU Xiaolong,et al.

The Application of Bundle Block Adjustment with Constraint Conditions in Platform Calibration of Four-Head Aerial Digital Camera

Acta Geodaeticaet Cartographica Sinica,2014,43(1)：66-73.
http://dx.doi.org/10.13485/j.cnki.11-2089.2014.0010