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

Attila Kuba, Murice Nivat

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6 Citations (Scopus)


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 μ=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.

Original languageEnglish
Pages (from-to)335-357
Number of pages23
JournalTheoretical Computer Science
Issue number2-3
Publication statusPublished - Nov 28 2005


  • Absorbed projection
  • Binary matrices
  • Discrete tomography

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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