Euclidean Structure from N ≥ 2 Parallel Circles: Theory and Algorithms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3951)


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.


Camera Calibration Absolute Signature Euclidean Structure Orthogonal Line Radical Axis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.IRIT-TCI, UPSToulouseFrance
  2. 2.PERCEPTION, INRIA Rhône-AlpesMontbonnotFrance
  3. 3.NLPR-IAChinese Academy of SciencesBeijingChina

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