A sufficient condition for non-uniqueness in binary tomography with absorption

Abstract

A new kind of discrete tomography problem is introduced: the reconstruction of discrete sets from their absorbed projections. A special case of this problem is discussed, namely, the uniqueness of the binary matrices with respect to their absorbed row and column sums when the absorption coefficient is = log((1+√5)/2). It is proved that if a binary matrix contains a special structure of 0s and 1s, called alternatively corner-connected component, then this binary matrix is non-unique with respect to its absorbed row and column sums. Since it has been proved in another paper [A. Kuba, M. Nivat, Reconstruction of discrete sets with absorption, Linear Algebra Appl. 339 (2001) 171–194] that this condition is also necessary, the existence of alternatively corner-connected component in a binary matrix gives a characterization of the non-uniqueness in this case of absorbed projections. © 2005 Elsevier B.V. All rights reserved.

DOI: 10.1016/j.tcs.2005.08.024

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@article{Kuba2005ASC, title={A sufficient condition for non-uniqueness in binary tomography with absorption}, author={Attila Kuba and Maurice Nivat}, journal={Theor. Comput. Sci.}, year={2005}, volume={346}, pages={335-357} }