In this paper we introduce the class of decomposable discretesets and give a polynomial algorithm for reconstructing discrete sets of this class from four projections. It is also shown that the class of decomposable discrete sets is more general than the class S′8 of hv-convex 8-but not 4-connected discrete sets which was studied in [3]. As a consequence we also get that the reconstruction from four projections in S′8can be solved in O(mn) time. © Springer-Verlag Berlin Heidelberg 2005.

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