Abstract
In this paper we propose an efficient closed form solution to the absolute orientation problem for cameras with an unknown focal length, from two 2D–3D point correspondences and the camera position. The problem can be decomposed into two simple sub-problems and can be solved with angle constraints. A polynomial equation of one variable is solved to determine the focal length, and then a geometric approach is used to determine the absolute orientation. The geometric derivations are easy to understand and significantly improve performance. Rewriting the camera model with the known camera position leads to a simpler and more efficient closed form solution, and this gives a single solution, without the multi-solution phenomena of perspective-three-point (P3P) solvers. Experimental results demonstrated that our proposed method has a better performance in terms of numerical stability, noise sensitivity, and computational speed, with synthetic data and real images.
Highlights
In this paper we propose an efficient closed form solution to the absolute orientation problem for cameras with an unknown focal length, from two 2D–3D point correspondences and the camera position
In this paper, we focus on the known position parameters [46] to solve the pose problem, and we give an efficient closed form solution to the absolute orientation problem with unknown focal length from two 2D–3D point correspondences
We propose an efficient closed form solution to the absolute orientation problem for cameras with unknown focal length from two 2D–3D point correspondences
Summary
In this paper we propose an efficient closed form solution to the absolute orientation problem for cameras with an unknown focal length, from two 2D–3D point correspondences and the camera position. The P3P needs minimal 2D–3D point correspondences, all P3P solvers have some disadvantages: a fully calibrated camera is needed and multi-solution phenomena exists. These disadvantages prevent their application when the intrinsic camera parameters change online or are unknown. When n ≥ 6, the pose estimation can be linearly estimated, known as direct linear transform (DLT) [18,32], and all the parameters of a fully uncalibrated camera can be obtained
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