### Abstract

One important class of discrete sets where the reconstruction from two given projections can be solved in polynomial time is the class of hv-convex 8-connected sets. The worst case complexity of the fastest algorithm known so far for solving the problem is of O(mn· min{m^{2},n^{2}}) [2]. However, as it is shown, in the case of 8-connected but not 4-connected sets we can give an algorithm with worst case complexity of O(mn·min{m,n}) by identifying the so-called S_{4}-components of the discrete set. Experimental results are also presented in order to investigate the average execution time of our algorithm.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Ingela Nystrom, Gabriella Sanniti di Baja, Stina Svensson |

Publisher | Springer Verlag |

Pages | 388-397 |

Number of pages | 10 |

ISBN (Electronic) | 3540204997, 9783540204992 |

DOIs | |

Publication status | Published - 2003 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2886 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Keywords

- Convex and connected discrete set
- Discrete tomography
- Reconstruction

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Balázs, P., Balogh, E., & Kuba, A. (2003). A fast algorithm for reconstructing hv-convex 8-connected but not 4-connected discrete sets. In I. Nystrom, G. S. di Baja, & S. Svensson (Eds.),

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 388-397). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2886). Springer Verlag. https://doi.org/10.1007/978-3-540-39966-7_37