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An Analytic Solution for the Perspective 4-Point Problem

Radu Horaud 1, 2 Bernard Conio 1 Olivier Leboulleux 1 Bernard Lacolle 3
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : The perspective n-point (PnP) problem is the problem of finding the position and orientation of a camera with respect to a scene object from n correspondence points. The authors propose an analytic solution for the perspective 4-point problem. The solution is found by replacing the four points with a pencil of three lines and by exploring the geometric constraints available with the perspective camera model. The P4P problem is cast into the problem of solving a biquadratic polynomial equation in one unknown.
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Radu Horaud, Bernard Conio, Olivier Leboulleux, Bernard Lacolle. An Analytic Solution for the Perspective 4-Point Problem. Computer Vision Graphics and Image Processing, Elsevier, 1989, 47 (1), pp.33--44. ⟨10.1016/0734-189X(89)90052-2⟩. ⟨inria-00589990⟩