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Revisiting the PnP Problem: A Fast, General and Optimal Solution

Zheng, Yinqiang; Kuang, Yubin LU ; Sugimoto, Shigeki; Åström, Karl LU and Okutomi, Masatoshi (2013) IEEE International Conference on Computer Vision (ICCV), 2013 In [Host publication title missing] p.2344-2351
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
computer vision, pose, pnp
in
[Host publication title missing]
pages
8 pages
publisher
Computer Vision Foundation
conference name
IEEE International Conference on Computer Vision (ICCV), 2013
external identifiers
  • Scopus:84898785848
language
English
LU publication?
yes
id
796e79a4-1c65-4d8f-9bc9-e329b47e65a4 (old id 4249625)
alternative location
http://www.cv-foundation.org/openaccess/content_iccv_2013/papers/Zheng_Revisiting_the_PnP_2013_ICCV_paper.pdf
date added to LUP
2014-02-12 14:24:55
date last changed
2016-12-04 04:45:09
@misc{796e79a4-1c65-4d8f-9bc9-e329b47e65a4,
  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.},
  author       = {Zheng, Yinqiang and Kuang, Yubin and Sugimoto, Shigeki and Åström, Karl and Okutomi, Masatoshi},
  keyword      = {computer vision,pose,pnp},
  language     = {eng},
  pages        = {2344--2351},
  publisher    = {ARRAY(0xb90f510)},
  series       = {[Host publication title missing]},
  title        = {Revisiting the PnP Problem: A Fast, General and Optimal Solution},
  year         = {2013},
}