Cylindrical Calibration for Hybrid Epipolar Configurations
Matrice Semi Fondamentale pour Système de Stéréoscopie Hybride
OPEN ACCESS
This paper deals with the calibration of a cylindrical omnidirectional imaging system,based on a rotating 2048 pixels linear camera which provides high definition panoramas. The two-step algorithm relies on line segment projections as calibration features,which are sinusoidal curves. A cylindrical image line detection algorithm is proposed,based on the dual principle of the Hough transform.Moreover, the use of Plücker coordinates introduces some new characteristics in the calibration process.This kind of formalism allows a linearization of the cylindrical projection,which is non-linear in the usual way. Results obtained from this first step are used to evaluate one of the intrinsic parameters,the other one being determined by a linear criterion minimization in the dual space, ie the sine magnitude space.
Résumé
Cet article présente le calibrage d'un capteur cylindrique omnidirectionnel,qui fournit des panoramas Haute Résolution par la mise en rotation d'une caméra CCD linéaire. L'algorithme utilise les segments de droite pour primitives,dont les projections sont des composées de sinusoïdes,et est constitué de deux étapes. Un algorithme de détection et d'identification de l'image de droites est proposé,selon une méthode proche de la transformée de Hough. De plus,l'utilisation des coordonnées de Plücker permet la linéarisation de la projection cylindrique. Les résultats extraits de la première étape sont utilisés pour l'évaluation du premier paramètre intrinsèque. Le second est quant à lui déterminé par l'intermédiaire de la minimisation d'un critère linéaire dans l'espace d'accumulation.
Non-Linear Calibration,Omnidirectional Imaging System,Plücker,Coordinates,Hough Transform.
Mots clés
Calibrage non linéaire,Imagerie Panoramique,Coordonnées de Plücker,Transformée de Hough.
[Omn] Proceedings of the IEEE Workshop on Omnidirectional Vision (OMNIVIS'00 05).
[Baker and Nayar] S. BAKER. and S. NAYAR,A theory of single-viewpoint catadioptric image formation. International Journal of Computer Vision, pages 175-196, (1999).
[Benosman] R. BENOSMAN, Reconstruction d'environnements perçus par un capteur panoramique de stéréovision et détermination des modèles CAO. PhD thesis, Université Pierre et Marie Curie, (1997).
[Benosman and Kang] R. BENOSMAN and S. KANG, Panoramic Vision: Theory, Sensors and Applications. Springer Verlag, (2001).
[Benosman et al.] R. BENOSMAN, T. MANIÈRE and J. DEVARS, Multidirectional stereovision sensor, calibration and scenes reconstruction. 13th International Conference on Pattern Recognition, A:161-165, (1996).
[Bunschoten and Kröse] R. BUNSCHOTEN and B. KRÖSE, Range estimation from a pair of omnidirectional images. Proc. IEEE Int. Conf. on Robotics and Automation, pages 1174-1179,(2001).
[Cao and Oh] Z.L. CAO, S. J OH and E.L. HALL, Dynamic omnidirectional vision for mobile robots. Journal of Robotics Systems, 3(1):5-17, (1986).
[Cauchois et al.] C. CAUCHOIS, E. BRASSART E, L. DELAHOCHE and A. CLERENTIN, 3d localization with conical vision. Proc. IEEE Workshop on Omnidirectional Vision OMNIVIS'03, (2003).
[Chang and Hebert] P. CHANG and M. HEBERT, Omnidirectional structure from motion. IEEE Workshop on Omnidirectional Vision (OMNIVIS), (2000).
[Duda and Hart] R.O. DUDA and P.E. HART, Use of the hough transform to detect lines and curves in pictures. Communications of the ACM, 15:11-15, (1972).
[Faugeras] O. FAUGERAS, Three-Dimensional Computer Vision. MIT Press. (1993)
[Gaspar et al.] J. GASPAR, C. DECCO, J. J. OKAMOTO and J. SANTOSVICTOR, Constant resolution omnidirectional cameras. Proc. of IEEE Workshop on Omnidirectional Vision Omnivis' 02, pages 27-34, (2002).
[Geyer and Daniilidis] C. GEYER and K. DANIILIDIS, A unifying theory for central panoramic systems and practical applications. Proc of ECCV, pages 445-461, (2000).
[Geyer and Daniilidis] C. GEYER and K. DANIILIDIS, Para-catadioptric calibration. IEEE Trans. Pattern Analysis and Machine Intelligence, (2002).
[Hartley] R. HARTLEY, In defence of 8-point algorithm. Proc. 5th Int. Conference on Computer Vision,, pages 1064-1070, (1995).
[Hartley and Zissermann] R. I. HARTLEY and A. ZISSERMANN, Multiple view geometry in computer vision. Cambridge University Press, (2000).
[Huang,] F. HUANG, Epipolar geometry and camera calibration of cylindrical panoramas. PhD thesis, Auckland University, (2000).
[Ishiguro et al.] I. ISHIGURO, M. YAMAMOTO and S. TSUJI, Omnidirectional stereo.IEEE Trans. on PAMI, 14:257-262, (1992).
[Longuet-Higgins] H. LONGUET-HIGGINS, A computer algorithm for reconstructing a scene from two projections. Nature, 293:133-135, (1981).
[Nayar] S. K. NAYAR, Catadioptric omnidirectional camera. Proc. of IEEE CVPR, pages 482-488, (1997).
[Peleg and Ben Ezra] S. PELEG and M. BEN EZRA, Stereo panoramic with a single camera. proc. of IEEE CVPR, 1:395-401, (1999).
[Plücker] J. PLÜCKER, On a new geometry of space. Philosophical Transactions of the Royal Society of London, pages 725-791, (1865).
[Shoemake] K. SHOEMAKE, Plucker coordinate tutorial. Ray-Tracing News vol 11, (1998).
[Shum et al.] H. Y. SHUM, A. KALAI and S. SEITZ, Omnivergent stereo. Proc. Seventh International Conference on Computer Vision (ICCV'99), (1999).
[Shum and Szeliski] H. Y. SHUM and R. SZELISKI, Stereo reconstruction from multiperspective cameras. Proc. of IEEE ICCV, 1:14-21, (1999).
[Smadja] L. Smadja, Génération d'environnements 3D denses à partir d'images panoramiques cylindriques. PhD thesis, UPMC, (2003).
[Smadja et al.] L. SMADJA, R. BENOSMAN and J. DEVARS, Determining epipolar constraint on cylindrical images and using it for 3d reconstruction. Proc. ICAR, (2001).
[Sturm] P. STURM, Mixing catadioptric and perspective cameras. Proceedings of the Workshop on Omnidirectional Vision, (2002).
[Swaminathan et al.] R. SWAMINATHAN, S. NAYAR and M. GROSSBERG, Designing mirrors for catadioptric systems that minimize image errors. IEEE Workshop on Omnidirectional Vision Omnivis'04, (2004).
[Tsai and Lenz] R. TSAI and R. LENZ, A new technique for fully autonomous and efficient 3d robotics hand/eye calibration. IEEE Trans Robotics Automation, 5:345-358, (1989).
[Tsai and Huang] R. Y. TSAI and T. S. HUANG, Uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces. IEEE Trans. on PAMI, 6:13-27, (1994).
[Won et al.] K. Y. WON, P. R. S. MENDOÇA and R. CIPOLLA, Camera calibration from surfaces of revolution. IEEE Trans. on PAMI, 25(2):147-161, (2003).
[Yagi and Kawato]Y. YAGI and S. KAWATO, Panorama scene analysis with conic projection.In Proceedings IEEE/RSJ International Workshop on Intelligent Robots and Systems '90, pages 181-187, Tsuchiura, (1990).
[Zhang] Z. ZHANG, Determining the epipolar geometry and its uncertainty: A review.International Journal of Computer Vision, 27(2):161-198, (1998).