Skip to main content
Log in

Unwrapping and stereo rectification for omnidirectional images

  • Published:
Journal of Zhejiang University-SCIENCE A Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Agarwala, A., Agrawala, M., Cohen, M., Salesin, D., Szeliski, R., 2006. Photographing Long Scenes with Multiviewpoint Panoramas. Proc. SIGGRAPH, p.853–861.

  • 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]

    Article  Google Scholar 

  • 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]

    Article  Google Scholar 

  • Benosman, R., Kang, S.B., 2001. Panoramic Vision: Sensors, Theory and Applications. Monographs in Computer Science. Springer-Verlag, New York.

    Google Scholar 

  • Geyer, C., Daniilidis, K., 2001. Catadioptric projective geometry, Int. J. Comput. Vis., 45(3):223–243. [doi:10.1023/A:1013610201135]

    Article  MATH  Google Scholar 

  • Geyer, C., Daniilidis, K., 2002a. Paracatadioptric camera calibration, IEEE Trans. Pattern Anal. Mach. Intell., 24(5):687–695. [doi:10.1109/34.1000241]

    Article  Google Scholar 

  • Geyer, C., Daniilidis, K., 2002b. Properties of the Catadioptric Fundamental Matrix. Proc. European Conf. on Computer Vision, p.140–154.

  • 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 

  • 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]

    Article  Google Scholar 

  • Gluckman, J.M., Nayar, S.K., 2000. Rectified Catadioptric Stereo Sensors, IEEE Conf. on Computer Vision and Pattern Recognition, 2:224–236.

    Google Scholar 

  • Gluckman, J.M., Thoresz, K., Nayar, S.K., 1998. Real Time Panorama Stereo. DARPA Image Understanding Workshop, p.299–303.

  • Hartley, R., Zisserman, A., 2000. Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge, UK.

    MATH  Google Scholar 

  • Kang, S.B., 2000. Catadioptric Self-calibration. Proc. IEEE Conf. on Computer Vision and Pattern Recognition, 1:201–207.

    Google Scholar 

  • 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.

  • 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]

    Article  Google Scholar 

  • Lockwood, E.H., 1967. A Book of Curves. Cambridge University Press, Cambridge, England, p.186–190.

    Google Scholar 

  • 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.

    MATH  Google Scholar 

  • McMillan, L., Bishop, G., 1995. Plenoptic Modeling: An Image-based Rendering System. Proc. SIGGRAPH, p.39–46.

  • 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]

  • Micusik, B., 2004. Two-view Geometry of Omnidirectional Cameras. PhD Thesis, Czech Technical University, Prague, Czech Republic.

    Google Scholar 

  • 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]

  • 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]

    Article  MATH  Google Scholar 

  • Shum, H.Y., He, L.W., 1999. Rendering with Concentric Mosaics. Proc. SIGGRAPH, p.299–306.

  • Shum, H.Y., Szeliski, R., 1995. Stereo Reconstruction from Multiperspective Panoramas. Proc. Int. Conf. on Computer Vision, p.14–21.

  • Spacek, L., 2005. A catadioptric sensor with multiple viewpoints, Rob. Auton. Syst., 51(1):3–15. [doi:10.1016/j.robot.2004.08.009]

    Article  Google Scholar 

  • Svoboda, T., Pajdla, T., 2002. Epipolar gometry for central catadioptric cameras, Int. J. Comput. Vis., 49(1):23–37. [doi:10.1023/A:1019869530073]

    Article  MATH  Google Scholar 

  • 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]

    Article  Google Scholar 

  • 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 

  • 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]

    Article  Google Scholar 

  • 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]

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xin Du.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 60502006, 60534070 and 90820306) and the Science and Technology Plan of Zhejiang Province, China (No. 2007C21007)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lei, J., Du, X., Zhu, Yf. et al. Unwrapping and stereo rectification for omnidirectional images. J. Zhejiang Univ. Sci. A 10, 1125–1139 (2009). https://doi.org/10.1631/jzus.A0820357

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/jzus.A0820357

Key words

CLC number

Navigation