### Abstract

The concept of a simple point is well known in digital topology: a black point in a binary picture is called a simple point if its deletion preserves topology. This paper introduces the notion of a simplifier point: a black point in a binary picture is simplifier if it is simple, and its deletion turns a non-simple border point into simple. We show that simplifier points are line end points for both (8, 4) and (4, 8) pictures on the square grid. Our result makes efficient implementation of endpoint-based topology-preserving 2D thinning algorithms possible.

Original language | English |
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Title of host publication | Combinatorial Image Analysis - 18th International Workshop, IWCIA 2017, Proceedings |

Publisher | Springer Verlag |

Pages | 3-15 |

Number of pages | 13 |

ISBN (Print) | 9783319591070 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Event | 18th International Workshop on Combinatorial Image Analysis, IWCIA 2017 - Plovdiv, Bulgaria Duration: Jun 19 2017 → Jun 21 2017 |

### 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 | 10256 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 18th International Workshop on Combinatorial Image Analysis, IWCIA 2017 |
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Country | Bulgaria |

City | Plovdiv |

Period | 6/19/17 → 6/21/17 |

### Fingerprint

### Keywords

- Digital topology
- Discrete geometry
- Thinning algorithms
- Topology preservation

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Image Analysis - 18th International Workshop, IWCIA 2017, Proceedings*(pp. 3-15). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10256 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-59108-7_1

**Simplifier points in 2D binary images.** / Palágyi, Kálmán.

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

*Combinatorial Image Analysis - 18th International Workshop, IWCIA 2017, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10256 LNCS, Springer Verlag, pp. 3-15, 18th International Workshop on Combinatorial Image Analysis, IWCIA 2017, Plovdiv, Bulgaria, 6/19/17. https://doi.org/10.1007/978-3-319-59108-7_1

}

TY - GEN

T1 - Simplifier points in 2D binary images

AU - Palágyi, Kálmán

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The concept of a simple point is well known in digital topology: a black point in a binary picture is called a simple point if its deletion preserves topology. This paper introduces the notion of a simplifier point: a black point in a binary picture is simplifier if it is simple, and its deletion turns a non-simple border point into simple. We show that simplifier points are line end points for both (8, 4) and (4, 8) pictures on the square grid. Our result makes efficient implementation of endpoint-based topology-preserving 2D thinning algorithms possible.

AB - The concept of a simple point is well known in digital topology: a black point in a binary picture is called a simple point if its deletion preserves topology. This paper introduces the notion of a simplifier point: a black point in a binary picture is simplifier if it is simple, and its deletion turns a non-simple border point into simple. We show that simplifier points are line end points for both (8, 4) and (4, 8) pictures on the square grid. Our result makes efficient implementation of endpoint-based topology-preserving 2D thinning algorithms possible.

KW - Digital topology

KW - Discrete geometry

KW - Thinning algorithms

KW - Topology preservation

UR - http://www.scopus.com/inward/record.url?scp=85020452641&partnerID=8YFLogxK

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U2 - 10.1007/978-3-319-59108-7_1

DO - 10.1007/978-3-319-59108-7_1

M3 - Conference contribution

AN - SCOPUS:85020452641

SN - 9783319591070

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

SP - 3

EP - 15

BT - Combinatorial Image Analysis - 18th International Workshop, IWCIA 2017, Proceedings

PB - Springer Verlag

ER -