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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 { m 2,n 2} ) [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{\cal S}_4-components of the discrete set. Experimental results are also presented in order to investigate the average execution time of our algorithm.

A Fast Algorithm for Reconstructing hv-Convex 8-Connected but Not 4-Connected Discrete Sets