Author:
Michael Q. Rieck
Affiliation:
Drake University, United States
Keyword(s):
P3P, Pose, Photogrammetry, Danger cylinder, Discriminant, Jacobian, Repeated solution, Double solution.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Computational Geometry
;
Computer Vision, Visualization and Computer Graphics
;
Human-Computer Interaction
;
Image Formation and Preprocessing
;
Methodologies and Methods
;
Motion and Tracking
;
Motion, Tracking and Stereo Vision
;
Pattern Recognition
;
Physiological Computing Systems
;
Real-Time Vision
;
Visually Guided Robotics
Abstract:
In the Perspective 3-Point Pose Problem (P3P), when the three reference points are equidistant from each other, this distance may be assumed to be one unit in length. A repeated solution to the problem then occurs when and only when 1+R1R2 +R2R3 +R3R1-R21-R22-R23 = 0, where R1;R2 and R3 are the squared distances from the camera’s focal point to the reference points. When the setup only approximately satisfies this equation, two nearly equal solutions can introduce substantial calculation errors. To better handle this circumstance, it may be preferable to behave as though the above equation holds precisely, and then invert a certain two-dimensional transformation to obtain the repeated solution. The inversion involves only a few basic arithmetic operations and square roots. This approach is more efficient, and more reliable, than the standard quartic equation approach to solving P3P, at least in this special case.