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

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.

• Författare: Yinqiang Zheng; Yubin Kuang; Shigeki Sugimoto; Karl Åström; Masatoshi Okutomi
• Avdelning/ar: Matematik LTH; Matematikcentrum; Mathematical Imaging Group; ELLIIT: the Linköping-Lund initiative on IT and mobile communication; eSSENCE: The e-Science Collaboration
• Publiceringsår: 2013
• Språk: Engelska
• Sidor: 2344-2351
• Publikation/Tidskrift/Serie: [Host publication title missing]
• Fulltext: - 512 kB; Download statistics
• Länkar: http://www.cv-foundation.org/openaccess/content_iccv_2013/papers/Zheng_Revisiting_the_PnP_2013_ICCV_paper.pdf
• Dokumenttyp: Konferensbidrag
• Förlag: Computer Vision Foundation
• Ämne: Mathematics
• Nyckelord: 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
• Forskningsgrupp: Mathematical Imaging Group