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Shape Reconstruction from an Image Sequence

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2059))

Abstract

This paper clarifies a suficient condition for the reconstruction of an object from its shadows. The objects considered are finite closed convex regions in three-dimensional Euclidean space. First we show a negative result that a series of shadows measured using a camera moving along a circle on a plane is insuficient for the full reconstruction of an object even if the object is convex. Then, we show a positive result that a series of pairs of shadows measured using a general stereo system with some geometrical assumptions is suficient for full reconstruction of a convex object.

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References

  1. J. Aloimonos, “Visual shape computation,” Proceedings of IEEE, Vol.76, pp.899–916, 1988.

    Article  Google Scholar 

  2. S.S. Skiena, “Interactive reconstruction via geometric probing,” IEEE Proceedings, Vol.80, pp.1364–1383, 1992.

    Article  Google Scholar 

  3. D.P. Dobkin, H. Edelsbrunner, and C.K. Yap, “Probing convex polytopes,” Proc. 18th ACM Symposium on Theory of Computing, pp.424–432. 1986.

    Google Scholar 

  4. V. Boltyanski, H. Martin, and P.S. Soltan, Excursions into Combinatorial Geometry, Springer-Verlag; Berlin, 1997.

    MATH  Google Scholar 

  5. R.S.-Y. Li, “Reconstruction of polygons from projections,” Information Processing Letters, Vol.28, pp.235–240, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Lindembaum and A. Bruckstein, “Reconstructing a convex polygon from binary perspective projections,” Pattern Recognition, Vol.23, pp.1343–1350, 1990.

    Article  MathSciNet  Google Scholar 

  7. A. Laurentini, “The visual hull concept for silhouette-bases image understanding,” IEEE PAMI Vol.16, pp.150–163, 1994.

    Google Scholar 

  8. A. Laurentini, “How for 3D shape can be understood from 2D silhouettes,” IEEE PAMI Vol.17, pp.188–195, 1995.

    Google Scholar 

  9. R.J. Gardner, Geometric Tomography, Cambridge University Press, Cambridge, 1995.

    MATH  Google Scholar 

  10. J.-Y. Zheng, “Acquiring 3-D models from sequences of contours,” IEEE Pattern Analysis and Machine Intelligence, Vol.16, pp.163–178, 1994.

    Article  Google Scholar 

  11. H.K. Tuy, “An inversion formula for cone-beam reconstruction,” SIAM J. Applied Mathematics, Vol.43, pp.546–552, 1983.

    Article  MathSciNet  Google Scholar 

  12. H.W. Guggenheimer, Applicable Geometry, Robert E. Kniegen Pub. Inc, New York 1977.

    MATH  Google Scholar 

  13. R. Vaillant and O.D. Faugeras, “Using external boundaries for 3-D object modeling,” IEEE Pattern Analysis and Machine Intelligence, Vol. 14, pp. 157–173, 1992.

    Article  Google Scholar 

  14. K. Kanatani, Geometric Computation for Machine Vision, Oxford University Press, Oxford, 1993

    MATH  Google Scholar 

  15. C. Hammaker, K.T. Smith, D.C. Solomon, and L. Wagner, “The divergent beam x-ray transform,” Rocky Mountain Journal of Mathematics, Vol.10, pp.253–283, 1980.

    Article  MathSciNet  Google Scholar 

  16. A. Imiya and K. Kawamoto, “Performance analysis of shape recovery by random sampling and voting,” pp.227–240, in R. Klette, H. Siegfried Stiel, M. A. Viergever and K.L. Vincken eds. Performance Characterization in Computer Vision, Kluwer Academic Publishers, Dordrecht, 2000.

    Google Scholar 

  17. K. Kutulakos and S. M. Seitz, “A theory of shape by space carving,” Proceedings of 7th ICCV, Vol. 1, pp.307–314, 1999.

    Google Scholar 

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© 2001 Springer-Verlag Berlin Heidelberg

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Imiya, A., Kawamoto, K. (2001). Shape Reconstruction from an Image Sequence. In: Arcelli, C., Cordella, L.P., di Baja, G.S. (eds) Visual Form 2001. IWVF 2001. Lecture Notes in Computer Science, vol 2059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45129-3_62

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  • DOI: https://doi.org/10.1007/3-540-45129-3_62

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42120-7

  • Online ISBN: 978-3-540-45129-7

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