TY - GEN
T1 - Local uniqueness under two directions in discrete tomography: A graph-theoretical approach
AU - Pagani, Silvia Maria Carla
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Discrete tomography
KW - Graph
KW - Lattice direction
KW - Region of uniqueness
KW - Uniqueness of reconstruction
KW - Discrete tomography
KW - Graph
KW - Lattice direction
KW - Region of uniqueness
KW - Uniqueness of reconstruction
UR - http://hdl.handle.net/10807/140138
UR - https://www.springer.com/series/558
U2 - 10.1007/978-3-030-20867-7_8
DO - 10.1007/978-3-030-20867-7_8
M3 - Conference contribution
SN - 978-3-030-20866-0
VL - 11564
T3 - LECTURE NOTES IN COMPUTER SCIENCE
SP - 96
EP - 107
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
T2 - 14th International Symposium on Mathematical Morphology, ISMM 2019
Y2 - 8 July 2019 through 10 July 2019
ER -