Detail publikačního výsledku

Distributivity of a segmentation lattice

PAVLÍK, J.

Originální název

Distributivity of a segmentation lattice

Anglický název

Distributivity of a segmentation lattice

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Segmentation; Closure space; Distributive lattice

Klíčová slova v angličtině

Segmentation; Closure space; Distributive lattice

Autoři

PAVLÍK, J.

Rok RIV

2024

Vydáno

15.11.2023

Nakladatel

ELSEVIER

Místo

AMSTERDAM

ISSN

0166-218X

Periodikum

DISCRETE APPLIED MATHEMATICS

Svazek

339

Číslo

0166-218X

Stát

Nizozemsko

Strany od

300

Strany do

316

Strany počet

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"
}