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Euclidean Structure from N>=2 Parallel Circles: Theory and Algorithms

Pierre Gurdjos 1 Peter Sturm 2 Yihong Wu 3
1 IRIT-TCI - Traitement et Compréhension d’Images
IRIT - Institut de recherche en informatique de Toulouse
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 : Our problem is that of recovering, in one view, the 2D Euclidean structure, induced by the projections of N parallel circles. This structure is a prerequisite for camera calibration and pose computation. Until now, no general method has been described for N > 2. The main contribution of this work is to state the problem in terms of a system of linear equations to solve.We give a closed-form solution as well as bundle adjustment-like refinements, increasing the technical applicability and numerical stability. Our theoretical approach generalizes and extends all those described in existing works for N = 2 in several respects, as we can treat simultaneously pairs of orthogonal lines and pairs of circles within a unified framework. The proposed algorithm may be easily implemented, using well-known numerical algorithms. Its performance is illustrated by simulations and experiments with real images.
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https://hal.inria.fr/inria-00387126
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  • HAL Id : inria-00387126, version 1

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Pierre Gurdjos, Peter Sturm, Yihong Wu. Euclidean Structure from N>=2 Parallel Circles: Theory and Algorithms. European Conference on Computer Vision, May 2006, Graz, Austria. pp.238-252. ⟨inria-00387126⟩

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