| 摘要: |
| PnP问题是计算机视觉、摄影测量学乃至数学领域的一个经典问题.系统地研究了P5P问题,用代数方法证明了下述结论:当5个控制点中任意3点不共线时,P5P问题最多有两个解,并且解的上限可以达到.同时给出了有惟一解和有两个解的代数条件以及求解P5P问题的具体算法.在物体定位、机器人导航等领域具有比较重要的应用价值. |
| 关键词: P5P问题 SVD(singular value decomposition)分解 坐标变换 |
| DOI： |
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| 基金项目:国家重点基础研究发展规划973资助项目(G1998030502); 国家自然科学基金资助项目(69975021,60075004,60033010) |
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| A Study on the P5P Problem |
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WU Fu chao,HU Zhan yi
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| Abstract: |
| The PnP problem is a classical problem in computer vision, photogrammetry, and even in mathematics. The P5P problem is systematically investigated in this paper. It is proved algebraically that if no 3 control points among the 5 ones are collinear, the P5P problem could have at most 2 solutions, and this upper bound is also attainable. In addition, algebraic conditions are provided for the case of the unique solution and that of the two solutions of the problem respectively and a practical algorithm to compute the admissible solutions also presented. The obtained results are of practical importance in applications such as object pose estimation and robot navigation. |
| Key words: P5P problem singular value decomposition rigid transformation |
