### Abstract

The reconstruction of hv-convex binary matrices from their absorbed projections is considered. Although this problem is NP-hard if the non-absorbed row and column sums are available, it is proved that such a reconstruction problem can be solved in polynomial time from absorbed projections when the absorption is represented by β=(1+√5)/2. Also a reconstruction algorithm is given to determine the whole structure of hv-convex binary matrices from such projections.

Original language | English |
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Pages (from-to) | 137-148 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 139 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Apr 30 2004 |

### Fingerprint

### Keywords

- Absorbed projections
- Discrete tomography
- Hv-convex binary matrices
- Numeration systems

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Applied Mathematics*,

*139*(1-3), 137-148. https://doi.org/10.1016/j.dam.2002.11.001

**Reconstruction of hv-convex binary matrices from their absorbed projections.** / Kuba, A.; Nagy, Antal; Balogh, Emese.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 139, no. 1-3, pp. 137-148. https://doi.org/10.1016/j.dam.2002.11.001

}

TY - JOUR

T1 - Reconstruction of hv-convex binary matrices from their absorbed projections

AU - Kuba, A.

AU - Nagy, Antal

AU - Balogh, Emese

PY - 2004/4/30

Y1 - 2004/4/30

N2 - The reconstruction of hv-convex binary matrices from their absorbed projections is considered. Although this problem is NP-hard if the non-absorbed row and column sums are available, it is proved that such a reconstruction problem can be solved in polynomial time from absorbed projections when the absorption is represented by β=(1+√5)/2. Also a reconstruction algorithm is given to determine the whole structure of hv-convex binary matrices from such projections.

AB - The reconstruction of hv-convex binary matrices from their absorbed projections is considered. Although this problem is NP-hard if the non-absorbed row and column sums are available, it is proved that such a reconstruction problem can be solved in polynomial time from absorbed projections when the absorption is represented by β=(1+√5)/2. Also a reconstruction algorithm is given to determine the whole structure of hv-convex binary matrices from such projections.

KW - Absorbed projections

KW - Discrete tomography

KW - Hv-convex binary matrices

KW - Numeration systems

UR - http://www.scopus.com/inward/record.url?scp=1842736980&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842736980&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2002.11.001

DO - 10.1016/j.dam.2002.11.001

M3 - Article

AN - SCOPUS:1842736980

VL - 139

SP - 137

EP - 148

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1-3

ER -