Mathematical Analysis of the Multisolution Phenomenon in the P3P Problem
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
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.
P3P, Quartic polynomial, Multiple solutions
IdentifiersURN: urn:nbn:se:kth:diva-163478DOI: 10.1007/s10851-014-0525-0ISI: 000350241300007ScopusID: 2-s2.0-84923702515OAI: oai:DiVA.org:kth-163478DiVA: diva2:800664
QC 201504072015-04-072015-04-072015-04-07Bibliographically approved