Network Flow Algorithms for Discrete Tomography
There exists an elegant correspondence between the problem of reconstructing a 0-1 lattice image from two of its projections and the problem of finding a maximum flow in a certain graph. In this chapter we describe how network flow algorithms can be used to solve a variety of problems from discrete tomography. First, we describe the network flow approach for two projections and several of its generalizations. Subsequently, we present an algorithm for reconstructing 0-1 images from more than two projections. The approach is extended to the reconstruction of 3D images and images that do not have an intrinsic lattice structure.
KeywordsOriginal Image Lattice Line Lattice Direction Point Edge Reconstruction Problem
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- 1.Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms and Applications. Prentice-Hall, Englewood Cliffs, NJ (1993).Google Scholar
- 3.Batenburg, K.J.: Reconstructing binary images from discrete X-rays. Tech. Rep. PNA-E0418, CWI, Amsterdam, The Netherlands (2004).Google Scholar
- 4.Bertsekas, D.P., Tseng, P.: RELAX-IV: A faster version of the RELAX code for solving minimum cost flow problems. LIDS Technical Report LIDS-P-2276, MIT, Cambridge, MA (1994).Google Scholar
- 5.Dürr, C.: Ryser’s algorithm can be implemented in linear time. http://www.lix.polytechnique.fr/~durr/Xray/Ryser/.
- 9.Goldberg, A.V.: An efficient implementation of a scaling minimum-cost flow algorithm. J. Algebra, 22, 1–29 (1997).Google Scholar
- 16.Jinschek, J.R., Calderon, H.A., Batenburg, K.J., Radmilovic, V., Kisielowski, C.: Discrete tomography of Ga and InGa particles from HREM image simulation and exit wave reconstruction. Mat. Res. Soc. Symp. Proc., 839, 4.5.1–4.5.6 (2004).Google Scholar
- 17.Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. SIAM, Philadelphia, PA (2001).Google Scholar
- 18.Mohammad-Djafari, A.: Binary polygonal shape image reconstruction from a small number of projections. ELEKTRIK, 5, 127–139 (1997).Google Scholar