Abstract
Camera calibration and 3D reconstruction are important issues in computer vision. Two applications of bracket algebra in these two issues are presented in this work. Firstly, a camera calibration method is proposed, which is from only distance ratios of object points. Thanks to the effective computations of brackets, this method does not need to set up any world coordinate system and thus can use the geometric information of irregular objects conveniently. Secondly, we represent the reconstruction solution of plane structure directly from four known control points and give some new and useful error analysis results. The solution based on brackets is concise and short, and the error analysis results can act as a theoretical guidance in practice. Simulations and experiments on real images validate our proposed camera calibration method, direct reconstruction solution and error analysis results.
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Yihong Wu received her Doctor of Science degree in Geometric Invariants and Applications from MMRC, Institute of Systems Science, Chinese Academy of Sciences, in 2001. From June 2001 to July 2003, she did her postdoctoral research in NLPR, Institute of Automation, Chinese Academy of Sciences. After then, she joined NLPR as an associate professor. Her research interests include polynomial elimination and applications, geometric invariant and applications, automated geometric theorem proving, camera calibration, camera pose determination, and 3D reconstruction etc.
Zhanyi Hu received the B.S. Degree in Automation from the North China University of Technology in 1985, the Ph.D. Degree (Docteur d’Etat) in Computer Science from the University of Liege, Belgium, in Jan. 1993. Since 1993, he has been with the Institute of Automation, Chinese Academy of Sciences. From May 1997 to May 1998, he also acted as a visiting scholar of Chinese University of Hong Kong on invitation. Dr. Hu now is a Research Professor of Computer Vision, a member of the Executive Expert Committee of the Chinese National High Technology R&D Program, a deputy editor-in-chief for Chinese Journal of CAD and CG, and an associate editor for Journal of Computer Science and Technology. His current research interests include Camera Calibration, 3D Reconstruction, Feature Extraction, and Vision Guided Robot Navigation etc.
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Wu, Y., Hu, Z. Camera Calibration and Direct Reconstruction from Plane with Brackets. J Math Imaging Vis 24, 279–293 (2006). https://doi.org/10.1007/s10851-005-3628-9
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DOI: https://doi.org/10.1007/s10851-005-3628-9