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

doi:10.1007/s10851-021-01062-y

	The Role of the Deltoidal Surface in the Solution Variation of the P3P Problem
	Wang, Bo1 ; Zhang, Caixia 2; Hu, Zhanyi1
发表期刊	JOURNAL OF MATHEMATICAL IMAGING AND VISION
ISSN	0924-9907
	2022-01-06
页码	10
通讯作者	Zhang, Caixia(zhangcx@ncut.edu.cn)
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.
关键词	P3P problem Multi-solution phenomenon Danger cylinder
DOI	10.1007/s10851-021-01062-y
关键词[WOS]	POSE ; VIEW
收录类别	SCI
语种	英语
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]
项目资助者	National Natural Science Foundation of China
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Artificial Intelligence ; Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000739229200001
出版者	SPRINGER
七大方向——子方向分类	三维视觉
引用统计
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/47164
专题	多模态人工智能系统全国重点实验室_机器人视觉
通讯作者	Zhang, Caixia
作者单位	1.Chinese Acad Sci, Inst Automat, Beijing, Peoples R China 2.North China Univ Technol, Coll Sci, Beijing, Peoples R China
第一作者单位	中国科学院自动化研究所
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.