Camera Calibration with One-dimensional Objects Based on the Heteroscedastic Error-in-variables Model
-
摘要: 多摄像机系统广泛应用于文化创意产业,其高精度标定是迫切需要解决的一个关键问题. 新近出现的摄像机一维标定方法能够克服标定物自身遮挡,特别适合标定多摄像机系统. 然而,现有的摄像机一维标定研究主要集中在降低一维标定物的运动约束,而标定精度较低的问题未受到应有的关注. 本文提出一种基于变量含异质噪声 (Heteroscedastic error-in-variables,HEIV)模型的高精度摄像机一维标定方法. 首先,推导出摄像机一维标定的计算模型;其次,利用该计算模型详细分析了一维标定中的噪声,得出摄像机一维标定可以视为一个HEIV问题的结论;最后给出了基于HEIV模型的摄像机一维标定算法. 与现有的算法相比,该方法可以显著改善一维标定的精度,并且受初始值影响小,收敛速度快. 实验结果验证了该方法的正确性和可行性.Abstract: Accurate camera calibration is a pre-requirement for widespread applications of the multi-camera system in cultural and creative industry. The newly emerging one-dimensional calibration is very suitable for multi-camera systems since one-dimensional objects are out of self-occlusions. However, the progress in one-dimensional calibration mainly focuses on reducing restrictions on the movement of one-dimensional objects, and the calibration accuracy still needs to be improved. In this paper, an accurate algorithm for one-dimensional calibration based on the heteroscedastic error-in-variables (HEIV) model is proposed. Firstly, a computational model of one-dimensional calibration is derived. Secondly, noises in one-dimensional calibration are analyzed in detail using this computational model, and we draw a conclusion that one-dimensional calibration can be seen as an HEIV problem. Finally, the proposed algorithm is elaborated. This algorithm has the advantages of high accuracy, rapid convergence and less insensitivity to initial conditions over the exiting algorithms. Experiments with both synthetic and real image data validate the proposed algorithm.
-
[1] Tsai R. An efficient and accurate camera calibration technique for 3d machine vision. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. Miami, USA: IEEE, 1986. 364-374 [2] Zhang Z Y. Flexible camera calibration by viewing a plane from unknown orientations. In: Proceedings of IEEE Conference on Computer Vision. Kerkya, Greece: IEEE, 1999. 666-673 [3] Duan F Q, Wu F C, Hu Z Y. Pose determination and plane measurement using a trapezium. Pattern Recognition Letter, 2008, 29(3): 223-231 [4] Zhang Z Y. Camera calibration with one-dimensional objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(7): 892-899 [5] Pollefeys M, Gool L V, Oosterlinck A. The modulus constraint: a new constraint for self-calibration. In: Proceedings of the International Conference on Pattern Recognition. Vienna, Austria, 1996. 349-353 [6] Hammarstedt P, Sturm P, Heyden A. Degenerate cases and closed-form solutions for camera calibration with onedimensional objects. In: Proceedings of IEEE Conference on Computer Vision. Beijing, China: IEEE, 2005. 317-324 [7] Wu F C, Hu Z Y, Zhu H J. Camera calibration with moving one-dimensional objects. Pattern Recognition, 2005, 38(5): 755-765 [8] Wang L, Wu F C, Hu Z Y. Multi-camera calibration with one-dimensional object under general motions. In: Proceedings of IEEE Conference on Computer Vision. Rio de Janeiro, Brazil: IEEE, 2007. 1-7 [9] Wang Liang, Wu Fu-Chao. Multi-camera calibration based on the one-dimensional object. Acta Automatica Sinica, 2007, 33(3): 225-231(王亮, 吴福朝. 基于一维标定物的多摄像机标定, 自动化学报, 2007, 33(3): 225-231) [10] Zhao Z J, Liu Y C, Zhang Z Y. Camera calibration with three noncollinear points under special motions. IEEE Transactions on Image Processing, 2008, 17(12): 2393-2402 [11] Miyagawa I, Arai H, Koike H. Simple camera calibration from a single image using five points on two orthogonal 1-D objects. EEE Transactions on Image Processing, 2010, 19(6): 1528-1538 [12] Duan Fu-Qing, Lv Ke, Zhou Ming-Quan. Central catadioptric camera calibration based on collinear space points. Acta Automatica Sinica, 2011, 37(11): 1296-1305(段福庆, 吕科, 周明全. 基于空间共线点的单光心反射折射摄像机标定, 自动化学报, 2011, 37(11): 1296-1305) [13] Duan F Q, Wu F C, Zhou M Q, Deng X M, Tian Y. Calibrating effective focal length for central catadioptric cameras using one space line. Pattern Recognition Letters, 2012, 33(5): 646-653 [14] Franca J, Stemmer M R, Franca M B M, Alves E G. Revisiting Zhang's 1D calibration algorithm. Pattern Recognition, 2010, 43(3): 1180-1187 [15] Wang L, Duan F Q. Zhang's one-dimensional calibration revisited with the heteroscedastic error-in-variables model. In: Proceedings of IEEE Conference on Image Processing. Brussels, Belgum: IEEE, 2011. 857-860 [16] Shi K, Dong Q, Wu F C. Weighted similarity-invariant linear algorithm for camera calibration with rotating 1-D objects. IEEE Transactions on Image Processing, 2012, 21(8): 3806-3812 [17] Hartley R. In defence of the eight-point algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(6): 580-593 [18] Soderstroma T, Wang L P, Pintelonc R, Schoukens J. Can errors-in-variables systems be identified from closed-loop experiments? Automatica, 2013, 49(2): 681-684 [19] Cerone V, Piga D, Regruto D. Setmembership error-in-variables identification through convex relaxation techniques. IEEE Transactions on Automatic Control, 2012, 57(2): 517-522 [20] Matei B C, Meer P. Estimation of nonlinear errors-in-variables models for computer vision application. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(10): 1537-1552 [21] Kanatani K. Optimization techniques for geometric estimation: beyond minimization. Structural, Syntactic, and Statistical Pattern Recognition, Lecture Notes in Computer Science, 2012, 7626: 11-30
点击查看大图
计量
- 文章访问数: 1784
- HTML全文浏览量: 85
- PDF下载量: 940
- 被引次数: 0