Abstract
In some applications, the tomographic reconstruction is not an end in itself. When the goal is rather to gather information about the object being studied, the question is if it is more interesting to directly extract these information from the projections without the reconstructing step. We would then know if less projections are needed to directly get the information than to reconstruct the object. In this paper, we address the problem of extracting quantitative information about an object namely an estimation of its area, an upper and a lower bound to the perimeter given its projections from point sources.
This work was supported by the Agence Nationale de la Recherche through contract ANR-2010-BLAN-0205-01.
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Abdmouleh, F., Daurat, A., Tajine, M.: Discrete Q-Convex Sets Reconstruction from Discrete Point X-Rays. In: Aggarwal, J.K., Barneva, R.P., Brimkov, V.E., Koroutchev, K.N., Korutcheva, E.R. (eds.) IWCIA 2011. LNCS, vol. 6636, pp. 321–334. Springer, Heidelberg (2011)
Balázs, P., Gara, M.: Decision Trees in Binary Tomography for Supporting the Reconstruction of hv-Convex Connected Images. In: Blanc-Talon, J., Bourennane, S., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2008. LNCS, vol. 5259, pp. 433–443. Springer, Heidelberg (2008)
Baudrier, É., Tajine, M., Daurat, A.: Convex-Set Perimeter Estimation from Its Two Projections. In: Aggarwal, J.K., Barneva, R.P., Brimkov, V.E., Koroutchev, K.N., Korutcheva, E.R. (eds.) IWCIA 2011. LNCS, vol. 6636, pp. 284–297. Springer, Heidelberg (2011)
Osserman, R.: The isoperimetric inequality. B. Am. Soc. 84, 1182–1238 (1978)
Van Dalen, B.: Boundary length of reconstructions in discrete tomography. SIAM J. Discrete Math. 25, 645–659 (2011)
Volčič, A.: A three-point solution to Hammer’s X-ray problem. J. London Math. Soc. 34, 349–359 (1986)
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Abdmouleh, F., Tajine, M. (2013). Reconstruction of Quantitative Properties from X-Rays. In: Gonzalez-Diaz, R., Jimenez, MJ., Medrano, B. (eds) Discrete Geometry for Computer Imagery. DGCI 2013. Lecture Notes in Computer Science, vol 7749. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37067-0_24
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DOI: https://doi.org/10.1007/978-3-642-37067-0_24
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