Morphological adjunctions represented by matrices in max-plus algebra for signal and image processing

DGMM 2022, IAPR Second International Conference on Discrete Geometry and Mathematical Morphology, Oct 2022, Strasbourg, France In discrete signal and image processing, many dilations and erosions can be written as the max-plus and min-plus product of a matrix on a vector. Previous studies considered...

Full description

Saved in:
Bibliographic Details
Main Authors Blusseau, Samy, Velasco-Forero, Santiago, Angulo, Jesus, Bloch, Isabelle
Format Journal Article
LanguageEnglish
Published 28.07.2022
Subjects
Mathematics - Operator Algebras
Mathematics - Representation Theory
Mathematics - Spectral Theory
Online AccessGet full text
DOI10.48550/arxiv.2207.13926

Cover

More Information
Summary:DGMM 2022, IAPR Second International Conference on Discrete Geometry and Mathematical Morphology, Oct 2022, Strasbourg, France In discrete signal and image processing, many dilations and erosions can be written as the max-plus and min-plus product of a matrix on a vector. Previous studies considered operators on symmetrical, unbounded complete lattices, such as Cartesian powers of the completed real line. This paper focuses on adjunctions on closed hypercubes, which are the complete lattices used in practice to represent digital signals and images. We show that this constrains the representing matrices to be doubly-0-astic and we characterise the adjunctions that can be represented by them. A graph interpretation of the defined operators naturally arises from the adjacency relationship encoded by the matrices, as well as a max-plus spectral interpretation.
DOI:10.48550/arxiv.2207.13926