The Perspective View of Three Points
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact and Approximate Solutions of the Perspective-Three-Point Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Review and analysis of solutions of the three point perspective pose estimation problem
International Journal of Computer Vision
Integrating virtual objects into real images for augmented reality
VRST '98 Proceedings of the ACM symposium on Virtual reality software and technology
New algorithms for the perspective-three-point problem
Journal of Computer Science and Technology
Complete Solution Classification for the Perspective-Three-Point Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
A general sufficient condition of four positive solutions of the P3P problem
Journal of Computer Science and Technology
Monocular model-based 3D tracking of rigid objects
Foundations and Trends® in Computer Graphics and Vision
Robust 3D Head Tracking Using Camera Pose Estimation
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
A Minimal Solution to the Generalised 3-Point Pose Problem
Journal of Mathematical Imaging and Vision
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
The unique solution for P3P problem
Proceedings of the 2009 ACM symposium on Applied Computing
A Fundamentally New View of the Perspective Three-Point Pose Problem
Journal of Mathematical Imaging and Vision
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In the Perspective 3-Point Pose Problem (P3P), the transformation that converts the triple of (unknown) camera-to-control-point distances, into the triple of (known) angle cosines between the projection lines, is generally locally invertible. However, this fails to be the case when the camera's focal point (center of perspective) is on the danger cylinder. This situation corresponds to a double solution to P3P, and presents extra difficulties in solving P3P.An extensive analysis of the danger cylinder setup leads to the introduction of a special rational function that proves to be quite useful in solving P3P in the danger cylinder case. This involves some rather long algebraic expressions that are best manipulated using mathematical software. Ultimately, some fairly simple formulas emerge that serve as a basis for an algorithm, called the Double Solution Algorithm (DSA). Experimental results comparing DSA with Grunert's quartic polynomial method demonstrate that DSA often has substantially greater accuracy. This is particularly so when the camera is relatively far from the control points, even if it is not very close to the danger cylinder.