### Abstract

A general operator may transform a binary picture by changing both black and white points. Sequential operators traverse the points of a picture, and consider a single point for possible alteration, while parallel operators can alter a set of points simultaneously. An orderindependent transition function yields the same sequential operator for arbitrary visiting orders. Two operators are called equivalent if they produce the same result for each input picture. A transition function is said to be equivalent if it specifies a pair of equivalent parallel and sequential operators. This paper establishes a necessary and sufficient condition for order-independent transition functions, a sufficient criterion for equivalent transition functions, and a sufficient condition for topologypreserving parallel general operators in arbitrary binary pictures.

Original language | English |
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Title of host publication | Progress in Pattern Recognition Image Analysis, Computer Vision and Applications - 19th Iberoamerican Congress, CIARP 2014, Proceedings |

Editors | Eduardo Bayro-Corrochano, Edwin Hancock |

Publisher | Springer Verlag |

Pages | 22-29 |

Number of pages | 8 |

ISBN (Electronic) | 9783319125671 |

DOIs | |

Publication status | Published - 2014 |

Event | 19th Iberoamerican Congress on Pattern Recognition, CIARP 2014 - Puerto Vallarta, Mexico Duration: Nov 2 2014 → Nov 5 2014 |

### 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 | 8827 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 19th Iberoamerican Congress on Pattern Recognition, CIARP 2014 |
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Country | Mexico |

City | Puerto Vallarta |

Period | 11/2/14 → 11/5/14 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Progress in Pattern Recognition Image Analysis, Computer Vision and Applications - 19th Iberoamerican Congress, CIARP 2014, Proceedings*(pp. 22-29). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8827). Springer Verlag. https://doi.org/10.1007/978-3-319-12568-8_3