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International Workshop on Mathematics Mechanization

International Workshop on Geometric Invariance and Applications in Engineering

IWMM 2004, GIAE 2004: Computer Algebra and Geometric Algebra with Applications pp 56–64Cite as

Some Necessary Conditions on the Number of Solutions for the P4P Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3519))

Abstract

The perspective-n-point (PnP) problem is to find the position and orientation of a camera with respect to a scene object from n correspondence points and is a widely used technique for pose determination in the computer vision community. Finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis, a key research issue of the problem in the literature. In this paper, we study the multi-solution phenomenon of the P4P problem and give some necessary conditions under which there are five positive solutions for the P4P problem. Moreover, we give a geometric configuration for the five solutions.

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Author information

Authors and Affiliations

  1. Department of Mathematics, College of Science, Shenzhen University, Shenzhen, 518060, P.R.China

    Jianliang Tang

Authors
  1. Jianliang Tang
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Editor information

Editors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, CAS, P.O. Box, 100080, Beijing, P.R. China

    Hongbo Li

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, U.S.A.

    Peter J. Olver

  3. Institute of Computer Science, Christian-Albrecht-University, 24098, Kiel, Germany

    Gerald Sommer

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© 2005 Springer-Verlag Berlin Heidelberg

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Tang, J. (2005). Some Necessary Conditions on the Number of Solutions for the P4P Problem. In: Li, H., Olver, P.J., Sommer, G. (eds) Computer Algebra and Geometric Algebra with Applications. IWMM GIAE 2004 2004. Lecture Notes in Computer Science, vol 3519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499251_6

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  • DOI: https://doi.org/10.1007/11499251_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26296-1

  • Online ISBN: 978-3-540-32119-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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