# Generation and Empirical Investigation of *hv*-Convex Discrete Sets

## Abstract

One of the basic problems in discrete tomography is the reconstruction 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.

## Keywords

discrete tomography*hv*-convex discrete set decomposable configuration random generation analysis of algorithms

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