Skip to main content

Shape Reconstruction by Line Voting in Discrete Space

  • Conference paper
Advances in Visual Computing (ISVC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4291))

Included in the following conference series:

  • 1750 Accesses

Abstract

Shape from silhouettes is a binary geometric tomography since both objects and projections, which are measured as silhouettes, are binary. In this paper, we formulate shape from silhouettes in the three-dimensional discrete space. This treatment of the problem implies an ambiguity theorem for the reconstruction of objects in discrete space. Furthermore, we show that in three-dimensional space, it is possible to reconstruct a class of non-convex objects from a collection of silhouettes though on a plane non-convex object is unreconstractable from any collection of silhouettes.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Guggenheimer, H.W.: Applicable Geometry. Robert E. Kniegen Pub, Inci, New York (1977)

    MATH  Google Scholar 

  2. Aloimonos, J.: Visual shape computation. Proceedings of IEEE 76, 899–916 (1988)

    Article  Google Scholar 

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

    Google Scholar 

  4. Campi, S.: Reconstructing a convex surface from certain measurements of its projections, bollettio U.M.I.  6, 945–959 (1986)

    Google Scholar 

  5. Boltyanski, V., Martin, H., Soltan, P.S.: Excursions into Combinatorial Geometry. Springer, Berlin (1997)

    MATH  Google Scholar 

  6. Kutulakos, K., Seitz, S.M.: A theory of shape by space carving. In: Proceedings of 7th ICCV, vol. 1, pp. 307–314 (1999)

    Google Scholar 

  7. Skiena, S.S.: Interactive reconstruction via geometric probing. IEEE Proceedings 80, 1364–1383 (1992)

    Article  Google Scholar 

  8. Skiena, S.S.: Probing convex polygon with half-planes. Journal of Algorithms 12, 359–374 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lindembaum, M., Bruckstein, A.: Reconstructing a convex polygon from binary perspective projections. Pattern Recognition 23, 1343–1350 (1990)

    Article  MathSciNet  Google Scholar 

  10. Laurentini, A.: The visual hull concept for silhouette-bases image understanding. IEEE PAMI 16, 150–163 (1994)

    Google Scholar 

  11. Laurentini, A.: How for 3D shape can be understood from 2D silhouettes. IEEE PAMI 17, 88–195 (1995)

    Google Scholar 

  12. Li, R.S.-Y.: Reconstruction of polygons from projections. Information Processing Letters 28, 235–240 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  13. Prince, J.L., Willsky, A.S.: Reconstructing convex sets from support line measurements. IEEE Trans PAMI 12, 377–389 (1990)

    Google Scholar 

  14. Rao, A.S., Goldberg, Y.K.: Shape from diameter: Recognizing polygonal parts with parallel-jaw gripper. International Journal of Robotics Research 13, 16–37 (1994)

    Article  Google Scholar 

  15. Kawamoto, K., Imiya, K.: Detection of spatial points and lines by random sampling and voting process. Pattern Recognition Letters 22, 199–207 (2001)

    Article  MATH  Google Scholar 

  16. Solmon, D.C.: The X-ray transform. Journal of Math. Anal. and Appl. 56, 61–83 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hammaker, C., Smith, K.T., Solomon, D.C., Wagner, L.: The divergent beam x-ray transform. Rocky Mountain Journal of Mathematics 10, 253–283 (1980)

    Article  MathSciNet  Google Scholar 

  18. Imiya, A., Kawamoto, K.: Shape reconstruction from an image sequences. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 677–686. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Imiya, A., Kawamoto, K.: Mathematical aspects of shape reconstruction from an image sequence. In: Proc. 1st Intl. Symp. 3D data Processing Visualization and Transformations, pp. 632–635 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sato, K., Imiya, A., Sakai, T. (2006). Shape Reconstruction by Line Voting in Discrete Space. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2006. Lecture Notes in Computer Science, vol 4291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11919476_61

Download citation

  • DOI: https://doi.org/10.1007/11919476_61

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-48628-2

  • Online ISBN: 978-3-540-48631-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics