On the Effect of Control-Point Spacing on the Multisolution Phenomenon in the P3P Problem
Joint Authors
Vynnycky, Michael
Reddy, G. M. M.
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-06-21
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The perspective 3-point (P3P) 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 possibility is to formulate it mathematically in terms of finding the solution to a quartic equation.
However, there is yet no quantitative knowledge as to how control-point spacing affects the solution structure—in particular, the multisolution phenomenon.
Here, we consider this problem through an algebraic analysis of the quartic’s coefficients and its discriminant and find that there are significant variations in the likelihood of two or four solutions, depending on how the spacing is chosen.
The analysis indicates that although it is never possible to remove the occurrence of the four-solution case completely, it could be possible to choose spacings that would maximize the occurrence of two real solutions.
Moreover, control-point spacing is found to impact significantly on the reality conditions for the solution of the quartic equation.
American Psychological Association (APA)
Vynnycky, Michael& Reddy, G. M. M.. 2018. On the Effect of Control-Point Spacing on the Multisolution Phenomenon in the P3P Problem. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1208124
Modern Language Association (MLA)
Vynnycky, Michael& Reddy, G. M. M.. On the Effect of Control-Point Spacing on the Multisolution Phenomenon in the P3P Problem. Mathematical Problems in Engineering No. 2018 (2018), pp.1-13.
https://search.emarefa.net/detail/BIM-1208124
American Medical Association (AMA)
Vynnycky, Michael& Reddy, G. M. M.. On the Effect of Control-Point Spacing on the Multisolution Phenomenon in the P3P Problem. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-13.
https://search.emarefa.net/detail/BIM-1208124
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1208124