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Geometric Interpretation of the Multi-solution Phenomenon in the P3P Problem

文献类型：期刊论文

作者Wang, Bo1; Hu, Hao2; Zhang, Caixia3
刊名JOURNAL OF MATHEMATICAL IMAGING AND VISION
出版日期2020-07-17
页码13
关键词P3P problem Multiple solutions Danger cylinder
ISSN号0924-9907
DOI10.1007/s10851-020-00982-5
通讯作者Zhang, Caixia(zhangcx@ncut.edu.cn)
英文摘要It is well known that the P3P problem could have 1, 2, 3 and at most 4 positive solutions under different configurations among its three control points and the position of the optical center. Since in any real applications, the knowledge on the exact number of possible solutions is a prerequisite for selecting the right one among all the possible solutions, and the study on the phenomenon of multiple solutions in the P3P problem has been an active topic since its very inception. In this work, we provide some new geometric interpretations on the multi-solution phenomenon in the P3P problem, and our main results include: (1) the necessary and sufficient condition for the P3P problem to have a pair of side-sharing solutions is the two optical centers of the solutions both lie on one of the three vertical planes to the base plane of control points; (2) the necessary and sufficient condition for the P3P problem to have a pair of point-sharing solutions is the two optical centers of the solutions both lie on one of the three so-called skewed danger cylinders;(3) if the P3P problem has other solutions in addition to a pair of side-sharing (point-sharing) solutions, these remaining solutions must be a point-sharing (side-sharing ) pair. In a sense, the side-sharing pair and the point-sharing pair are companion pairs; (4) there indeed exist such P3P problems that have four completely distinct solutions, i.e., the solutions sharing neither a side nor a point, closing a long guessing issue in the literature. In sum, our results provide some new insights into the nature of the multi-solution phenomenon in the P3P problem, and in addition to their academic value, they could also be used as some theoretical guidance for practitioners in real applications to avoid occurrence of multiple solutions by properly arranging the control points.
WOS关键词POSE ; VIEW
资助项目National Natural Science Foundation of China[61873264] ; National Natural Science Foundation of China[61333015] ; National Natural Science Foundation of China[61421004] ; National Natural Science Foundation of China[61403373] ; National Natural Science Foundation of China[61503004]
WOS研究方向Computer Science ; Mathematics
语种英语
WOS记录号WOS:000549662100001
出版者SPRINGER
资助机构National Natural Science Foundation of China
源URL[http://ir.ia.ac.cn/handle/173211/40171]  
专题精密感知与控制研究中心_人工智能与机器学习
通讯作者Zhang, Caixia
作者单位1.Chinese Acad Sci, Inst Automat, Beijing 100190, Peoples R China
2.Univ Southern Calif, Ming Hsieh Dept Elect Engn, Los Angels, CA USA
3.North China Univ Technol, Sci Coll, Beijing 100041, Peoples R China
推荐引用方式
GB/T 7714		 Wang, Bo,Hu, Hao,Zhang, Caixia. Geometric Interpretation of the Multi-solution Phenomenon in the P3P Problem[J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION,2020:13.
APA Wang, Bo,Hu, Hao,&Zhang, Caixia.(2020).Geometric Interpretation of the Multi-solution Phenomenon in the P3P Problem.JOURNAL OF MATHEMATICAL IMAGING AND VISION,13.
MLA Wang, Bo,et al."Geometric Interpretation of the Multi-solution Phenomenon in the P3P Problem".JOURNAL OF MATHEMATICAL IMAGING AND VISION (2020):13.

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来源：自动化研究所

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