One of the basic problems in discrete tomography is thereconstruction 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. {\textcopyright} 2008 Springer-Verlag Berlin Heidelberg.

}, isbn = {978-3-540-78274-2}, doi = {10.1007/978-3-540-78275-9_10}, author = {P{\'e}ter Bal{\'a}zs}, editor = {Valentin E Brimkov and Reneta P Barneva and Herbert A Hauptman} }