Reconstruction of Discrete Sets with Absorption
A generalization of a classical discrete tomography problem is considered: Reconstruct binary matrices from their absorbed row and columns sums, i.e., when some known absorption is supposed. It is math-ematically interesting when the absorbed projection of a matrix element is the same as the absorbed projection of the next two consecutive el-ements together. We show that, in this special case, the non-uniquely determined matrices contain a certain configuration of 0s and 1s, called alternatively corner-connected components. Furthermore, such matrices can be transformed into each other by switchings the 0s and 1s of these components.
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