New insights on multi-solution distribution of the P3P problem
文献类型：期刊论文
| 作者 | Wang, Bo1 ; Hu, Hao2; Zhang, Caixia3
|
| 刊名 | IMAGE AND VISION COMPUTING
 |
| 出版日期 | 2020-11-01 |
| 卷号 | 103页码:9 |
| 关键词 | P3P problem Multi-solution phenomenon Root-solution relation Toroid |
| ISSN号 | 0262-8856 |
| DOI | 10.1016/j.imavis.2020.104009 |
| 通讯作者 | Zhang, Caixia(zhangcx@ncut.edu.cn) |
| 英文摘要 | Traditionally, the P3P problemis solved by firstly transforming its 3 quadratic equations into a quartic one, then by locating the roots of the resulting quartic equation and verifying whether a root does really correspond to a true solution of the P3P problem itself. It is well known that a root of the quartic equation could correspond to 2, or 1, or even null solution at all to the P3P problem, and up to now, no explicit relationship between the P3P solution and the root of its quartic equation is available in the literature. In thiswork, we showthat when the optical center is outside of all the 6 toroids defined by the control point triangle, each positive root of the Grunert's quartic equationmust correspond to a true solution of the P3P problem, and the corresponding P3P problemcannot have a unique solution, it must have either 2 positive solutions or 4 positive solutions. In addition, we show that when the optical center passes through any one of the 3 toroids among these 6 toroids (except possibly for two concentric circles), the number of the solutions of the corresponding P3P problem always changes by 1, either increased by 1 or decreased by 1. Furthermore we showthat such changed solutions always locate in a small neighborhood of control points, hence the 3 toroids are critical surfaces of the P3P problem and the 3 control points are 3 singular points of solutions. A notable example is that when the optical center passes through the outer surface of the union of the 6 toroids from the outside to inside, the number of the solutions must always decrease by 1. Our results are the first in the literature to give an explicit and geometrically intuitive relationship between the P3P solutions and the roots of its quartic equation, aside its academic values, it could also act as some theoretical guidance for P3P practitioners to properly arrange their control points to avoid undesirable solutions. (c) 2020 Elsevier B.V. All rights reserved. |
| WOS关键词 | POSE ; VIEW |
| 资助项目 | National Key R&D Program of China[2016YFD0700100] ; National Natural Science Foundation of China (NSFC)[61873264] ; National Natural Science Foundation of China (NSFC)[61421004] ; National Natural Science Foundation of China (NSFC)[61333015] ; National Natural Science Foundation of China (NSFC)[61403373] ; National Natural Science Foundation of China (NSFC)[61503004] |
| WOS研究方向 | Computer Science ; Engineering ; Optics |
| 语种 | 英语 |
| WOS记录号 | WOS:000582804000011 |
| 出版者 | ELSEVIER |
| 资助机构 | National Key R&D Program of China ; National Natural Science Foundation of China (NSFC) |
| 源URL | [http://ir.ia.ac.cn/handle/173211/41744]  |
| 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 Angeles, CA 90007 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. New insights on multi-solution distribution of the P3P problem[J]. IMAGE AND VISION COMPUTING,2020,103:9. |
| APA | Wang, Bo,Hu, Hao,&Zhang, Caixia.(2020).New insights on multi-solution distribution of the P3P problem.IMAGE AND VISION COMPUTING,103,9. |
| MLA | Wang, Bo,et al."New insights on multi-solution distribution of the P3P problem".IMAGE AND VISION COMPUTING 103(2020):9. |
入库方式： OAI收割
来源：自动化研究所
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