In some circumstances it is preferable, instead of modeling the real world as a continuous space, facing directly the discrete problem. It may happen in the framework of Tomography, where we can employ several tools relying on discrete models: this is Discrete Tomography. In this work we start our investigation from a limit case of the discretization process, namely the grid model, and then show how we can extend our approach to a more general framework. It turns out that, if we employ X-rays in the strip model whose width is under a given threshold, uniqueness of reconstruction, which came from exploiting the line structure of X-rays in the grid model, is still achieved. Moreover, we wrote a program which enumerates all possible sets of four valid directions which ensure uniqueness of reconstruction in a given lattice grid.

Brocchi, S., Dulio, P., Pagani, S. M. C., Extension to fat X-rays of uniqueness results for the grid model in discrete tomography, Comunicazione, in RECENT ADVANCES in SYSTEMS, (Zakynthos, 2015-07-16), Valeri Mladenov, Sofia 2015: 393-397 [http://hdl.handle.net/10807/78112]

Extension to fat X-rays of uniqueness results for the grid model in discrete tomography

Dulio, Paolo;Pagani, Silvia Maria Carla
2015

Abstract

In some circumstances it is preferable, instead of modeling the real world as a continuous space, facing directly the discrete problem. It may happen in the framework of Tomography, where we can employ several tools relying on discrete models: this is Discrete Tomography. In this work we start our investigation from a limit case of the discretization process, namely the grid model, and then show how we can extend our approach to a more general framework. It turns out that, if we employ X-rays in the strip model whose width is under a given threshold, uniqueness of reconstruction, which came from exploiting the line structure of X-rays in the grid model, is still achieved. Moreover, we wrote a program which enumerates all possible sets of four valid directions which ensure uniqueness of reconstruction in a given lattice grid.
Inglese
RECENT ADVANCES in SYSTEMS
9th International Conference on Systems (part of CSCC 2015)
Zakynthos
Comunicazione
16-lug-2015
20-mag-2016
Valeri Mladenov
Brocchi, S., Dulio, P., Pagani, S. M. C., Extension to fat X-rays of uniqueness results for the grid model in discrete tomography, Comunicazione, in RECENT ADVANCES in SYSTEMS, (Zakynthos, 2015-07-16), Valeri Mladenov, Sofia 2015: 393-397 [http://hdl.handle.net/10807/78112]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/78112
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