Publication detail
Topographic spaces over ordered monoids
PAVLÍK, J.
English title
Topographic spaces over ordered monoids
Type
journal article - other
Language
en
Original abstract
A topography on a set is considered to be a collection of features described by two valuations: distance and elevation. Spaces with such structure will be studied on a general level, with generalized metric (gem) and pseudometric (pseudogem). We show many pseudogem distances and characteristics, particularly those related to the elevation function. We focus on paths in the topographic images and cohesiveness (generalized continuity) of their compositions with the elevation function. Special emphasis is also placed on the spaces arising from the digital geometry which have applications in image processing.
English abstract
A topography on a set is considered to be a collection of features described by two valuations: distance and elevation. Spaces with such structure will be studied on a general level, with generalized metric (gem) and pseudometric (pseudogem). We show many pseudogem distances and characteristics, particularly those related to the elevation function. We focus on paths in the topographic images and cohesiveness (generalized continuity) of their compositions with the elevation function. Special emphasis is also placed on the spaces arising from the digital geometry which have applications in image processing.
Keywords in English
generalized metric space; ordered monoid; path connectedness; topography
Released
29.06.2015
Publisher
Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
Location
Brno
ISSN
1805-3610
Volume
18053629
Number
1
Pages from–to
31–59
Pages count
29
BIBTEX
@article{BUT128604,
author="Jan {Pavlík},
title="Topographic spaces over ordered monoids",
year="2015",
volume="18053629",
number="1",
month="June",
pages="31--59",
publisher="Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky",
address="Brno",
issn="1805-3610"
}