Discrete tomography determination of bounded lattice sets from four X-rays

作者：Brunetti S^*; Dulio P; Peri C

来源：Discrete Applied Mathematics, 2013, 161(15): 2281-2292.

DOI：10.1016/j.dam.2012.09.010

• Discrete tomography
• Unique reconstruction
• Generating functions

We deal with the question of uniqueness, namely to decide when an unknown finite set of points in Z(2) is uniquely determined by its X-rays corresponding to a given set S of lattice directions. In Hajdu (2005) [11] proved that for any fixed rectangle A in Z(2) there exists a non trivial set S of four lattice directions, depending only on the size of A, such that any two subsets of A can be distinguished by means of their X-rays taken in the directions in S. The proof was given by explicitly constructing a suitable set S in any possible case. We improve this result by showing that in fact whole families of suitable sets of four directions can be found, for which we provide a complete characterization. This permits us to easily solve some related problems and the computational aspects.

• 出版日期2013-10