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 PnP problem revisited Wu, YH; Hu, ZY 2006 发表期刊 JOURNAL OF MATHEMATICAL IMAGING AND VISION 卷号 24期号:1页码:131-141 文章类型 Article 摘要 Perspective-n-Point camera pose determination, or the PnP problem, has attracted much attention in the literature. This paper gives a systematic investigation on the PnP problem from both geometric and algebraic standpoints, and has the following contributions: Firstly, we rigorously prove that the PnP problem under distance-based definition is equivalent to the PnP problem under orthogonal-transformation-based definition when n > 3, and equivalent to the PnP problem under rotation-transformation-based definition when n = 3. Secondly, we obtain the upper bounds of the number of solutions for the PnP problem under different definitions. In particular, we show that for any three non-collinear control points, we can always find out a location of optical center such that the P3P problem formed by these three control points and the optical center can have 4 solutions, its upper bound. Additionally a geometric way is provided to construct these 4 solutions. Thirdly, we introduce a depth-ratio based approach to represent the solutions of the whole PnP problem. This approach is shown to be advantageous over the traditional elimination techniques. Lastly, degenerated cases for coplanar or collinear control points are also discussed. Surprisingly enough, it is shown that if all the control points are collinear, the PnP problem under distance-based definition has a unique solution, but the PnP problem under transformation-based definition is only determined up to one free parameter. 关键词 Perspective-n-point Camera Pose Determination Distance-based Definition Transformation-based Definition Depth-ratio Based Equation Upper Bound Of The Number Of Solutions WOS标题词 Science & Technology ; Technology ; Physical Sciences 关键词[WOS] PERSPECTIVE-3-POINT PROBLEM ; POSE ESTIMATION ; EFFICIENT ; POINTS 收录类别 SCI 语种 英语 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:000235460400006 引用统计 被引频次：48[WOS]   [WOS记录]     [WOS相关记录] 文献类型 期刊论文 条目标识符 http://ir.ia.ac.cn/handle/173211/9334 专题 09年以前成果 作者单位 Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100080, Peoples R China 推荐引用方式GB/T 7714 Wu, YH,Hu, ZY. PnP problem revisited[J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION,2006,24(1):131-141. APA Wu, YH,&Hu, ZY.(2006).PnP problem revisited.JOURNAL OF MATHEMATICAL IMAGING AND VISION,24(1),131-141. MLA Wu, YH,et al."PnP problem revisited".JOURNAL OF MATHEMATICAL IMAGING AND VISION 24.1(2006):131-141.
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