The Reconstruction of Polyominoes from Approximately Orthogonal Projections

The reconstruction of discrete two-dimensional pictures from their projection is one of the central problems in the areas of medical diagnostics, computer-aided tomography, pattern recognition, image processing, and data compression. In this note, we determine the computational complexity of the problem of reconstruction of polyominoes from their approximately orthogonal projections. We will prove that it is NPcomplete if we reconstruct polyominoes, horizontal convex polyominoes and vertical convex polyominoes. Moreover we will give the polynomial algorithm for the reconstruction of hv-convex polyominoes that has time complexity O(mn).