SCIENTIA SINICA Informationis, Volume 47 , Issue 4 : 482-491(2017) https://doi.org/10.1360/N112016-00198

## Generality of the multi-solution phenomenon in the P3P problem

• AcceptedNov 24, 2016
• PublishedFeb 13, 2017
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### Abstract

The P3P problem is a significant single-view-based pose estimation method, and its multi-solution phenomenon has been the focus of investigation since its inception. In this work, we demonstrate from a geometrical point of view that when the distance from the camera's optical center to the three control points is relatively large, the corresponding P3P problem cannot have a unique solution in general; alternatively, or it should have at least two solutions satisfying the three original constraints. A further contribution of this study is the finding that the intersection of the three 3D pumpkin surfaces in the P3P problem can be generally deduced from the intersection of the three 2D intersecting curves of the three pumpkin surfaces with the control point plane, which provides a new way to investigate the multi-solution phenomenon. Our results may be significant for both P3P theorists and practitioners.

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