大角度立体像对相对定向的混合共轭梯度算法
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摘要
无初值依赖的快速收敛是大角度相对定向解算的关键所在。为此,本文提出一种混合共轭梯度算法,具体过程是:①采用随机爬山算法对给定的相对定向元素初值进行随机扰动,产生保证优化方向的初值;②局部优化中以超线性收敛的共轭梯度法取代相对定向中的最速下降法,以提高其收敛速度;③全局收敛条件为计算误差小于规定的限差。对比试验表明,混合共轭梯度算法无初值依赖性,具有较高的解算精度和较少的迭代次数。
The fast convergence without initial value dependence is the key of large angle relative directional solution. Therefore, a hybrid conjugate gradient algorithm is proposed in this paper. The concrete process is: ① stochastic hill climbing(SHC) algorithm is used to make random disturbance to the given initial value of the relative directional element, and the new value to guarantee the optimization direction is generated; ② In local optimization, super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate; ③ The global convergence condition is that the calculation error is less than the prescribed limit error. The comparison experiment shows that the method proposed in this paper is independent of initial value, has higher accuracy and fewer iterations.
The fast convergence without initial value dependence is the key of large angle relative directional solution. Therefore, a hybrid conjugate gradient algorithm is proposed in this paper. The concrete process is: ① stochastic hill climbing(SHC) algorithm is used to make random disturbance to the given initial value of the relative directional element, and the new value to guarantee the optimization direction is generated; ② In local optimization, super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate; ③ The global convergence condition is that the calculation error is less than the prescribed limit error. The comparison experiment shows that the method proposed in this paper is independent of initial value, has higher accuracy and fewer iterations.
引文
[1] 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. ZHANG Jianqing, PAN Li, WANG Shugen. The principles of photogrammetry[M]. 2nd ed. Wuhan: Wuhan University Press, 2009.
[2] 王之卓. 摄影测量原理[M]. 武汉: 武汉大学出版社, 2007. WANG Zhizhuo. The principles of photogrammetry[M]. Wuhan: Wuhan University Press, 2007.
[3] 张永军, 胡丙华, 张剑清. 基于多种同名特征的相对定向方法研究[J]. 测绘学报, 2011, 40(2): 194-199. ZHANG Yongjun, HU Binghua, ZHANG Jianqing. Relative orientation based on multiple conjugate features[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(2): 194-199.
[4] 张祖勋, 张剑清. 数字摄影测量学[M]. 2版. 武汉: 武汉大学出版社, 2012. ZHANG Zuxun, ZHANG Jianqing. Digital photogrammetry[M]. 2nd ed. Wuhan: Wuhan University Press, 2012.
[5] 袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京:科学出版社, 1997. YUAN Yaxiang, SUN Wenyu. Optimal theories and methods[M]. Beijing: Science Press, 1997.
[6] 张光澄. 非线性最优化计算方法[M]. 高等教育出版社, 2005. ZHANG Guangcheng. Computational methods for nonlinear optimization[M]. Beijing: Higher Education Press, 2005.
[7] 李巍, 董明利, 孙鹏, 等. 大尺寸摄影测量局部参数优化相对定向方法[J]. 仪器仪表学报, 2014, 35(9): 2053-2060. LI Wei, DONG Mingli, SUN Peng, et al. Relative orientation method for large-scale photogrammetry with local parameter optimization[J]. Chinese Journal of Scientific Instrument, 2014, 35(9): 2053-2060.
[8] TRIGGS B, MCLAUCHLAN P F, HARTLEY R I, et al. Bundle adjustment-a modern synthesis[M]. Berlin: Springer, 2000, 1883: 298-372.
[9] STEWéNIUS H, ENGELS C, NISTéR D. Recent developments on direct relative orientation[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2006, 60(4): 284-294.
[10] 陈义, 陆珏, 郑波. 近景摄影测量中大角度问题的探讨[J]. 测绘学报, 2008, 37(4): 458-463, 468. DOI: 10.3321/j.issn:1001-1595.2008.04.010.CHEN Yi, LU Yu, ZHENG Bo. Research on close-range photogrammetry with big rotation angle[J]. Acta Geodaetica et Cartographica Sinica, 2008, 37(4): 458-463, 468. DOI: 10.3321/j.issn:1001-1595.2008.04.010.
[11] 陆珏, 陈义, 郑波. 多基线近景摄影测量连续像对相对定向[J]. 同济大学学报(自然科学版), 2010, 38(3): 442-447. LU Jue, CHEN Yi, ZHENG Bo. Research on dependent relative orientation in multi-baseline close-range photogrammetry[J]. Journal of Tongji University (Natural Science), 2010, 38(3): 442-447.
[12] NIST D. An efficient solution to the five-point relative pose problem[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 26(6): 756-770.
[13] 于起峰, 尚洋. 摄像测量学原理与应用研究[M]. 北京: 科学出版社, 2009. YU Qifeng, SHANG Yang. Videometrics: principles and researches[M]. Beijing: Science Press, 2009.
[14] KUKELOVA Z, BUJNAK M, PAJDLA T. Polynomial eigenvalue solutions to minimal problems in computer vision[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(7): 1381-1393.
[15] WANG Wenbin, LIU Guihua, LIU Xianyong, et al. Two removal tactics of pseudo solutions for essential matrix five-point algorithm[J]. Opto-Electronic Engineering, 2010, 37(8): 46-52.
[16] 张征宇, 朱龙, 黄叙辉, 等. 基于前方交会的5点相对定向[J]. 光学学报, 2015, 35(1): 231-238. ZHANG Zhengyu, ZHU Long, HUANG Xuhui, et al. Five-point relative orientation based on forward intersection[J]. Acta Optica Sinica, 2015, 35(1): 231-238.
[17] 袁修孝, 陈时雨, 钟灿. 基于基础矩阵的倾斜航摄影像相对定向方法[J]. 武汉大学学报(信息科学版), 2016, 41(8): 995-1000. YUAN Xiuxiao, CHEN Shiyu, ZHONG Can. Oblique aerial image relative orientation based on fundamental matrix[J]. Geomatics and Information Science of Wuhan University, 2016, 41(8): 995-1000.
[18] ZHANG Yongjun, HUANG Xu, HU Xiangyun, et al. Direct relative orientation with four independent constraints[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2011, 66(6): 809-817.
[19] WANG J, LIN Z, REN C. Relative orientation in low altitude photogrammetry survey[J]. ISPRS International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2012(1): 463-467.
[20] 杨阿华, 李学军, 刘涛, 等. 基于直接解算与迭代优化的相对定向方法[J]. 计算机应用, 2014, 34(6): 1706-1710. YANG Ahua, LI Xuejun, LIU Tao, et al. Relative orientation approach based on direct resolving and iterative refinement[J]. Journal of Computer Applications, 2014, 34(6): 1706-1710.
[21] 周拥军, 邓才华. 利用HGA和单位四元数的相对定向解法[J]. 武汉大学学报(信息科学版), 2011, 36(6): 670-673. ZHOU Yongjun, DENG Caihua. A new method for relative orientation with hybrid genetic algorithm and unit quaternion[J]. Geomatics and Information Science of Wuhan University, 2011, 36(6): 670-673.
[22] HUANG Xuri, KELKAR M. Performance comparison of heuristic combinatorial alorithms for seismic inversion[C]//Proceedings of 1995 SEG Annual Meeting. Houston, Texas: Society of Exploration Geophysicists, 1995: 1025-1027.
[23] 席少霖. 非线性最优化方法[M]. 北京: 高等教育出版社, 1992. XI Shaolin. The method of nonlinear optimization[M]. Beijing: Higher Education Press, 1992.
[24] POLYAK B T. The conjugate gradient method in extremal problems[J]. USSR Computational Mathematics and Mathematical Physics, 1969, 9(4): 94-112.
[25] 涂进. 基于模拟退火算法的聚类分析在数据挖掘中的应用[D]. 重庆: 重庆大学, 2003. TU Jin. Study on clustering analysis in data mining based on simulated annealing algorithm[D]. Chongqing: Chongqing University, 2003.
[2] 王之卓. 摄影测量原理[M]. 武汉: 武汉大学出版社, 2007. WANG Zhizhuo. The principles of photogrammetry[M]. Wuhan: Wuhan University Press, 2007.
[3] 张永军, 胡丙华, 张剑清. 基于多种同名特征的相对定向方法研究[J]. 测绘学报, 2011, 40(2): 194-199. ZHANG Yongjun, HU Binghua, ZHANG Jianqing. Relative orientation based on multiple conjugate features[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(2): 194-199.
[4] 张祖勋, 张剑清. 数字摄影测量学[M]. 2版. 武汉: 武汉大学出版社, 2012. ZHANG Zuxun, ZHANG Jianqing. Digital photogrammetry[M]. 2nd ed. Wuhan: Wuhan University Press, 2012.
[5] 袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京:科学出版社, 1997. YUAN Yaxiang, SUN Wenyu. Optimal theories and methods[M]. Beijing: Science Press, 1997.
[6] 张光澄. 非线性最优化计算方法[M]. 高等教育出版社, 2005. ZHANG Guangcheng. Computational methods for nonlinear optimization[M]. Beijing: Higher Education Press, 2005.
[7] 李巍, 董明利, 孙鹏, 等. 大尺寸摄影测量局部参数优化相对定向方法[J]. 仪器仪表学报, 2014, 35(9): 2053-2060. LI Wei, DONG Mingli, SUN Peng, et al. Relative orientation method for large-scale photogrammetry with local parameter optimization[J]. Chinese Journal of Scientific Instrument, 2014, 35(9): 2053-2060.
[8] TRIGGS B, MCLAUCHLAN P F, HARTLEY R I, et al. Bundle adjustment-a modern synthesis[M]. Berlin: Springer, 2000, 1883: 298-372.
[9] STEWéNIUS H, ENGELS C, NISTéR D. Recent developments on direct relative orientation[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2006, 60(4): 284-294.
[10] 陈义, 陆珏, 郑波. 近景摄影测量中大角度问题的探讨[J]. 测绘学报, 2008, 37(4): 458-463, 468. DOI: 10.3321/j.issn:1001-1595.2008.04.010.CHEN Yi, LU Yu, ZHENG Bo. Research on close-range photogrammetry with big rotation angle[J]. Acta Geodaetica et Cartographica Sinica, 2008, 37(4): 458-463, 468. DOI: 10.3321/j.issn:1001-1595.2008.04.010.
[11] 陆珏, 陈义, 郑波. 多基线近景摄影测量连续像对相对定向[J]. 同济大学学报(自然科学版), 2010, 38(3): 442-447. LU Jue, CHEN Yi, ZHENG Bo. Research on dependent relative orientation in multi-baseline close-range photogrammetry[J]. Journal of Tongji University (Natural Science), 2010, 38(3): 442-447.
[12] NIST D. An efficient solution to the five-point relative pose problem[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 26(6): 756-770.
[13] 于起峰, 尚洋. 摄像测量学原理与应用研究[M]. 北京: 科学出版社, 2009. YU Qifeng, SHANG Yang. Videometrics: principles and researches[M]. Beijing: Science Press, 2009.
[14] KUKELOVA Z, BUJNAK M, PAJDLA T. Polynomial eigenvalue solutions to minimal problems in computer vision[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(7): 1381-1393.
[15] WANG Wenbin, LIU Guihua, LIU Xianyong, et al. Two removal tactics of pseudo solutions for essential matrix five-point algorithm[J]. Opto-Electronic Engineering, 2010, 37(8): 46-52.
[16] 张征宇, 朱龙, 黄叙辉, 等. 基于前方交会的5点相对定向[J]. 光学学报, 2015, 35(1): 231-238. ZHANG Zhengyu, ZHU Long, HUANG Xuhui, et al. Five-point relative orientation based on forward intersection[J]. Acta Optica Sinica, 2015, 35(1): 231-238.
[17] 袁修孝, 陈时雨, 钟灿. 基于基础矩阵的倾斜航摄影像相对定向方法[J]. 武汉大学学报(信息科学版), 2016, 41(8): 995-1000. YUAN Xiuxiao, CHEN Shiyu, ZHONG Can. Oblique aerial image relative orientation based on fundamental matrix[J]. Geomatics and Information Science of Wuhan University, 2016, 41(8): 995-1000.
[18] ZHANG Yongjun, HUANG Xu, HU Xiangyun, et al. Direct relative orientation with four independent constraints[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 2011, 66(6): 809-817.
[19] WANG J, LIN Z, REN C. Relative orientation in low altitude photogrammetry survey[J]. ISPRS International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2012(1): 463-467.
[20] 杨阿华, 李学军, 刘涛, 等. 基于直接解算与迭代优化的相对定向方法[J]. 计算机应用, 2014, 34(6): 1706-1710. YANG Ahua, LI Xuejun, LIU Tao, et al. Relative orientation approach based on direct resolving and iterative refinement[J]. Journal of Computer Applications, 2014, 34(6): 1706-1710.
[21] 周拥军, 邓才华. 利用HGA和单位四元数的相对定向解法[J]. 武汉大学学报(信息科学版), 2011, 36(6): 670-673. ZHOU Yongjun, DENG Caihua. A new method for relative orientation with hybrid genetic algorithm and unit quaternion[J]. Geomatics and Information Science of Wuhan University, 2011, 36(6): 670-673.
[22] HUANG Xuri, KELKAR M. Performance comparison of heuristic combinatorial alorithms for seismic inversion[C]//Proceedings of 1995 SEG Annual Meeting. Houston, Texas: Society of Exploration Geophysicists, 1995: 1025-1027.
[23] 席少霖. 非线性最优化方法[M]. 北京: 高等教育出版社, 1992. XI Shaolin. The method of nonlinear optimization[M]. Beijing: Higher Education Press, 1992.
[24] POLYAK B T. The conjugate gradient method in extremal problems[J]. USSR Computational Mathematics and Mathematical Physics, 1969, 9(4): 94-112.
[25] 涂进. 基于模拟退火算法的聚类分析在数据挖掘中的应用[D]. 重庆: 重庆大学, 2003. TU Jin. Study on clustering analysis in data mining based on simulated annealing algorithm[D]. Chongqing: Chongqing University, 2003.