### Abstract

There is an increasing demand for a new measure of convexity for discrete sets for various applications. For example, the well-known measures for h-, v-, and hv-convexity of discrete sets in binary tomography pose rigorous criteria to be satisfied. Currently, there is no commonly accepted, unified view on what type of discrete sets should be considered nearly hv-convex, or to what extent a given discrete set can be considered convex, in case it does not satisfy the strict conditions. We propose a novel directional convexity measure for discrete sets based on various properties of the configuration of 0s and 1s in the set. It can be supported by proper theory, is easy to compute, and according to our experiments, it behaves intuitively. We expect it to become a useful alternative to other convexity measures in situations where the classical definitions cannot be used.

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) |

Pages | 9-16 |

Number of pages | 8 |

Volume | 8259 LNCS |

Edition | PART 2 |

DOIs | |

Publication status | Published - 2013 |

Event | 18th Iberoamerican Congress on Pattern Recognition, CIARP 2013 - Havana, Cuba Duration: Nov 20 2013 → Nov 23 2013 |

### Publication series

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

Number | PART 2 |

Volume | 8259 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 18th Iberoamerican Congress on Pattern Recognition, CIARP 2013 |
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Country | Cuba |

City | Havana |

Period | 11/20/13 → 11/23/13 |

### Fingerprint

### Keywords

- Binary tomography
- Convexity measure
- Discrete geometry

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(PART 2 ed., Vol. 8259 LNCS, pp. 9-16). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8259 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-41827-3_2

**Directional convexity measure for binary tomography.** / Tasi, Tamás Sámuel; Nyúl, L.; Balázs, Péter.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*PART 2 edn, vol. 8259 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 8259 LNCS, pp. 9-16, 18th Iberoamerican Congress on Pattern Recognition, CIARP 2013, Havana, Cuba, 11/20/13. https://doi.org/10.1007/978-3-642-41827-3_2

}

TY - GEN

T1 - Directional convexity measure for binary tomography

AU - Tasi, Tamás Sámuel

AU - Nyúl, L.

AU - Balázs, Péter

PY - 2013

Y1 - 2013

N2 - There is an increasing demand for a new measure of convexity for discrete sets for various applications. For example, the well-known measures for h-, v-, and hv-convexity of discrete sets in binary tomography pose rigorous criteria to be satisfied. Currently, there is no commonly accepted, unified view on what type of discrete sets should be considered nearly hv-convex, or to what extent a given discrete set can be considered convex, in case it does not satisfy the strict conditions. We propose a novel directional convexity measure for discrete sets based on various properties of the configuration of 0s and 1s in the set. It can be supported by proper theory, is easy to compute, and according to our experiments, it behaves intuitively. We expect it to become a useful alternative to other convexity measures in situations where the classical definitions cannot be used.

AB - There is an increasing demand for a new measure of convexity for discrete sets for various applications. For example, the well-known measures for h-, v-, and hv-convexity of discrete sets in binary tomography pose rigorous criteria to be satisfied. Currently, there is no commonly accepted, unified view on what type of discrete sets should be considered nearly hv-convex, or to what extent a given discrete set can be considered convex, in case it does not satisfy the strict conditions. We propose a novel directional convexity measure for discrete sets based on various properties of the configuration of 0s and 1s in the set. It can be supported by proper theory, is easy to compute, and according to our experiments, it behaves intuitively. We expect it to become a useful alternative to other convexity measures in situations where the classical definitions cannot be used.

KW - Binary tomography

KW - Convexity measure

KW - Discrete geometry

UR - http://www.scopus.com/inward/record.url?scp=84893169866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893169866&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-41827-3_2

DO - 10.1007/978-3-642-41827-3_2

M3 - Conference contribution

AN - SCOPUS:84893169866

SN - 9783642418266

VL - 8259 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 9

EP - 16

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -