Publication result detail

Distributivity of a segmentation lattice

PAVLÍK, J.

Original Title

Distributivity of a segmentation lattice

English Title

Distributivity of a segmentation lattice

Type

WoS Article

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.

English 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

Key words in English

Segmentation; Closure space; Distributive lattice

Authors

PAVLÍK, J.

RIV year

2024

Released

15.11.2023

Publisher

ELSEVIER

Location

AMSTERDAM

ISBN

0166-218X

Periodical

DISCRETE APPLIED MATHEMATICS

Volume

339

Number

0166-218X

State

Kingdom of the Netherlands

Pages from

300

Pages to

316

Pages count

17

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"
}