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.
Pagani, S. M. C., Local uniqueness under two directions in discrete tomography: A graph-theoretical approach, Paper, in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), (Saarbrücken, 08-10 July 2019), Springer Verlag, Cham 2019:<<LECTURE NOTES IN COMPUTER SCIENCE>>,11564 96-107. 10.1007/978-3-030-20867-7_8 [http://hdl.handle.net/10807/140138]
Local uniqueness under two directions in discrete tomography: A graph-theoretical approach
Pagani, Silvia Maria Carla
Primo
2019
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.
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