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A Note on the Number of Solutions of the Noncoplanar P4P Problem

Authors:

F. C. WuAuthors Info & Claims

IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 24, Issue 4

Pages 550 - 555

https://doi.org/10.1109/34.993561

Published: 01 April 2002 Publication History

Abstract

In the literature, the PnP problem is indistinguishably defined as either to determine the distances of the control points from the camera's optical center or to determine the transformation matrices from the object-centered frame to the camera-centered frame. In this paper, we show that these two definitions are generally not equivalent. In particular, we prove that, if the four control points are not coplanar, the upper bound of the P4P problem under the distance-based definition is 5 and also attainable, whereas the upper bound of the P4P problem under the transformation-based definition is only 4. Finally, we study the conditions under which at least two, three, four, and five different positive solutions exist in the distance based noncoplanar P4P problem.

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Cited By

Cao MJia WZhao YLi SLiu X(2018)Fast and robust absolute camera pose estimation with known focal lengthNeural Computing and Applications10.5555/3197883.319790029:5(1383-1398)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.5555/3197883.3197900
Cao MJia WZhao YLi SLiu X(2017)RETRACTED ARTICLE: Fast and robust absolute camera pose estimation with known focal lengthNeural Computing and Applications10.1007/s00521-017-3032-629:5(1383-1398)Online publication date: 7-Jul-2017
https://dl.acm.org/doi/10.1007/s00521-017-3032-6
Guo Y(2013)A Novel Solution to the P4P Problem for an Uncalibrated CameraJournal of Mathematical Imaging and Vision10.1007/s10851-012-0360-045:2(186-198)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1007/s10851-012-0360-0
Show More Cited By

Index Terms

A Note on the Number of Solutions of the Noncoplanar P4P Problem
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision representations
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 24, Issue 4

April 2002

144 pages

ISSN:0162-8828

Issue’s Table of Contents

Copyright © Copyright © 2002 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

Publication History

Published: 01 April 2002

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Cited By

Cao MJia WZhao YLi SLiu X(2018)Fast and robust absolute camera pose estimation with known focal lengthNeural Computing and Applications10.5555/3197883.319790029:5(1383-1398)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.5555/3197883.3197900
Cao MJia WZhao YLi SLiu X(2017)RETRACTED ARTICLE: Fast and robust absolute camera pose estimation with known focal lengthNeural Computing and Applications10.1007/s00521-017-3032-629:5(1383-1398)Online publication date: 7-Jul-2017
https://dl.acm.org/doi/10.1007/s00521-017-3032-6
Guo Y(2013)A Novel Solution to the P4P Problem for an Uncalibrated CameraJournal of Mathematical Imaging and Vision10.1007/s10851-012-0360-045:2(186-198)Online publication date: 1-Feb-2013
https://dl.acm.org/doi/10.1007/s10851-012-0360-0
Zhang SDing YHao KXu LGoodman EChen GWhitley DDing Y(2009)An immune evolutionary algorithm based pose estimation method for parallel manipulatorProceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation10.1145/1543834.1543936(745-750)Online publication date: 12-Jun-2009
https://dl.acm.org/doi/10.1145/1543834.1543936
Faugère JMoroz GRouillier FEl Din MSendra JGonzalez-Vega L(2008)Classification of the perspective-three-point problem, discriminant variety and real solving polynomial systems of inequalitiesProceedings of the twenty-first international symposium on Symbolic and algebraic computation10.1145/1390768.1390782(79-86)Online publication date: 20-Jul-2008
https://dl.acm.org/doi/10.1145/1390768.1390782
Duan FWu FHu Z(2008)Pose determination and plane measurement using a trapeziumPattern Recognition Letters10.1016/j.patrec.2007.09.01829:3(223-231)Online publication date: 1-Feb-2008
https://dl.acm.org/doi/10.1016/j.patrec.2007.09.018
Wang GWu QJi Z(2007)Pose estimation from circle or parallel lines in a single imageProceedings of the 8th Asian conference on Computer vision - Volume Part II10.5555/1775728.1775772(363-372)Online publication date: 18-Nov-2007
https://dl.acm.org/doi/10.5555/1775728.1775772
Su J(2007)Camera calibration based on receptive fieldsPattern Recognition10.1016/j.patcog.2007.01.02440:10(2837-2845)Online publication date: 1-Oct-2007
https://dl.acm.org/doi/10.1016/j.patcog.2007.01.024
Wang GWu QJi Z(2007)Pose Estimation from Circle or Parallel Lines in a Single ImageComputer Vision – ACCV 200710.1007/978-3-540-76390-1_36(363-372)Online publication date: 18-Nov-2007
https://dl.acm.org/doi/10.1007/978-3-540-76390-1_36
Gao XTang J(2006)On the Probability of the Number of Solutions for the P4P ProblemJournal of Mathematical Imaging and Vision10.1007/s10851-006-5149-625:1(79-86)Online publication date: 1-Jul-2006
https://dl.acm.org/doi/10.1007/s10851-006-5149-6
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