Publication 2002 Issue No. 4 - April Abstract - A Note on the Number of Solutions of the Noncoplanar P4P Problem
A Note on the Number of Solutions of the Noncoplanar P4P Problem
April 2002 (vol. 24 no. 4)
pp. 550-555
 ASCII Text x 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. 550-555, April, 2002.
 BibTex x @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 = {0162-8828},year = {2002},pages = {550-555},doi = {http://doi.ieeecomputersociety.org/10.1109/34.993561},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Pattern Analysis and Machine IntelligenceTI - A Note on the Number of Solutions of the Noncoplanar P4P ProblemIS - 4SN - 0162-8828SP550EP555EPD - 550-555A1 - Z.Y. Hu, A1 - F.C. Wu, PY - 2002KW - The Noncoplanar P4P ProblemKW - rigid transformationKW - upper boundVL - 24JA - IEEE Transactions on Pattern Analysis and Machine IntelligenceER -

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 object-centered frame to the camera-centered 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 distance-based definition is 5 and also attainable, whereas the upper bound of the P4P problem under the transformation-based 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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Index Terms:
The Noncoplanar P4P Problem, rigid transformation, upper bound
Citation:
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. 550-555, April 2002, doi:10.1109/34.993561