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Mathematical Analysis of the Multisolution Phenomenon in the P3P Problem
KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Casting of Metals. University of Limerick, Ireland .ORCID iD: 0000-0002-8318-1251
2015 (English)In: Journal of Mathematical Imaging and Vision, ISSN 0924-9907, E-ISSN 1573-7683, Vol. 51, no 2, 326-337 p.Article in journal (Refereed) Published
Abstract [en]

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 %.

Place, publisher, year, edition, pages
2015. Vol. 51, no 2, 326-337 p.
Keyword [en]
P3P, Quartic polynomial, Multiple solutions
National Category
Other Mathematics
URN: urn:nbn:se:kth:diva-163478DOI: 10.1007/s10851-014-0525-0ISI: 000350241300007ScopusID: 2-s2.0-84923702515OAI: diva2:800664

QC 20150407

Available from: 2015-04-07 Created: 2015-04-07 Last updated: 2015-04-07Bibliographically approved

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Vynnycky, Michael
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