An Efficient Solution to the Perspective-n-Point Problem for Camera With Unknown Focal Length

To achieve lower time consumption in pose estimation of an uncalibrated camera, a novel and efficient method to the Perspective-n-Point problem (PnP) is proposed in this article. An uncalibrated camera refers to a camera whose focal length, one of the key parameters of PnP, is unknown. Compared to the traditional methods of PnP for uncalibrated cameras, the focal length is eliminated in our proposed method by projecting the given three-dimensional points vertically onto the image plane. Then, a new plane is determined by the projection points and the corresponding 3D points. Further, utilizing the orthogonal characteristic between the normal vector of the plane and the in-plane vector, we construct the PnP problem for an uncalibrated camera as a 20th-order polynomial system, which can easily be solved. As compared to recent PnP methods for uncalibrated cameras, our method has comparable accuracy at a lower computation cost when handling sets with between 8 and 40 points.