On an Application of Lattice Integral Transforms in Image Processing

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302HC1" target="_blank" >RIV/61988987:17610/22:A2302HC1 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2227-7390/10/21/4077?type=check_update&version=1" target="_blank" >https://www.mdpi.com/2227-7390/10/21/4077?type=check_update&version=1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math10214077" target="_blank" >10.3390/math10214077</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On an Application of Lattice Integral Transforms in Image Processing

Popis výsledku v původním jazyce

The lattice integral transforms have been introduced to generalize lower and upper fuzzy transforms for lattice-valued functions that are used to approximate original functions from below and above. They are defined in complete analogy with classical integral transforms, particularly, the product of a lattice-valued function and a fuzzy relation called the integral kernel is integrated by a Sugeno-like fuzzy integral. In the article, we first investigate the conditions under which lattice integral transforms preserve (reverse) constant functions, which appears to be a fundamental presumption for a successful approximation of lattice-valued functions. Further, we show how the lattice integral transforms can be applied in image processing, more specifically, in non-linear filtering, compression/decompression, and opening/closing of images. We demonstrate that the filters based on integral transforms generalize the popular median filter as well as minimum and maximum filters, and also opening and closing defined using fuzzy morphological erosion and dilation. We illustrate the proposed methods in various selected images.

Název v anglickém jazyce

On an Application of Lattice Integral Transforms in Image Processing

Popis výsledku anglicky

The lattice integral transforms have been introduced to generalize lower and upper fuzzy transforms for lattice-valued functions that are used to approximate original functions from below and above. They are defined in complete analogy with classical integral transforms, particularly, the product of a lattice-valued function and a fuzzy relation called the integral kernel is integrated by a Sugeno-like fuzzy integral. In the article, we first investigate the conditions under which lattice integral transforms preserve (reverse) constant functions, which appears to be a fundamental presumption for a successful approximation of lattice-valued functions. Further, we show how the lattice integral transforms can be applied in image processing, more specifically, in non-linear filtering, compression/decompression, and opening/closing of images. We demonstrate that the filters based on integral transforms generalize the popular median filter as well as minimum and maximum filters, and also opening and closing defined using fuzzy morphological erosion and dilation. We illustrate the proposed methods in various selected images.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centrum pro výzkum a vývoj metod umělé intelligence v automobilovém průmyslu regionu</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematics

ISSN

22277390

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

21

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

30

Strana od-do

1-30

Kód UT WoS článku

000885813700001

EID výsledku v databázi Scopus

2-s2.0-85141822888