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Triangulation

Richard Hartley Peter Sturm 1
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 : In this paper, we consider the problem of finding the position of a point in space given its position in two images taken with cameras with known calibration and pose. This process requires the intersection of two known rays in space, and is commonly known as triangulation. In the absence of noise, this problem is trivial. When noise is present, the two rays will not generally meet, in which case it is necessary to find the best point of intersection. This problem is especially critical in affine and projective reconstruction in which there is no meaningful metric information about the object space. It is desirable to find a triangulation method that is invariant to projective transformations of space. This paper solves that problem by assuming a gaussian noise model for perturbation of the image coordinates. The triangulation problem then may be formulated as a least-squares minimization problem. In this paper a non-iterative solution is given that finds a global minimum. It is shown that in certain configurations, local minima occur, methods show that it consistently gives superior results.
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https://hal.inria.fr/inria-00525693
Contributor : Peter Sturm <>
Submitted on : Tuesday, October 12, 2010 - 2:35:24 PM
Last modification on : Friday, June 26, 2020 - 4:04:03 PM

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Richard Hartley, Peter Sturm. Triangulation. Computer Vision and Image Understanding, Elsevier, 1997, 68 (2), pp.146-157. ⟨10.1006/cviu.1997.0547⟩. ⟨inria-00525693⟩

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