Detail publikace

Distributivity of a segmentation lattice

PAVLÍK, J.

Anglický název

Distributivity of a segmentation lattice

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

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 anglicky

Segmentation; Closure space; Distributive lattice

Vydáno

15.11.2023

Nakladatel

ELSEVIER

Místo

AMSTERDAM

ISSN

0166-218X

Ročník

339

Číslo

0166-218X

Strany od–do

300–316

Počet stran

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"
}