一种求解单像空间后方交会的监督学习方法
|
摘要
单像空间后方交会可描述为非线性最小二乘问题,不可导、法方程系数矩阵病态以及陷入局部极值是造成其数值过程不收敛的主要原因。不同地区的控制点空间分布不具相似性,若把同一地区同一组控制点之下数张已知外方位元素的像片看作一个样本集,则在给定每个外方位元素初值的前提下,可通过监督学习方法求取外方位元素的整体下降方向;而对于单像空间后方交会中因前述原因不收敛的情况,则可采用整体下降方向近似解算。以此为出发点,提出一种单像空间后方交会求解的监督学习方法,主要过程是:①训练阶段,利用监督学习过程,对同一测区内不同姿态像片所组成的样本集进行整体外方位元素的求解,得到该测区外方位元素的整体下降方向集合;②测试阶段,对该测区的任意像片,给定外方位元素的初值,直接采用训练阶段得到的整体下降方向集合进行外方位元素的迭代求解。对比试验表明,该方法在数值过程收敛性与初值依赖性上均表现出较强的优势,并能克服欧拉角法因法方程系数矩阵病态而无法收敛的情况。
The space resection of single image can be described as a problem of non-linear least squares,and the non-derivative, ill-conditioned coefficient matrix of normal equation and local extremum are main reasons for non-convergence in its numerical procedure. The spatial distribution of control points in different regions is not similar. If we put down the multiple images and have known their exterior orientation elements regarding the same control points under the same region, as a sample set, the overall descent direction can be obtained by supervised learning under the circumstance that every initial values of exterior orientation elements have been given. What's more, in the case of non-convergence in original space resection of single image because of the reasons mentioned before, it can be approximately solved by using the overall descent direction. From this angle, a supervised learning method for solving space resection of single image is proposed. The process mainly includes: ①Training stage, in which supervised learning process is utilized and the descend direction set of exterior orientation elements is obtained by solving the overall exterior orientation elements of images set with different attitude in the same survey area. ②Testing stage, in which for any image in study area, the exterior orientation elements can be calculated iteratively if the initial value and the descend direction set were given from the process of supervised training. Experimental results show that the method in this paper is more efficient in numerical procedure convergence and dependence of the initial value than the current there realized. Besides, it can overcome the non-convergence of Euler angles caused by the ill-conditioned coefficient matrix of normal equation, which is essentially the gradient matrix.
The space resection of single image can be described as a problem of non-linear least squares,and the non-derivative, ill-conditioned coefficient matrix of normal equation and local extremum are main reasons for non-convergence in its numerical procedure. The spatial distribution of control points in different regions is not similar. If we put down the multiple images and have known their exterior orientation elements regarding the same control points under the same region, as a sample set, the overall descent direction can be obtained by supervised learning under the circumstance that every initial values of exterior orientation elements have been given. What's more, in the case of non-convergence in original space resection of single image because of the reasons mentioned before, it can be approximately solved by using the overall descent direction. From this angle, a supervised learning method for solving space resection of single image is proposed. The process mainly includes: ①Training stage, in which supervised learning process is utilized and the descend direction set of exterior orientation elements is obtained by solving the overall exterior orientation elements of images set with different attitude in the same survey area. ②Testing stage, in which for any image in study area, the exterior orientation elements can be calculated iteratively if the initial value and the descend direction set were given from the process of supervised training. Experimental results show that the method in this paper is more efficient in numerical procedure convergence and dependence of the initial value than the current there realized. Besides, it can overcome the non-convergence of Euler angles caused by the ill-conditioned coefficient matrix of normal equation, which is essentially the gradient matrix.
引文
[1]Zhang Zuxun,Zhang Jianqing.Digital Photogrammetry[M].Wuhan:Wuhan University Press,1996(张祖勋,张剑清.数字摄影测量学[M].武汉:武汉大学出版社,1996)
[2]Wang Zhizhuo.The Principles of Photogrammetry[M].Wuhan:Wuhan University Press,2007(王之卓.摄影测量原理[M].武汉:武汉大学出版社,2007)
[3]Yuan Xiuxiao.Some Investigations of Image Orientation in Aerial Photogrammetry[J].Advances in Earth Science,2007,22(8):828-834(袁修孝.航空摄影测量影像定向的若干探讨[J].地球科学进展,2007,22(8):828-834)
[4]Tang Limin.Research on the Ill-posed and Solving Methods of Nonlinear Least Squares Problem[D].Changsha:Central South University,2011(唐利民.非线性最小二乘的不适定性及算法研究[D].长沙:中南大学,2011)
[5]Haralick B M,Lee C N,Ottenberg K,et al.Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem[J].International Journal of Computer Vision,1994,13(3):331-356
[6]Feng Wenhao.Close Range Photogrammetry[M].Wuhan:Wuhan University Press,2002(冯文灏.近景摄影测量[M].武汉:武汉大学出版社,2002)
[7]Fu Zhongliang,Zhou Fan,Yu Zhiqiang.A Space Resection Synthesized the Multiple Features[J].Acta Geodaetica et Cartographica Sinica,2014,43(8):827-834(付仲良,周凡,俞志强.综合多种特征的后方交会法[J].测绘学报,2014,43(8):827-834)
[8]Li Fei,Hao Weifeng,Wang Wenrui,et al.The Perturbation Analysis of Nonlinear Ill-conditioned Solution[J].Acta Geodaetica et Cartographica Sinica,2011,40(1):5-9(李斐,郝卫峰,王文睿,等.非线性病态问题解算的扰动分析[J].测绘学报,2011,40(1):5-9)
[9]Guo Zhonglei,Zhai Jingsheng,Deng Kailiang.Space Resection of Big Attitude Image Based on Levenberg-Marquardt Method[J].Geomatics and Information Science of Wuhan University,2016,41(4):565-568(郭忠磊,翟京生,邓凯亮.基于LM方法的大姿态角影像空间后方交会[J].武汉大学学报·信息科学版,2016,41(4):565-568)
[10]He Jing,Li Yongshu.A Mosaic Method in Unmanned Aerial Vehicle Images Based on Feature Points and Optimal Path[J].Remote Sensing Technology and Application,2012,27(2):173-219(何敬,李永树.基于特征点和最优路径的无人机影像拼接方法[J].遥感技术与应用,2012,27(2):173-219)
[11]Ji Q,Costa M S,Haralick R M,et al.A Robust Linear Least-Squares Estimation of Camera Exterior Orientation Using Multiple Geometric Features[J].ISPRS Journal of Photogrammetry and Remote Sensing,2000,55(2):75-93
[12]Guan Yunlan,Cheng Xiaojun,Zhou Shijian,et al.A Solution to Space Resection Based on Unit Quaternion[J].Acta Geodaetica et Cartographica Sinica,2008,37(1):30-35(官云兰,程效军,周世健,等.基于单位四元数的空间后方交会解算[J].测绘学报,2008,37(1):30-35)
[13]Lepetit V,Moreno-Noguer F,Fua P.EPn P:An Accurate O(n)Solution to the Pn P Problem[J].International Journal of Computer Vision,2009,81(2):155-166
[14]Penatesanchez A,Andradecetto J,Morenonoguer F.Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(10):2 387-2 400
[15]Gong Hui,Jiang Ting,Jiang Gangwu,et al.AGlobally Convergent Algorithm of Space Resection Based on Quaternion[J].Acta Geodaetica et Cartographica Sinica,2011,40(5):639-645(龚辉,姜挺,江刚武,等.一种基于四元数的空间后方交会全局收敛算法[J].测绘学报,2011,40(5):639-645)
[16]Jiang Gangwu,Jiang Ting,Wang Yong,et al.Space Resection Indepentent of Initial Value Based on Unit Quaternions[J].Acta Geodaetica et Cartographica Sinica,2007,36(2):169-175(江刚武,姜挺,王勇,等.基于单位四元数的无初值依赖空间后方交会[J].测绘学报,2007,36(2):169-175)
[17]Zhang Yongjun,Wu Lei,Lin Liwen,et al.Condition Numbers for Evaluation of Ill-posed Problems in Photogrammetry[J].Geomatics and Information Science of Wuhan University,2010,35(3):308-312(张永军,吴磊,林立文,等.摄影测量中病态问题的条件数指标分析[J].武汉大学学报·信息科学版,2010,35(3):308-312)
[18]Wang Hailiang,Xiang Maosheng,Li Yang,et al.The Analysis of Two Single Image Space Resection Models[J].Optical Technique,2010,36(1):14-19(王海亮,向茂生,李杨,等.两种单像空间后方交会模型分析[J].光学技术,2010,36(1):14-19)
[19]Wang Zhenjie.Regularization of Ill-posed Problems in Surverying[M].Beijing:Science Press,2006(王振杰.测量中不适定问题的正则化解法[M].北京:科学出版社,2006)
[20]Ge Xuming,Wu Jicang.Generalized Regularization to Ill-posed Total Least Squares Problem[J].Acta Geodaetica et Cartographica Sinica,2012,41(3):372-377(葛旭明,伍吉仓.病态总体最小二乘问题的广义正则化[J].测绘学报,2012,41(3):372-377)
[21]Ou Jikun.Uniform Expression of Solutions of Illposed Problems in Surveying Adjustment and the Fitting Method by Selection of the Parameter Weights[J].Acta Geodaetica et Cartographica Sinica,2004,33(4):283-288(欧吉坤.测量平差中不适定问题的统一表达和选权拟合法[J].测绘学报,2004,33(4):283-288)
[22]Jiang Tao,Li Jiancheng,Wang Zhengtao,et al.Solution of Ill-posed Problem in Downward Continuation of Airborne Gravity[J].Acta Geodaetica et Cartographica Sinica,2011,40(6):684-689(蒋涛,李建成,王正涛,等.航空重力向下延拓病态问题求解[J].测绘学报,2011,40(6):684-689)
[23]Yan Li,Nie Qian,Zhao Zhan.Space Resection of Line Scanner CCD Image Based on the Description of Quaternions[J].Geomatics and Information Science of Wuhan University,2010,35(2):201-204(闫利,聂前,赵展.利用单位四元数描述线阵CCD影像的空间后方交会[J].武汉大学学报·信息科学版,2010,35(2):201-204)
[24]The Subject Group of Surveying Adjustment of Institute of Surveying and Mapping of Wuhan University.Error Theory and Fundation of Surveying Adjustment[M].2nd ed.Wuhan:Wuhan University Press,2009(武汉大学测绘学院测量平差学科组.误差理论与测量平差基础[M].2版.武汉:武汉大学出版社,2009)
[25]Xi Shaolin.The Method of Nonlinear Optimization[M].Beijing:Higher Education Press,1992(席少霖.非线性最优化方法[M].北京:高等教育出版社,1992)
[26]Zhang Jianqing,Pan Li,Wang Shugen.The Principles of Photogrammetry[M].2nd ed.Wuhan:Wuhan University Press,2009(张剑清,潘励,王树根.摄影测量学原理[M].2版.武汉:武汉大学出版社,2009)
[2]Wang Zhizhuo.The Principles of Photogrammetry[M].Wuhan:Wuhan University Press,2007(王之卓.摄影测量原理[M].武汉:武汉大学出版社,2007)
[3]Yuan Xiuxiao.Some Investigations of Image Orientation in Aerial Photogrammetry[J].Advances in Earth Science,2007,22(8):828-834(袁修孝.航空摄影测量影像定向的若干探讨[J].地球科学进展,2007,22(8):828-834)
[4]Tang Limin.Research on the Ill-posed and Solving Methods of Nonlinear Least Squares Problem[D].Changsha:Central South University,2011(唐利民.非线性最小二乘的不适定性及算法研究[D].长沙:中南大学,2011)
[5]Haralick B M,Lee C N,Ottenberg K,et al.Review and Analysis of Solutions of the Three Point Perspective Pose Estimation Problem[J].International Journal of Computer Vision,1994,13(3):331-356
[6]Feng Wenhao.Close Range Photogrammetry[M].Wuhan:Wuhan University Press,2002(冯文灏.近景摄影测量[M].武汉:武汉大学出版社,2002)
[7]Fu Zhongliang,Zhou Fan,Yu Zhiqiang.A Space Resection Synthesized the Multiple Features[J].Acta Geodaetica et Cartographica Sinica,2014,43(8):827-834(付仲良,周凡,俞志强.综合多种特征的后方交会法[J].测绘学报,2014,43(8):827-834)
[8]Li Fei,Hao Weifeng,Wang Wenrui,et al.The Perturbation Analysis of Nonlinear Ill-conditioned Solution[J].Acta Geodaetica et Cartographica Sinica,2011,40(1):5-9(李斐,郝卫峰,王文睿,等.非线性病态问题解算的扰动分析[J].测绘学报,2011,40(1):5-9)
[9]Guo Zhonglei,Zhai Jingsheng,Deng Kailiang.Space Resection of Big Attitude Image Based on Levenberg-Marquardt Method[J].Geomatics and Information Science of Wuhan University,2016,41(4):565-568(郭忠磊,翟京生,邓凯亮.基于LM方法的大姿态角影像空间后方交会[J].武汉大学学报·信息科学版,2016,41(4):565-568)
[10]He Jing,Li Yongshu.A Mosaic Method in Unmanned Aerial Vehicle Images Based on Feature Points and Optimal Path[J].Remote Sensing Technology and Application,2012,27(2):173-219(何敬,李永树.基于特征点和最优路径的无人机影像拼接方法[J].遥感技术与应用,2012,27(2):173-219)
[11]Ji Q,Costa M S,Haralick R M,et al.A Robust Linear Least-Squares Estimation of Camera Exterior Orientation Using Multiple Geometric Features[J].ISPRS Journal of Photogrammetry and Remote Sensing,2000,55(2):75-93
[12]Guan Yunlan,Cheng Xiaojun,Zhou Shijian,et al.A Solution to Space Resection Based on Unit Quaternion[J].Acta Geodaetica et Cartographica Sinica,2008,37(1):30-35(官云兰,程效军,周世健,等.基于单位四元数的空间后方交会解算[J].测绘学报,2008,37(1):30-35)
[13]Lepetit V,Moreno-Noguer F,Fua P.EPn P:An Accurate O(n)Solution to the Pn P Problem[J].International Journal of Computer Vision,2009,81(2):155-166
[14]Penatesanchez A,Andradecetto J,Morenonoguer F.Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(10):2 387-2 400
[15]Gong Hui,Jiang Ting,Jiang Gangwu,et al.AGlobally Convergent Algorithm of Space Resection Based on Quaternion[J].Acta Geodaetica et Cartographica Sinica,2011,40(5):639-645(龚辉,姜挺,江刚武,等.一种基于四元数的空间后方交会全局收敛算法[J].测绘学报,2011,40(5):639-645)
[16]Jiang Gangwu,Jiang Ting,Wang Yong,et al.Space Resection Indepentent of Initial Value Based on Unit Quaternions[J].Acta Geodaetica et Cartographica Sinica,2007,36(2):169-175(江刚武,姜挺,王勇,等.基于单位四元数的无初值依赖空间后方交会[J].测绘学报,2007,36(2):169-175)
[17]Zhang Yongjun,Wu Lei,Lin Liwen,et al.Condition Numbers for Evaluation of Ill-posed Problems in Photogrammetry[J].Geomatics and Information Science of Wuhan University,2010,35(3):308-312(张永军,吴磊,林立文,等.摄影测量中病态问题的条件数指标分析[J].武汉大学学报·信息科学版,2010,35(3):308-312)
[18]Wang Hailiang,Xiang Maosheng,Li Yang,et al.The Analysis of Two Single Image Space Resection Models[J].Optical Technique,2010,36(1):14-19(王海亮,向茂生,李杨,等.两种单像空间后方交会模型分析[J].光学技术,2010,36(1):14-19)
[19]Wang Zhenjie.Regularization of Ill-posed Problems in Surverying[M].Beijing:Science Press,2006(王振杰.测量中不适定问题的正则化解法[M].北京:科学出版社,2006)
[20]Ge Xuming,Wu Jicang.Generalized Regularization to Ill-posed Total Least Squares Problem[J].Acta Geodaetica et Cartographica Sinica,2012,41(3):372-377(葛旭明,伍吉仓.病态总体最小二乘问题的广义正则化[J].测绘学报,2012,41(3):372-377)
[21]Ou Jikun.Uniform Expression of Solutions of Illposed Problems in Surveying Adjustment and the Fitting Method by Selection of the Parameter Weights[J].Acta Geodaetica et Cartographica Sinica,2004,33(4):283-288(欧吉坤.测量平差中不适定问题的统一表达和选权拟合法[J].测绘学报,2004,33(4):283-288)
[22]Jiang Tao,Li Jiancheng,Wang Zhengtao,et al.Solution of Ill-posed Problem in Downward Continuation of Airborne Gravity[J].Acta Geodaetica et Cartographica Sinica,2011,40(6):684-689(蒋涛,李建成,王正涛,等.航空重力向下延拓病态问题求解[J].测绘学报,2011,40(6):684-689)
[23]Yan Li,Nie Qian,Zhao Zhan.Space Resection of Line Scanner CCD Image Based on the Description of Quaternions[J].Geomatics and Information Science of Wuhan University,2010,35(2):201-204(闫利,聂前,赵展.利用单位四元数描述线阵CCD影像的空间后方交会[J].武汉大学学报·信息科学版,2010,35(2):201-204)
[24]The Subject Group of Surveying Adjustment of Institute of Surveying and Mapping of Wuhan University.Error Theory and Fundation of Surveying Adjustment[M].2nd ed.Wuhan:Wuhan University Press,2009(武汉大学测绘学院测量平差学科组.误差理论与测量平差基础[M].2版.武汉:武汉大学出版社,2009)
[25]Xi Shaolin.The Method of Nonlinear Optimization[M].Beijing:Higher Education Press,1992(席少霖.非线性最优化方法[M].北京:高等教育出版社,1992)
[26]Zhang Jianqing,Pan Li,Wang Shugen.The Principles of Photogrammetry[M].2nd ed.Wuhan:Wuhan University Press,2009(张剑清,潘励,王树根.摄影测量学原理[M].2版.武汉:武汉大学出版社,2009)