The reconstruction of binary patterns from their projections

Abstract

Given the horizontal and vertical projections of a finite binary pattern f , can we reconstruct the original pattern f ? In this paper we give a characterization of patterns that are reconstructable from their projections. Three algorithms are developed to reconstruct both unambiguous and ambiguous patterns. It is shown that an unambiguous pattern can be perfectly reconstructed in time m × n and that a pattern similar to an ambiguous pattern can also be constructed in time m × n , where m , n are the dimensions of the pattern frame.