Publication detail

Distributivity of a segmentation lattice

PAVLÍK, J.

Original Title

Type

journal article in Web of Science

Language

English

Original Abstract

Closure spaces, namely the finite ones, with closed singletons are studied on the level of segmentations - partitions of the space into closed subsets. Segmentations form a lattice and we study spaces for which this lattice is distributive. Studying these spaces may help understanding mathematical background for segmentation of a digital image. A crucial notion is that of connectively irreducible sets which can be defined in any finite closure space. The paper provides several equivalent conditions for segmentational distributivity in terms of triples of closed sets, connected systems of closed sets, property of induced closure operator on down-sets of connectively irreducible sets, and finally by restriction (or disability) of existence of certain sublattices.& COPY; 2023 Elsevier B.V. All rights reserved.

Keywords

Segmentation; Closure space; Distributive lattice

Authors

PAVLÍK, J.

Released

15. 11. 2023

Publisher

ELSEVIER

Location

AMSTERDAM

ISBN

0166-218X

Periodical

Discrete Applied Mathematics

Year of study

339

Number

0166-218X

State

Kingdom of the Netherlands

Pages from

300

Pages to

316

Pages count

URL

https://doi.org/10.1016/j.dam.2023.06.028

BibTex

@article{BUT186835,
  author="Jan {Pavlík}",
  title="Distributivity of a segmentation lattice",
  journal="Discrete Applied Mathematics",
  year="2023",
  volume="339",
  number="0166-218X",
  pages="300--316",
  doi="10.1016/j.dam.2023.06.028",
  issn="0166-218X",
  url="https://doi.org/10.1016/j.dam.2023.06.028"
}