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Z.Y. Hu, F.C. Wu, "A Note on the Number of Solutions of the Noncoplanar P4P Problem," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp. 550555, April, 2002.  
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@article{ 10.1109/34.993561, author = {Z.Y. Hu and F.C. Wu}, title = {A Note on the Number of Solutions of the Noncoplanar P4P Problem}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {24}, number = {4}, issn = {01628828}, year = {2002}, pages = {550555}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.993561}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  A Note on the Number of Solutions of the Noncoplanar P4P Problem IS  4 SN  01628828 SP550 EP555 EPD  550555 A1  Z.Y. Hu, A1  F.C. Wu, PY  2002 KW  The Noncoplanar P4P Problem KW  rigid transformation KW  upper bound VL  24 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
In the literature, the PnP problem is indistinguishably defined as either to determine the distances of the control points from the camera's optical center or to determine the transformation matrices from the objectcentered frame to the cameracentered frame. In this paper, we show that these two definitions are generally not equivalent. In particular, we prove that, if the four control points are not coplanar, the upper bound of the P4P problem under the distancebased definition is 5 and also attainable, whereas the upper bound of the P4P problem under the transformationbased definition is only 4. Finally, we study the conditions under which at least two, three, four, and five different positive solutions exist in the distance based noncoplanar P4P problem.
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