Publication detail

Distributivity of a segmentation lattice

PAVLÍK, J.

English title

Distributivity of a segmentation lattice

Type

journal article in Web of Science

Language

en

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 in English

Segmentation; Closure space; Distributive lattice

Released

15.11.2023

Publisher

ELSEVIER

Location

AMSTERDAM

ISSN

0166-218X

Volume

339

Number

0166-218X

Pages from–to

300–316

Pages count

17

BIBTEX


@article{BUT186835,
  author="Jan {Pavlík},
  title="Distributivity of a segmentation lattice",
  year="2023",
  volume="339",
  number="0166-218X",
  month="November",
  pages="300--316",
  publisher="ELSEVIER",
  address="AMSTERDAM",
  issn="0166-218X"
}