Generation and Empirical Investigation of hv-Convex Discrete Sets
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.
Keywordsdiscrete tomography hv-convex discrete set decomposable configuration random generation analysis of algorithms
- 1.Balázs, P.: A decomposition technique for reconstructing discrete sets from four projections. Image and Vision Computing, accepted.Google Scholar
- 2.Balázs, P.: On the ambiguity of reconstructing hv-convex binary matrices with decomposable configurations. Acta Cybernetica, submitted.Google Scholar
- 3.Balázs, P.: Reconstruction of discrete sets from their projections using geometrical priors. Doctoral Dissertation at the University of Szeged (in preparation)Google Scholar
- 16.Shoup, V.: NTL: A library for doing number theory, http://www.shoup.net/ntl
- 17.Sloane, N.J.A.: The on-line encyclopedia of integer sequences, http://www.research.att.com/~njas/sequences/