Self-calibration of a 1D Projective Camera and its Application to the Self-calibration of a 2D Projective Camera

Olivier Faugeras 1 Long Quan 2 Peter Sturm 2
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
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 : We introduce the concept of self-calibration of a 1D projective camera from point correspondences, and describe a method for uniquely determining the two internal parameters of a 1D camera based on the trifocal tensor of three 1D images. The method requires the estimation of the trifocal tensor which can be achieved linearly with no approximation unlike the trifocal tensor of 2D images, and solving for the roots of a cubic polynomial in one variable. Interestingly enough, we prove that a 2D camera undergoing a planar motion reduces to a 1D camera. From this observation, we deduce a new method for self-calibrating a 2D camera using planar motions. Both the self-calibration method for a 1D camera and its applications for 2D camera calibration are demonstrated on real image sequences. Other applications including 2D affine camera self-calibration are also discussed.
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Olivier Faugeras, Long Quan, Peter Sturm. Self-calibration of a 1D Projective Camera and its Application to the Self-calibration of a 2D Projective Camera. European Conference on Computer Vision (ECCV '98), Jun 1998, Freiburg, Germany. pp.36-52, ⟨10.1007/BFb0055658⟩. ⟨inria-00525684⟩

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