Revisiting the PnP Problem: A Fast, General and Optimal Solution
Zheng, Yinqiang; Kuang, Yubin; Sugimoto, Shigeki; Åström, Karl, et al. (2013). Revisiting the PnP Problem: A Fast, General and Optimal Solution [Host publication title missing], 2344 - 2351. IEEE International Conference on Computer Vision (ICCV), 2013. Sydney, Australia: Computer Vision Foundation
Conference Proceeding/Paper
|
Published
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English
Authors:
Zheng, Yinqiang
;
Kuang, Yubin
;
Sugimoto, Shigeki
;
Åström, Karl
, et al.
Department:
Mathematics (Faculty of Engineering)
Centre for Mathematical Sciences
Mathematical Imaging Group
ELLIIT: the Linköping-Lund initiative on IT and mobile communication
eSSENCE: The e-Science Collaboration
Research Group:
Mathematical Imaging Group
Abstract:
In this paper, we revisit the classical perspective-n-point (PnP) problem, and propose the first non-iterative O(n) solution that is fast, generally applicable and globally optimal. Our basic idea is to formulate the PnP problem into a functional minimization problem and retrieve all its stationary points by using the Gr¨obner basis technique. The novelty lies in a non-unit quaternion representation to parameterize the rotation and a simple but elegant formulation of the PnP problem into an unconstrained optimization problem. Interestingly, the polynomial system arising from its first-order optimality condition assumes two-fold symmetry, a nice property that can be utilized to improve speed and numerical stability of a Gr¨obner basis solver. Experiment results have demonstrated that, in terms of accuracy, our proposed solution is definitely better than the state-ofthe- art O(n) methods, and even comparable with the reprojection error minimization method.
Keywords:
computer vision ;
pose ;
pnp
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