Affiliations: [a] Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Via Roma, 56, 53100 Siena - Italy. sara.brunetti@unisi.it | [b] Università Cattolica S. C., Via Emilia Parmense, 84, 29122 Piacenza - Italy. carla.peri@unicatt.it
Correspondence:
[*]
Address for correspondence: Università Cattolica S. C., Via Emilia Parmense, 84, 29122 Piacenza, Italy.
Note: [†] Networking support was provided by the EXTREMA COST Action MP1207.
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.
Keywords: Additive set, weakly bad configuration, uniqueness problem, X-ray
