Reconstruction of 8-connected but not 4-connected hv-convex discrete sets

The reconstruction of 8-connected but not 4-connected hv-convex discrete sets from few projections is considered. An algorithm is given with worst case complexity of O(mnmin{m,n}) to reconstruct all sets with given horizontal and vertical projections. Experimental results are also presented. It is shown, that using also the diagonal projections the algorithm can be speeded up having complexity of O(mn) and in this case the solution is uniquely determined. Finally, we consider the possible generalizations of our results to solve the problem in more general classes.