Object Pose: The Link between Weak Perspective, Para Perspective, and Full Perspective

Radu Horaud 1 Stéphane Christy Fadi Dornaika
1 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 : Recently, Dementhon & Davis (1994) proposed a method for determining the pose of a 3-D object with respect to a camera from 3-D to 2-D point correspondences. The method consists of iteratively improving the pose computed with a weak perspective camera model to converge, at the limit, to a pose estimation computed with a perspective camera model. In this paper we give a simple derivation of Dementhon and Davis' method and we show that it belongs to a larger class of methods where the perspective camera model is approximated either at zero order (weak perspective) or first order (para perspective). We analyse the convergence of these methods and we conclude that the iterative para perspective method has better convergence properties than the iterative weak perspective method. We introduce a simple way of taking into account the orthogonality constraint associated with the rotation matrix. We analyse the sensitivity to camera calibration errors and we define the optimal experimental setup with respect to imprecise camera calibration. We compare the results obtained with this method and with a non-linear optimization method.
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Radu Horaud, Stéphane Christy, Fadi Dornaika. Object Pose: The Link between Weak Perspective, Para Perspective, and Full Perspective. RR-2356, INRIA. 1994. ⟨inria-00074321⟩

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