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

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Author

  • Yinqiang Zheng
  • Yubin Kuang
  • Shigeki Sugimoto
  • Karl Åström
  • Masatoshi Okutomi

Summary, in English

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.

Publishing year

2013

Language

English

Pages

2344-2351

Publication/Series

[Host publication title missing]

Document type

Conference paper

Publisher

Computer Vision Foundation

Topic

  • Mathematics

Keywords

  • computer vision
  • pose
  • pnp

Conference name

IEEE International Conference on Computer Vision (ICCV), 2013

Conference date

2013-12-01 - 2013-12-08

Conference place

Sydney, Australia

Status

Published

Research group

  • Mathematical Imaging Group