Generation and reconstruction of hv-convex 8-connected discrete sets

An algorithm is given to generate 2-dimensional hv-convex 8-connected discrete sets uniformly. This algorithm is based on an extension of a theory previously used for a more special class of hv-convex discrete sets. The second part of the paper deals with the reconstruction of hv-convex 8-connected discrete sets. The main idea of this algorithm is to rewrite the whole reconstruction problem as a 2SAT problem. Using some a priori knowledge we reduced the number of iterations and the number of clauses in the 2SAT expression which results in reduction of execution time

A benchmark set for the reconstruction of hv-convex discrete sets

AbstractIn this paper we summarize the most important generation methods developed for the subclasses of hv-convex discrete sets. We also present some new generation techniques to complement the former ones thus making it possible to design a complete benchmark set for testing the performance of reconstruction algorithms on the class of hv-convex discrete sets and its subclasses. By using this benchmark set the paper also collects several statistics on hv-convex discrete sets, which are of great importance in the analysis of algorithms for reconstructing such kinds of discrete sets