### Abstract

A reduction transforms a binary picture only by deleting some black points to white ones. Sequential reductions traverse the black points of a picture, and focus on the actually visited point for possible deletion, while parallel reductions delete all ‘deletable’ black points simultaneously. Two reductions are called equivalent if they produce the same result for each input picture. A deletion rule is said to be equivalent if it provides a pair of equivalent sequential and parallel reductions. Thinning and shrinking algorithms iterate reductions until no points are deleted. If a black point is not deleted in an iteration step, it is taken into consideration again in the next step. This work examine fixpoints of iterated reductions with equivalent deletion rules, i.e., ‘survival’ points whose rechecking is not needed in the remaining iterations.

Original language | English |
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Title of host publication | Combinatorial Image Analysis - 19th International Workshop, IWCIA 2018, Proceedings |

Editors | Reneta P. Barneva, João Manuel R.S Tavares, Valentin E. Brimkov |

Publisher | Springer Verlag |

Pages | 17-27 |

Number of pages | 11 |

ISBN (Print) | 9783030052874 |

DOIs | |

Publication status | Published - Jan 1 2018 |

Event | 19th International Workshop on Combinatorial Image Analysis, IWCIA 2018 - Porto, Portugal Duration: Nov 22 2018 → Nov 24 2018 |

### 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 | 11255 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 19th International Workshop on Combinatorial Image Analysis, IWCIA 2018 |
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Country | Portugal |

City | Porto |

Period | 11/22/18 → 11/24/18 |

### Fingerprint

### Keywords

- Digital geometry and topology
- Equivalent reduction
- Thinning

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Image Analysis - 19th International Workshop, IWCIA 2018, Proceedings*(pp. 17-27). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11255 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-05288-1_2