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The Role of the Deltoidal Surface in the Solution Variation of the P3P Problem

文献类型：期刊论文

作者Wang, Bo2; Zhang, Caixia1; Hu, Zhanyi2
刊名JOURNAL OF MATHEMATICAL IMAGING AND VISION
出版日期2022-01-06
页码10
关键词P3P problem Multi-solution phenomenon Danger cylinder
ISSN号0924-9907
DOI10.1007/s10851-021-01062-y
通讯作者Zhang, Caixia(zhangcx@ncut.edu.cn)
英文摘要Traditionally the danger cylinder is intimately related to the solution stability in P3P problem. In this work, we show that the danger cylinder is also closely related to the multiple-solution phenomenon. More specifically, we show that when the optical center lies on the danger cylinder, of the 3 possible P3P solutions, i.e., one double solution, and two other solutions, the optical center of the double solution still lies on the danger cylinder, but the optical centers of the other two solutions no longer lie on the danger cylinder. And when the optical center moves on the danger cylinder, accordingly the optical centers of the two other solutions of the corresponding P3P problem form a new surface, characterized by a polynomial equation of degree 12 in the optical center coordinates, called the deltoidal surface of danger cylinder (DSDC). This indicates the danger cylinder always has a companion deltoidal surface. For the significance of DSDC, we show that when the optical center passes through the DSDC, the number of solutions of P3P constraint system must change by 2, or DSDC acts as a delimitating surface of the P3P solution space. These new findings shed some new lights on the P3P multi-solution phenomenon, an important issue in P3P study.
WOS关键词POSE ; VIEW
资助项目National Natural Science Foundation of China[61873264] ; National Natural Science Foundation of China[61772444] ; National Natural Science Foundation of China[61503004]
WOS研究方向Computer Science ; Mathematics
语种英语
WOS记录号WOS:000739229200001
出版者SPRINGER
资助机构National Natural Science Foundation of China
源URL[http://ir.ia.ac.cn/handle/173211/47163]  
专题自动化研究所_模式识别国家重点实验室_机器人视觉团队
通讯作者Zhang, Caixia
作者单位1.North China Univ Technol, Coll Sci, Beijing, Peoples R China
2.Chinese Acad Sci, Inst Automat, Beijing, Peoples R China
推荐引用方式
GB/T 7714		 Wang, Bo,Zhang, Caixia,Hu, Zhanyi. The Role of the Deltoidal Surface in the Solution Variation of the P3P Problem[J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION,2022:10.
APA Wang, Bo,Zhang, Caixia,&Hu, Zhanyi.(2022).The Role of the Deltoidal Surface in the Solution Variation of the P3P Problem.JOURNAL OF MATHEMATICAL IMAGING AND VISION,10.
MLA Wang, Bo,et al."The Role of the Deltoidal Surface in the Solution Variation of the P3P Problem".JOURNAL OF MATHEMATICAL IMAGING AND VISION (2022):10.

入库方式： OAI收割

来源：自动化研究所

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