Local uniqueness under two directions in discrete tomography: A graph-theoretical approach

Risultato della ricerca: Contributo in libroContributo a convegno

Abstract

The goal of discrete tomography is to reconstruct an image, seen as a finite set of pixels, by knowing its projections along given directions. Uniqueness of reconstruction cannot be guaranteed in general, because of the existence of the switching components. Therefore, instead of considering the uniqueness problem for the whole image, in this paper we focus on local uniqueness, i.e., we seek what pixels have uniquely determined value. Two different kinds of local uniqueness are presented: one related to the structure of the directions and of the grid supporting the image, having as a sub-case the region of uniqueness (ROU), and the other one depending on the available projections. In the case when projections are taken along two lattice directions, both kinds of uniqueness have been characterized in a graph-theoretical reformulation. This paper is intended to be a starting point in the construction of connections between pixels with uniquely determined value and graphs.
Lingua originaleEnglish
Titolo della pubblicazione ospiteLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pagine96-107
Numero di pagine12
Volume11564
DOI
Stato di pubblicazionePubblicato - 2019
Evento14th International Symposium on Mathematical Morphology, ISMM 2019 - Saarbrücken
Durata: 8 lug 201910 lug 2019

Serie di pubblicazioni

NomeLECTURE NOTES IN COMPUTER SCIENCE

Convegno

Convegno14th International Symposium on Mathematical Morphology, ISMM 2019
CittàSaarbrücken
Periodo8/7/1910/7/19

Keywords

  • Discrete tomography
  • Graph
  • Lattice direction
  • Region of uniqueness
  • Uniqueness of reconstruction

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