A fast algorithm for reconstructing hv-convex 8-connected but not 4-connected discrete sets

Abstract

One important class of discrete sets where the reconstruction from two given projections can be solved in polynomial time is the class of hv-convex 8-connected sets. The worst case complexity of the fastest algorithm known so far for solving the problem is of O(mn· min{m2,n2}) [2]. However, as it is shown, in the case of 8-connected but not 4-connected sets we can give an algorithm with worst case complexity of O(mn·min{m,n}) by identifying the so-called S4-components of the discrete set. Experimental results are also presented in order to investigate the average execution time of our algorithm. © Springer-Verlag Berlin Heidelberg 2003.