Abstract
The aim of this paper is to study the reconstruction of binary images from two projections using a priori images that are similar to the unknown image. Reconstruction of images from a few projections is preferred to reduce radiation hazards. It is well known that the problem of reconstructing images from a few projections is ill-posed. To handle the ill-posedness of the problem, a priori information such as convexity, connectivity and periodicity are used to limit the number of possible solutions. We use a priori images that are similar to the unknown image, to reduce the class of images having the same two projections. The a priori similar images may be obtained in many ways such as by considering images of neighboring slices or images of the same slice, taken in previous time instances. In this paper, we give a polynomial time algorithm to reconstruct binary image from two projections such that the reconstructed image is optimally close to the a priori similar images. We obtain a solution to our problem by reducing our problem to min cost integral max flow problem.
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References
Chrobak, M., Durr, C.: Reconstructing polyatomic structures from discrete X-rays: NP-completeness proof for three atoms. Theoretical Computer Science 259, 81–98 (2001)
Gale, D.: A theorem on flows in networks. Pacific. J. Math. 7, 1073–1082 (1957)
Gardner, R.J., Gritzmann, P.: Discrete tomography: Determination of finite sets by X-rays. Trans. Amer. Math. Soc. 349(9), 2271–2295 (1997)
Hermann, G.T., Kuba, A.: Discrete tomography in medical imaging. Proceedings of the IEEE 91(10), 1612–1626 (2003)
Hermann, G.T., Kuba, A.: Discrete tomography: Foundations, algorithms and applications. Birkhäuser, Basel (1999)
Irving, R.W., Jerrum, M.R.: Three-dimensional statistical data security problems. SIAM Journal of Computing 23(1), 170–184 (1994)
Kiesielolowski, C., Schwander, P., Baumann, F.H., Seibt, M., Kim, Y., Ourmazd, A.: An approach to quantitative high-resolution transmission electron microscopy of crystalline materials. Ultramicroscopy 58(9), 131–135 (1995)
Kuba, A., Rusko, L., Rodek, L., Kiss, Z.: Preliminary studies of discrete tomography in neutron imaging. IEEE Transactions on Nuclear Science 52(1), 375–379 (2005)
Matej, S., Vardi, A., Hermann, G.T., Vardi, E.: Binary tomography using Gibbs priors. In: Discrete tomography: Foundations, algorithms, and applications, Birkhauser, Basel (1999)
Prause, G.P.M., Onnasch, D.G.W.: Binary reconstruction of the heart chambers from biplane angiographic image sequence. IEEE Transactions on Medical Imaging 15(4), 532–559 (1996)
Ryser, H.J.: Combinatorial properties of matrices of zeroes and ones. Canad. J. Math. 9, 371–377 (1957)
Shliferstien, A.R., Chien, Y.T.: Switching components and the ambiguity problem in the reconstruction of pictures from their projections. Pattern Recognition 10(5), 327–340 (1978)
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Masilamani, V., Krithivasan, K. (2008). A Min-Cost-Max-Flow Based Algorithm for Reconstructing Binary Image from Two Projections Using Similar Images. In: Brimkov, V.E., Barneva, R.P., Hauptman, H.A. (eds) Combinatorial Image Analysis. IWCIA 2008. Lecture Notes in Computer Science, vol 4958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78275-9_36
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DOI: https://doi.org/10.1007/978-3-540-78275-9_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78274-2
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