Paper Info
Title
On the non-additive sets of uniqueness in a finite grid
Abstract
In Discrete Tomography there is a wide literature concerning (weakly) bad configurations. These occur in dealing with several questions concerning the important issues of uniqueness and additivity. Discrete lattice sets which are additive with respect to a given set S of lattice directions are uniquely determined by X-rays in the direction of S. These sets are characterized by the absence of weakly bad configurations for S. On the other side, if a set has a bad configuration with respect to S, then it is not uniquely determined by the X-rays in the directions of S, and consequently it is also non-additive. Between these two opposite situations there are also the non-additive sets of uniqueness, which deserve interest in Discrete Tomography, since their unique reconstruction cannot be derived via the additivity property. In this paper we wish to investigate possible interplays among such notions in a given lattice grid $\mathcal{A}$, under X-rays taken in directions belonging to a set S of four lattice directions.
Year
DOI
Venue
2013
10.1007/978-3-642-37067-0_25
DGCI
Keywords
Field
DocType
important issue,bad configuration,Discrete Tomography,additivity property,non-additive set,discrete lattice set,weakly bad configuration,opposite situation,lattice direction,finite grid,lattice grid
Uniqueness,Discrete mathematics,Additive function,Combinatorics,Lattice (order),Discrete tomography,Mathematics,Grid
Conference
Citations 
PageRank 
References 
6
0.48
12
Authors
3
Name
Order
Citations
PageRank
Sara Brunetti112216.23
Paolo Dulio23112.39
Carla Peri3246.73