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 mathematically interesting when the absorbed projection of a matrix element is the same as the absorbed projection of the next two consecutive elements 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.

• Type: Conference
• Year: 2000
• Where: DGCI
• Authors: Attila Kuba, Maurice Nivat
• Keywords: Absorbed Projection, Absorbed Row, DGCI 2000, Discrete Geometry, Reconstruct Binary Matrices