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

  • Authors:

  • Attila Kuba;Murice Nivat

  • Affiliations:

  • Department of Image Processing and Computer Graphics, University of Szeged, Szeged, Hungary;Laboratoire d'Informatique Algorithmique: Fondements et Applications, Université Paris Denis-Diderot, Paris, France

  • Venue:
  • Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
  • Year:
  • 2005

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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 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.