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PnP problem revisited
Wu, YH; Hu, ZY
AbstractPerspective-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.
KeywordPerspective-n-point Camera Pose Determination Distance-based Definition Transformation-based Definition Depth-ratio Based Equation Upper Bound Of The Number Of Solutions
WOS HeadingsScience & Technology ; Technology ; Physical Sciences
Indexed BySCI
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Artificial Intelligence ; Computer Science, Software Engineering ; Mathematics, Applied
WOS IDWOS:000235460400006
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Document Type期刊论文
AffiliationChinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, Beijing 100080, Peoples R China
Recommended Citation
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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