Journal of Zhejiang University-SCIENCE A

, Volume 10, Issue 8, pp 1125–1139 | Cite as

Unwrapping and stereo rectification for omnidirectional images

  • Jie Lei
  • Xin Du
  • Yun-fang Zhu
  • Ji-lin Liu


Omnidirectional imaging sensors have been used in more and more applications when a very large field of view is required. In this paper, we investigate the unwrapping, epipolar geometry and stereo rectification issues for omnidirectional vision when the particular mirror model and the camera parameters are unknown in priori. First, the omnidirectional camera is calibrated under the Taylor model, and the parameters related to this model are obtained. In order to make the classical computer vision algorithms of conventional perspective cameras applicable, the ring omnidirectional image is unwrapped into two kinds of panoramas: cylinder and cuboid. Then the epipolar geometry of arbitrary camera configuration is analyzed and the essential matrix is deduced with its properties being indicated for ring images. After that, a simple stereo rectification method based on the essential matrix and the conformal mapping is proposed. Simulations and real data experimental results illustrate that our methods are effective for the omnidirectional camera under the constraint of a single view point.

Key words

Single point of view Calibration Catadioptric image unwrapping Omnidirectional stereo vision Epipolar geometry Essential matrix Conformal mapping 

CLC number

TP317.4 TP391 


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  1. Agarwala, A., Agrawala, M., Cohen, M., Salesin, D., Szeliski, R., 2006. Photographing Long Scenes with Multiviewpoint Panoramas. Proc. SIGGRAPH, p.853–861.Google Scholar
  2. Baker, S., Nayar, S.K., 1999. A theory of single-viewpoint catadioptic image formation, Int. J. Comput. Vis., 35(2):175–196. [doi:10.1023/A:1008128724364]CrossRefGoogle Scholar
  3. Barreto, J.P., Araujo, H., 2005. Geometric properties of central catadioptric line images and their application in calibration, IEEE Trans. Pattern Anal. Mach. Intell., 27(8):1327–1333. [doi:10.1109/TPAMI.2005.163]CrossRefGoogle Scholar
  4. Benosman, R., Kang, S.B., 2001. Panoramic Vision: Sensors, Theory and Applications. Monographs in Computer Science. Springer-Verlag, New York.Google Scholar
  5. Geyer, C., Daniilidis, K., 2001. Catadioptric projective geometry, Int. J. Comput. Vis., 45(3):223–243. [doi:10.1023/A:1013610201135]CrossRefzbMATHGoogle Scholar
  6. Geyer, C., Daniilidis, K., 2002a. Paracatadioptric camera calibration, IEEE Trans. Pattern Anal. Mach. Intell., 24(5):687–695. [doi:10.1109/34.1000241]CrossRefGoogle Scholar
  7. Geyer, C., Daniilidis, K., 2002b. Properties of the Catadioptric Fundamental Matrix. Proc. European Conf. on Computer Vision, p.140–154.Google Scholar
  8. Geyer, C., Daniilidis, K., 2003a. Conformal Rectification of Omnidirectional Stereo Pairs. Computer Vision and Pattern Recognition Workshop, 7:73–78. [doi:10.1109/CVPRW.2003.10082]Google Scholar
  9. Geyer, C., Daniilidis, K., 2003b. Mirror in Motion: Epipolar Geometry and Motion Estimation, Proc. Ninth IEEE Int. Conf. on Computer Vision, 2:766–773. [doi:10.1109/ICCV.2003.1238426]CrossRefGoogle Scholar
  10. Gluckman, J.M., Nayar, S.K., 2000. Rectified Catadioptric Stereo Sensors, IEEE Conf. on Computer Vision and Pattern Recognition, 2:224–236.Google Scholar
  11. Gluckman, J.M., Thoresz, K., Nayar, S.K., 1998. Real Time Panorama Stereo. DARPA Image Understanding Workshop, p.299–303.Google Scholar
  12. Hartley, R., Zisserman, A., 2000. Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge, UK.zbMATHGoogle Scholar
  13. Kang, S.B., 2000. Catadioptric Self-calibration. Proc. IEEE Conf. on Computer Vision and Pattern Recognition, 1:201–207.Google Scholar
  14. Lin, S.S., Bajcsy, R., 2003. High Resolution Catadioptric Omni-directional Stereo Sensor for Robot Vision. IEEE Int. Conf. on Robotics and Automation, p.1694–1699.Google Scholar
  15. Lin, S.S., Bajcsy, R., 2006. Single-view-point omnidirectional catadioptric cone mirror imager, IEEE Trans. Pattern Anal. Mach. Intell., 28(5):840–845. [doi:10.1109/TPAMI.2006.106]CrossRefGoogle Scholar
  16. Lockwood, E.H., 1967. A Book of Curves. Cambridge University Press, Cambridge, England, p.186–190.Google Scholar
  17. Ma, Y., Soatto, S., Kosecka, J., Sastry, S.S., 2003. An Invitation to 3-D Vision: From Images to Geometric Models. Springer-Verlag, New York, USA.zbMATHGoogle Scholar
  18. McMillan, L., Bishop, G., 1995. Plenoptic Modeling: An Image-based Rendering System. Proc. SIGGRAPH, p.39–46.Google Scholar
  19. Mei, C., Rives, P., 2007. Single View Point Omnidirectional Camera Calibration from Planar Grids. Proc. IEEE Int. Conf. on Robotics and Automation, p.3945–3950. [doi:10.1109/ROBOT.2007.364084]Google Scholar
  20. Micusik, B., 2004. Two-view Geometry of Omnidirectional Cameras. PhD Thesis, Czech Technical University, Prague, Czech Republic.Google Scholar
  21. Scaramuzza, D., Martinelli, A., Siegwart, R., 2006. A Toolbox for Easy Calibrating Omnidirectional Cameras. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, p.5695–5701. [doi:10.1109/IROS.2006.282372]Google Scholar
  22. Scharstein, D., Szeliski, R., 2002. A taxonomy and evaluation of dense two-frame stereo correspondence algorithms, Int. J. Comput. Vis., 47:7–42. [doi:10.1023/A:1014573219977]CrossRefzbMATHGoogle Scholar
  23. Shum, H.Y., He, L.W., 1999. Rendering with Concentric Mosaics. Proc. SIGGRAPH, p.299–306.Google Scholar
  24. Shum, H.Y., Szeliski, R., 1995. Stereo Reconstruction from Multiperspective Panoramas. Proc. Int. Conf. on Computer Vision, p.14–21.Google Scholar
  25. Spacek, L., 2005. A catadioptric sensor with multiple viewpoints, Rob. Auton. Syst., 51(1):3–15. [doi:10.1016/j.robot.2004.08.009]CrossRefGoogle Scholar
  26. Svoboda, T., Pajdla, T., 2002. Epipolar gometry for central catadioptric cameras, Int. J. Comput. Vis., 49(1):23–37. [doi:10.1023/A:1019869530073]CrossRefzbMATHGoogle Scholar
  27. Yagi, Y., Nishii, W., Yamazawa, K., Yachida, M., 1996. Rolling Motion Estimation for Mobile Robot by Using Omnidirectional Image Sensor HyperOmniVision. Proc. 13th Int. Conf. on Pattern Recognition, 1:946–950. [doi:10.1109/ICPR.1996.546163]CrossRefGoogle Scholar
  28. Yamazawa, K., Yagi, Y., Yachida, M., 1993. Omnidirectional Imaging with Hyperboloidal Projection. Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2:1029–1034.Google Scholar
  29. Ying, X.H., Hu, Z.Y., 2004. Catadioptric camera calibration using geometric invariants, IEEE Trans. Pattern Anal. Mach. Intell., 26(10):1260–1271. [doi:10.1109/TPAMI.2004.79]CrossRefGoogle Scholar
  30. Ying, X.H., Zha, H.B., 2008. Identical projective geometric properties of central catadioptric line images and sphere images with applications to calibration, Int. J. Comput. Vis., 78(1):89–105. [doi:10.1007/s11263-007-0082-8]CrossRefGoogle Scholar

Copyright information

© Zhejiang University and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Institute of Information and Communication EngineeringZhejiang UniversityHangzhouChina
  2. 2.Zhejiang Provincial Key Laboratory of Information Network TechnologyHangzhouChina
  3. 3.College of Computer and Information EngineeringZhejiang Gongshang UniversityHangzhouChina

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