A Note on the Number of Solutions of the Noncoplanar P4P Problem
A Note on the Number of Solutions of the Noncoplanar P4P Problem
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DOI：
10.1109/34.993561
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发表时间：
2002-04
期刊：
影响因子：
--
通讯作者：
Zhanyi Hu;Fuchao Wu
中科院分区：
文献类型：
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作者：
Zhanyi Hu;Fuchao Wu
在文献中，Pynomial问题被不可否认地定义为确定控制点到相机光学中心的距离或确定从物心框架到相机中心框架的变换矩阵。我们表明，这两个定义一般是不等价的。特别是，我们证明了，如果四个控制点是不共面的，基于距离的定义下的P4P问题的上限是5，也是可达到的，而基于变换的定义下的P4P问题的上限只有4。最后，我们研究了基于距离的非共面P4P问题至少存在两个、三个、四个和五个不同正解的条件。
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. 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.