Generation and Empirical Investigation of hv-Convex Discrete Sets

  • Péter Balázs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4522)

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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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Péter Balázs
    • 1
  1. 1.Department of Computer Graphics and Image Processing, University of Szeged, Árpád tér 2, H-6720 SzegedHungary

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