Euclidean Structure from N Geq 2 Parallel Circles: Theory and Algorithms
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.
Cite
Text
Gurdjos et al. "Euclidean Structure from N Geq 2 Parallel Circles: Theory and Algorithms." European Conference on Computer Vision, 2006. doi:10.1007/11744023_19Markdown
[Gurdjos et al. "Euclidean Structure from N Geq 2 Parallel Circles: Theory and Algorithms." European Conference on Computer Vision, 2006.](https://mlanthology.org/eccv/2006/gurdjos2006eccv-euclidean/) doi:10.1007/11744023_19BibTeX
@inproceedings{gurdjos2006eccv-euclidean,
title = {{Euclidean Structure from N Geq 2 Parallel Circles: Theory and Algorithms}},
author = {Gurdjos, Pierre and Sturm, Peter F. and Wu, Yihong},
booktitle = {European Conference on Computer Vision},
year = {2006},
pages = {238-252},
doi = {10.1007/11744023_19},
url = {https://mlanthology.org/eccv/2006/gurdjos2006eccv-euclidean/}
}