Abstract
General camera models relax the constraint on central projection and characterize cameras as mappings between each pixel and the corresponding projection rays. This allows to describe most cameras types, including classical pinhole cameras, cameras with various optical distortions, catadioptric cameras and other acquisition devices. We deal with the structure from motion problem for such general models. We first consider an hierarchy of general cameras first introduced in [28] where the cameras are described according to the number of points and lines that have a non-empty intersection with all the projection rays. Then we propose a study of the multi-view geometry of such cameras and a new formulation of multi-view matching tensors working for projection rays crossing the same 3D line, the counterpart of the fundamental matrices and the multifocal tensors of the standard perspective cameras. We also delineate a method to estimate such tensors and recover the motion between the views.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baker, S., Nayar, S.K.: A theory of single-viewpoint catadioptric image formation. International Journal of Computer Vision 35(2), 175–196 (1999). DOI 10.1023/A:1008128724364
Bakstein, H., Pajdla, T.: An overview of non-central cameras. In B. Likar, Editor, Proceedings of the Computer Vision Winter Workshop, Ljubljana, Slovenia, February 2001, pp. 223–233.
Barreto, J., Araujo, H.: Paracatadioptric camera calibration using lines. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV ’03), vol. 2, pp. 1359–1365. IEEE Computer Society, Los Alamitos, CA, USA (2003). DOI 10.1109/ICCV.2003.1238648
Bouguet, J.Y.: Camera calibration toolbox for matlab. http://www.vision.caltech.edu/bouguetj
Bronnimann, H., Everett, H., Lazard, S., Sottile, F., Whitesides, S.: Transversals to line segments in three-dimensional space. Discrete Compututational Geometry 34(3), 381–390 (2005). DOI http://dx.doi.org/10.1007/s00454-005-1183-1
Caglioti, V., Gasparini, S.: On the localization of straight lines in 3D space from single 2D images. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR ’05), vol. 1, pp. 1129–1134. IEEE Computer Society, Los Alamitos, CA, USA (2005). DOI 10.1109/CVPR.2005.257
Caglioti, V., Gasparini, S.: “How many planar viewing surfaces are there in noncentral catadioptric cameras?” Towards singe-image localization of space lines. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR ’06), vol. 1, pp. 1266–1273. IEEE Computer Society, Los Alamitos, CA, USA (2006). DOI 10.1109/CVPR.2006.1
Faugeras, O., Mourrain, B.: On the geometry and algebra of the point and line correspondences between n images. In: CVPR95, pp. 951–956 (1995). DOI 10.1109/ICCV.1995.466832
Feldman, D., Pajdla, T., Weinshall, D.: On the epipolar geometry of the crossed-slits projection. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV ’03), vol. 2, pp. 988–995. IEEE Computer Society, Washington, DC, USA (2003). DOI 10.1109/ICCV.2003.1238456
Fermuller, C., Aloimonos, Y., Baker, P., Pless, R., Neumann, J., Stuart, B.: Multi-camera networks: eyes from eyes. In: Proceedings of the 1st Workshop on Omnidirectional Vision (OMNIVIS 2000), Hilton Head, S.C., USA, 2000, pp. 11–18. DOI 10.1109/OMNVIS.2000.853797
Firoozfam, P., Negahdaripour, S.: Multi-camera conical imaging; calibration and robust 3D motion estimation for ROV based mapping and positioning. In: Proceedings of OCEANS MTS/IEEE Conference and Exhibition, vol. 3, pp. 1595–1602 (2002). DOI 10.1109/OCEANS.2002.1191873
Geyer, C., Daniilidis, K.: Paracatadioptric camera calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(5), 687–695 (2002). DOI 10.1109/34.1000241
Geyer, C., Daniilidis, K.: Mirrors in motion: epipolar geometry and motion estimation. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV ’03), pp. 766–773. IEEE Computer Society, Los Alamitos, CA, USA (2003). DOI 10.1109/ICCV.2003.1238426
Grossberg, M., Nayar, S.: A general imaging model and a method for finding its parameters. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV ’01), pp. 108–115. IEEE Computer Society, Los Alamitos, CA, USA (2001)
Gupta, R., Hartley, R.I.: Linear pushbroom cameras. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(9), 963–975 (1997). DOI 10.1109/34.615446
Hartley, R.I.: Lines and points in three views and the trifocal tensor. International Journal of Computer Vision 22(2), 125–140 (1997). DOI http://dx.doi.org/10.1023/A:1007936012022
Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, second edn. Cambridge University Press (2004)
Hicks, R., Bajcsy, R.: Catadioptric sensors that approximate wide-angle perspective projections. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR ’00), vol. 1, pp. 545–551. IEEE Computer Society, Los Alamitos, CA, USA (2000). DOI 10.1109/CVPR.2000.855867
Hilbert, D., Cohn-Vossen, S.: Geometry and the Imagination. Chelsea Publishing Co., New York: Chelsea (1932)
Ishiguro, H., Yamamoto, M., Tsuji, S.: Omni-directional stereo. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(2), 257–262 (1992). DOI 10.1109/34.121792
Lanman, D., Wachs, M., Taubin, G., Cukierman, F.: Reconstructing a 3D line from a single catadioptric image. In: Proceedings of the International Symposium on 3D Data Processing, Visualization and Transmission, pp. 89–96 (2006). DOI 10.1109/3DPVT.2006.115
Micusik, B., Pajdla, T.: Autocalibration & 3D reconstruction with non-central catadioptric cameras. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR ’04), vol. 1, pp. 58–65. IEEE Computer Society, Los Alamitos, CA, USA (2004). DOI 10.1109/CVPR.2004.1315014
Peleg, S., Ben-Ezra, M.: Stereo panorama with a single camera. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR ’99), vol. 1. IEEE Computer Society, Los Alamitos, CA, USA (1999). DOI 10.1109/CVPR.1999.786969
Pless, R.: Using many cameras as one. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR ’03), vol. 2, pp. 587–93, Madison, WI, USA, 2003. DOI 10.1109/CVPR.2003.1211520
Scaramuzza, D., Martinelli, A., Siegwart, R.: A toolbox for easily calibrating omnidirectional cameras. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5695–5701, Beijing, China, 2006. DOI 10.1109/IROS.2006.282372
Shum, H.Y., Kalai, A., Seitz, S.: Omnivergent stereo. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV ’99), vol. 1, pp. 22–29. IEEE Computer Society, Los Alamitos, CA, USA (1999). DOI 10.1109/ICCV.1999.791193
Sturm, P.: Mixing catadioptric and perspective cameras. In: Proceedings of the 3rd Workshop on Omnidirectional Vision (OMNIVIS 2002), pp. 37–44. IEEE Computer Society, Los Alamitos, CA, USA (2002). DOI 10.1109/OMNVIS.2002.1044489
Sturm, P.: Multi-view geometry for general camera models. In: Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR ’05), vol. 1, pp. 206–212. IEEE Computer Society, Los Alamitos, CA, USA (2005). DOI 10.1109/CVPR.2005.237
Svoboda, T., Pajdla, T.: Epipolar geometry for central catadioptric cameras. International Journal of Computer Vision 49(1), 23–37 (2002). DOI 10.1023/A:1019869530073
Swaminathan, R., Nayar, S.: Nonmetric calibration of wide-angle lenses and polycameras. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(10), 1172–1178 (2000)
Teller, S., Hohmeyer, M.: Determining the lines through four lines. Journal of Graphics Tools 4(3), 11–22 (1999)
Thirthala, S., Pollefeys, M.: Multi-view geometry of 1D radial cameras and its application to omnidirectional camera calibration. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV ’05), vol. 2, pp. 1539–1546, Beijing, China, 2005. DOI 10.1109/ICCV.2005.158
Weng, J., Huang, T., Ahuja, N.: Motion and structure from line correspondences: Closed-form solution, uniqueness, and optimization. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(3), 318–336 (1992). DOI 10.1109/34.120327
Zomet, A., Feldman, D., Peleg, S., Weinshall, D.: Mosaicing new views: The crossed-slits projection. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(6), 741–754 (2003). DOI 10.1109/TPAMI.2003.1201823
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag London Limited
About this chapter
Cite this chapter
Gasparini, S., Sturm, P. (2009). Multi-View Matching Tensors from Lines for General Camera Models. In: Aja-Fernández, S., de Luis García, R., Tao, D., Li, X. (eds) Tensors in Image Processing and Computer Vision. Advances in Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-84882-299-3_9
Download citation
DOI: https://doi.org/10.1007/978-1-84882-299-3_9
Publisher Name: Springer, London
Print ISBN: 978-1-84882-298-6
Online ISBN: 978-1-84882-299-3
eBook Packages: Computer ScienceComputer Science (R0)