Mathematical Analysis of the Multisolution Phenomenon in the P3P Problem

The perspective 3-point problem, also known as pose estimation, has its origins in camera calibration and is of importance in many fields: for example, computer animation, automation, image analysis and robotics. One line of activity involves formulating it mathematically in terms of finding the sol...

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Veröffentlicht in:Journal of mathematical imaging and vision 2015-02, Vol.51 (2), p.326-337
Hauptverfasser: Vynnycky, M., Kanev, K.
Format: Artikel
Sprache:eng
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Zusammenfassung:The perspective 3-point problem, also known as pose estimation, has its origins in camera calibration and is of importance in many fields: for example, computer animation, automation, image analysis and robotics. One line of activity involves formulating it mathematically in terms of finding the solution to a quartic equation. However, in general, the equation does not have a unique solution, and in some situations there are no solutions at all. Here, we present a new approach to the solution of the problem; this involves closer scrutiny of the coefficients of the polynomial, in order to understand how many solutions there will be for a given set of problem parameters. We find that, if the control points are equally spaced, there are four positive solutions to the problem at 25 % of all available spatial locations for the control-point combinations, and two positive solutions at the remaining 75 %.
ISSN:0924-9907
1573-7683
1573-7683
DOI:10.1007/s10851-014-0525-0