Kruppa方程与摄像机自标定.pdf

　 第 27 卷　第 5 期 2001 年 9 月 自　动　化　学　报 ACTA AUTOMAT ICA SINICA Vol. 27, No. 5 Sept. , 2001 Kruppa方程与摄像机自标定1) 雷　成 1 　　吴福朝 1, 2 　　胡占义 1 1(中国科学院自动化所模式识别国家重点实验室　北京　100080) 2(安徽大学人工智能研究所　合肥　230039) ( E -mail : l eic@n lpr. ia. ac. cn) 摘　要　首先研究探讨了基于绝对二次曲线 ( the absolute conic)进行摄像机自标定鲁棒性差的 内在原因. 研究发现,该类方法鲁棒性不足的原因主要有三个方面: 1)在目标函数的全局最小点 处存在大范围的平坦区域, 使得任何数值优化算法难以达到全局最小点; 2)当存在噪声时, 上 述平坦区域内会出现大量局部极小值, 这样数值优化算法就非常容易收敛到靠近初值的局部极 小值, 使得算法对初始值的选取十分敏感; 3)当有噪声时, 目标函数的全局最小值极易偏离正 确值. 这样,即使数值算法找到了全局最小值,该最小值也不再对应正确的摄像机内参数值. 鉴 于上述情况, 探讨了如何通过平面场景来确定内参数矩阵的初始值, 而后进一步利用 Kruppa 方 程的约束来精化内参数矩阵的二步式方法. 关键词　绝对二次曲线, Kruppa方程, 摄像机自标定. 1) 国家自然科学基金(、国家“973”计划( G1998030502-3)、中国科学院机器人学开放 实验室( RL 200010)资助. 收稿日期　1999-12-23　　收修改稿日期　2000-08-28 KRUPPA EQUATIONS AND CAMERA SELF -CALIBRATION LEI Cheng1　WU Fu-Chao1, 2　HU Zhan-Yi1 1(N ational L abor atory of P attern Recogni tion, Insti tute of Automation Chinese Academy of Sciences, Beij ing　100080) 2( Insti tute of Ar tif icial I ntel lig ence, Anhui University , H ef ei　230039) ( E -mail : l eic@n lpr. ia. ac. cn) Abstr act　 It is well recognized that the IAC ( Image of the Absolut e Conic) based camera calibrat ion techniques are not quit e robust , however, there are few reports on it s underlying reasons in the lit erature. In this paper, we find that t he following three sources largely contribut e to the non-robustness of the IAC based techniques: 1) The global minimum of the cos t funct ion lies on a large flat area, which makes any numeri- cal opt imization methods difficult to reach it. 2) With noise, many local minimums could appear in the above flat area, which makes any numerical opt imization methods quite sensit ive to the choice of the init ial point s ince the used method could converge easily to the local minimum close to the init ial point . 3) With noise, t he point corre- sponding to the global minimum of the cost funct ion could deviat e s ignificant ly from the one sought for, t hus it is difficult to get the