In this paper we consider the uniqueness issues in Discrete Tomography. A special class of geometric objects, widely considered in the literature, is represented by additive sets. These sets are uniquely determined by their X-rays, and they are also reconstructible in polynomial time by use of linear programming. Recently, additivity has been extended to J-additivity to provide a more general treatment of known concepts and results. A further generalization of additivity, called bounded additivity is obtained by restricting to sets contained in a given orthogonal box. In this work, we investigate these two generalizations from a geometrical point of view and analyze the interplay between them.

Brunetti, S., Peri, C., On J-additivity and bounded additivity, <<FUNDAMENTA INFORMATICAE>>, 2016; 2016 /146 (2): 185-195. [doi:10.3233/FI-2016-1380] [http://hdl.handle.net/10807/87298]

On J-additivity and bounded additivity

Peri, Carla
Secondo
2016

Abstract

In this paper we consider the uniqueness issues in Discrete Tomography. A special class of geometric objects, widely considered in the literature, is represented by additive sets. These sets are uniquely determined by their X-rays, and they are also reconstructible in polynomial time by use of linear programming. Recently, additivity has been extended to J-additivity to provide a more general treatment of known concepts and results. A further generalization of additivity, called bounded additivity is obtained by restricting to sets contained in a given orthogonal box. In this work, we investigate these two generalizations from a geometrical point of view and analyze the interplay between them.
Inglese
Brunetti, S., Peri, C., On J-additivity and bounded additivity, <>, 2016; 2016 /146 (2): 185-195. [doi:10.3233/FI-2016-1380] [http://hdl.handle.net/10807/87298]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/87298
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