Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Reconstructing hv-convex polyominoes from orthogonal projections
Information Processing Letters
The reconstruction of binary patterns from their projections
Communications of the ACM
The Reconstruction of Convex Polyominoes from Horizontal and Vertical Projections
SOFSEM '98 Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Characterization of Binary Patterns and Their Projections
IEEE Transactions on Computers
The Reconstruction of Some 3D Convex Polyominoes from Orthogonal Projections
SOFSEM '02 Proceedings of the 29th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
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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 NP-complete 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(m3n3).