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.
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Guggenheimer, H.W.: Applicable Geometry. Robert E. Kniegen Pub, Inci, New York (1977)
Aloimonos, J.: Visual shape computation. Proceedings of IEEE 76, 899–916 (1988)
Dobkin, D.P., Edelsbrunner, H., Yap, C.K.: Probing convex polytopes. In: Proc. 18th ACM Symposium on Theory of Computing, pp. 424–432 (1986)
Campi, S.: Reconstructing a convex surface from certain measurements of its projections, bollettio U.M.I. 6, 945–959 (1986)
Boltyanski, V., Martin, H., Soltan, P.S.: Excursions into Combinatorial Geometry. Springer, Berlin (1997)
Kutulakos, K., Seitz, S.M.: A theory of shape by space carving. In: Proceedings of 7th ICCV, vol. 1, pp. 307–314 (1999)
Skiena, S.S.: Interactive reconstruction via geometric probing. IEEE Proceedings 80, 1364–1383 (1992)
Skiena, S.S.: Probing convex polygon with half-planes. Journal of Algorithms 12, 359–374 (1991)
Lindembaum, M., Bruckstein, A.: Reconstructing a convex polygon from binary perspective projections. Pattern Recognition 23, 1343–1350 (1990)
Laurentini, A.: The visual hull concept for silhouette-bases image understanding. IEEE PAMI 16, 150–163 (1994)
Laurentini, A.: How for 3D shape can be understood from 2D silhouettes. IEEE PAMI 17, 88–195 (1995)
Li, R.S.-Y.: Reconstruction of polygons from projections. Information Processing Letters 28, 235–240 (1988)
Prince, J.L., Willsky, A.S.: Reconstructing convex sets from support line measurements. IEEE Trans PAMI 12, 377–389 (1990)
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)
Kawamoto, K., Imiya, K.: Detection of spatial points and lines by random sampling and voting process. Pattern Recognition Letters 22, 199–207 (2001)
Solmon, D.C.: The X-ray transform. Journal of Math. Anal. and Appl. 56, 61–83 (1976)
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)
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)
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)
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© 2006 Springer-Verlag Berlin Heidelberg
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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
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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
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