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The Space of All Stereo Images

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Published:01 June 2002Publication History
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Abstract

A theory of stereo image formation is presented that enables a complete classification of all possible stereo views, including non-perspective varieties. Towards this end, the notion of epipolar geometry is generalized to apply to multiperspective images. It is shown that any stereo pair must consist of rays lying on one of three varieties of quadric surfaces. A unified representation is developed to model all classes of stereo views, based on the concept of a quadric view. The benefits include a unified treatment of projection and triangulation operations for all stereo views. The framework is applied to derive new types of stereo image representations with unusual and useful properties. Experimental examples of these images are constructed and used to obtain 3D binocular object reconstructions.

References

  1. Adelson, E.H. and Bergen, J.R. 1991. The Plenoptic Function and the Elements of Early Vision. MIT Press: Cambridge, MA.Google ScholarGoogle Scholar
  2. Baker, S. and Nayar, S. 1999. A theory of single-viewpoint catadioptric image formation. Int. J. of Computer Vision, 35(2):175-196. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Bolles, R.C., Baker, H.H., and Marimont, D.H. 1987. Epipolar-plane image analysis: An approach to determining structure from motion. Int. J. of Computer Vision, 1(1):7-55.Google ScholarGoogle ScholarCross RefCross Ref
  4. Davidhazy, A. 1987. Principles of peripheral photography. Industrial Photography. Available at http://www.rit.edu/~andpph/text-peripheral-basics.html.Google ScholarGoogle Scholar
  5. Gupta, R. and Hartley, R.I. 1997. Linear pushbroom cameras. IEEE Trans. Pattern Analysis and Machine Intell., 19(9):963-975. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Hilbert, D. and Cohn-Vossen, S. 1991. Geometry and the Imagination . AMS Chelsea: Providence, RI.Google ScholarGoogle Scholar
  7. Ishiguro, H., Yamamoto, M., and Tsuji, S. 1992. Omni-directional stereo. PAMI, 14:257-262. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Koenderink, J.J. and van Doorn, A.J. 1991. Affine structure from motion. J. Opt. Soc. Am. A, 8:377-385.Google ScholarGoogle ScholarCross RefCross Ref
  9. Loop, C. and Zhang, Z. 1999. Computing rectifying homographies for stereo vision. In Proc. Computer Vision and Pattern Recognition Conf.Google ScholarGoogle Scholar
  10. McMillan, L. and Bishop, G. 1995. Plenoptic modeling: An image-based rendering system. In Proc. SIGGRAPH 95, pp. 39-46. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Nayar, S.K. and Karmarkar, A. 2000. 360 × 360 mosaics. In Proc. Computer Vision and Pattern Recognition Conf., pp. 388-395.Google ScholarGoogle Scholar
  12. Pajdla, T. 2001. Epipolar geometry of some non-classical cameras. In Proceedings of Computer Vision Winter Workshop. Slovenian Pattern Recognition Society, pp. 223-233.Google ScholarGoogle Scholar
  13. Peleg, S. and Ben-Ezra, M. 1999. Stereo panorama with a single camera. In Proc. Computer Vision and Pattern Recognition Conf., pp. 395-401.Google ScholarGoogle Scholar
  14. Peleg, S. and Herman, J. 1997. Panoramic mosaics by manifold projection. In Proc. Computer Vision and Pattern Recognition Conf., pp. 338-343. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Peleg, S., Pritch, Y., and Ben-Ezra, M. 2000. Cameras for stereo panoramic imaging. In Proc. Computer Vision and Pattern Recognition Conf., pp. 208-214.Google ScholarGoogle Scholar
  16. Rademacher, P. and Bishop, G. 1998. Multiple-center-of-projection images. In Proceedings of SIGGRAPH 98, pp. 199-206. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Roy, S., Meunier, J., and Cox, I. 1997. Cylindrical rectification to minimize epipolar distortion. In Proc. Computer Vision and Pattern Recognition Conf, pp. 393-399. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Shum, H.-Y. and He, L.-W. 1999. Rendering with concentric mosaics. In Proceedings of SIGGRAPH 99, pp. 299-306. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Shum, H.-Y., Kalai, A., and Seitz, S.M. 1999. Omnivergent stereo. In Proc. 7th Int. Conf. on Computer Vision, pp. 22- 29.Google ScholarGoogle Scholar
  20. Shum, H.-Y. and Szeliski, R. 1999. Stereo reconstruction from multiperspective panoramas. In Proc. Seventh Int. Conf. on Computer Vision, pp. 14-21.Google ScholarGoogle Scholar
  21. Svoboda, T., Pajdla, T., and Hlavac, V. 1998. Epipolar geometry for panoramic cameras. In Proc. 5th Eur. Conf. on Computer Vision, pp. 218-232. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Wood, D.N., Finkelstein, A., Hughes, J.F., Thayer, C.E., and Salesin, D.H. 1997. Multiperspective panoramas for cel animation. In Proc. SIGGRAPH 97, pp. 243-250. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Zitnick, C.L. and Kanade, T. 2000. A cooperative algorithm for stereo matching and occlusion detection. IEEE Trans. on Pattern Analysis and Machine Intelligence, 22(7). Google ScholarGoogle ScholarDigital LibraryDigital Library

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      • Published in

        cover image International Journal of Computer Vision
        International Journal of Computer Vision  Volume 48, Issue 1
        Marr Prize Special Issue
        June 2002
        61 pages

        Copyright © Copyright © 2002 Kluwer Academic Publishers

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        Kluwer Academic Publishers

        United States

        Publication History

        • Published: 1 June 2002

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