01787nas a2200169   4500008004100000020002200041022001400063245007000077210006900147260004900216300001400265520115400279100002001433700002801453700003001481856010601511       2007                        eng d  a978-3-540-73039-2  a0302-974300aGeneration and empirical investigation of hv-Convex discrete sets0 aGeneration and empirical investigation of hvConvex discrete sets  aAalborg, DenmarkbSpringer VerlagcJune 2007  a344 - 3533 a<p>One of the basic problems in discrete tomography is thereconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfils some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. Since the reconstruction from two projections in the class of so-called hv-convex sets is NP-hard this class is suitable to test the efficiency of newly developed reconstruction algorithms. However, until now no method was known to generate sets of this class from uniform random distribution and thus only ad hoc comparison of several reconstruction techniques was possible. In this paper we first describe a method to generate some special hv-convex discrete sets from uniform random distribution. Moreover, we show that the developed generation technique can easily be adapted to other classes of discrete sets, even for the whole class of hv- convexes. Several statistics are also presented which are of great importance in the analysis of algorithms for reconstructing hv-convex sets. © Springer-Verlag Berlin Heidelberg 2007.</p>1 aBalázs, Péter1 aErsbøll, Bjarne, Kjær1 aPedersen, Kim, Steenstrup  uhttps://www.inf.szte.hu/publication/generation-and-empirical-investigation-of-hv-convex-discrete-sets