Journal ArticleDOI
Reconstruction of discrete sets from two absorbed projections: an algorithm
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TLDR
Two left and right horizontal absorbed projections along a single direction uniquely determine a row of a binary matrix and a polynomial time algorithm is given which reconstructs such a row.About:
This article is published in Electronic Notes in Discrete Mathematics.The article was published on 2003-03-01. It has received 5 citations till now. The article focuses on the topics: Time complexity & Logical matrix.read more
Citations
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Journal ArticleDOI
A sufficient condition for non-uniqueness in binary tomography with absorption
Attila Kuba,Murice Nivat +1 more
TL;DR: It is proved that if a binary matrix contains a special structure of 0s and 1s, called alternatively corner-connected component, then this binary matrix is non-unique with respect to its absorbed row and column sums.
Book ChapterDOI
Algebraic Discrete Tomography
Lajos Hajdu,Robert Tijdeman +1 more
TL;DR: In this article, the authors present an algebraic theory of patterns that can be applied in discrete tomography for any dimension, and show that the difference of two such patterns yields a configuration with vanishing line sums.
Journal ArticleDOI
Reconstruction of factor structures using discrete tomography method
TL;DR: The aim was to estimate the volumes of homogeneous structures whose contrast / intensity was changing with time, using only few projections of the structures using discrete tomography.
Book ChapterDOI
Two remarks on reconstructing binary vectors from their absorbed projections
Attila Kuba,Gerhard J. Woeginger +1 more
TL;DR: Two small results are proved on the reconstruction of binary matrices from their absorbed projections: if the absorption constant is the positive root of x2 + x – 1 = 0, then every row is uniquely determined by its left and right projections.
Book ChapterDOI
Emission Discrete Tomography
TL;DR: In this article, three problems of emission discrete tomography (EDT) are presented: the first problem is the reconstruction of measurable plane sets from two absorbed projections, and the second problem is reconstruction of binary matrices from their absorbed row and columns sums if the absorption coefficient is μ 0 = log((1+v/5)/2).
References
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Book
Discrete tomography : foundations, algorithms, and applications
Gabor T. Herman,Attila Kuba +1 more
TL;DR: In this paper, Kuba, Gabor T. Herman, Eilat Vardi, and Cun-Hui Zhang present an algebraic solution for Discrete Tomography.
Journal ArticleDOI
The reconstruction of two-directionally connected binary patterns from their two orthogonal projections
TL;DR: It is proved that after a finite number of iterative steps this algorithm produces all thex- andy-directionally connected binary patterns belonging to the given two projections.
Book ChapterDOI
Reconstruction of Discrete Sets with Absorption
Attila Kuba,Maurice Nivat +1 more
TL;DR: It is shown that, in this special case, the nonuniquely determined matrices contain a certain configuration of 0s and 1s, called alternatively corner-connected components, and such matrices can be transformed into each other by switchings the 1s and 0s of these components.
Journal ArticleDOI
A sufficient condition for non-uniqueness in binary tomography with absorption
Attila Kuba,Murice Nivat +1 more
TL;DR: It is proved that if a binary matrix contains a special structure of 0s and 1s, called alternatively corner-connected component, then this binary matrix is non-unique with respect to its absorbed row and column sums.
Book ChapterDOI
Reconstruction of Binary Matrices from Absorbed Projections
TL;DR: This work shows that this reconstruction problem can be linked to a 3SAT problem if the absorption is characterized with the constant � = ln((1 + �5)/2).