On the number of hv-convex discrete sets

Authors:
Péter Balázs
Affiliations:
Department of Image Processing and Computer Graphics, University of Szeged, Szeged, Hungary
Venue:
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Year:
2008

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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 fulfills some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. The class of hv-convex discrete sets and its subclasses have a well-developed theory. Several reconstruction algorithms as well as some complexity results are known for those classes. The key to achieve polynomial-time reconstruction of an hv-convex discrete set is to have the additional assumption that the set is connected as well. This paper collects several statistics on hv-convex discrete sets, which are of great importance in the analysis of algorithms for reconstructing such kind of discrete sets.