### 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.

Original language | English |
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Pages (from-to) | 335-357 |

Number of pages | 23 |

Journal | Theoretical Computer Science |

Volume | 346 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - Nov 28 2005 |

### Keywords

- Absorbed projection
- Binary matrices
- Discrete tomography

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Theoretical Computer Science*,

*346*(2-3), 335-357. https://doi.org/10.1016/j.tcs.2005.08.024