Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Reconstructing hv-convex polyominoes from orthogonal projections
Information Processing Letters
The reconstruction of polyominoes from their orthogonal projections
Information Processing Letters
Reconstruction of lattice sets from their horizontal, vertical and diagonal X-rays
Discrete Mathematics
An algorithm reconstructing convex lattice sets
Theoretical Computer Science
Determination of Q-convex sets by X-rays
Theoretical Computer Science
Fast filling operations used in the reconstruction of convex lattice sets
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
On the non-additive sets of uniqueness in a finite grid
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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Filling operations are procedures which are used in Discrete Tomography for the reconstruction of lattice sets having some convexity constraints. Many algorithms have been published giving fast implementations of these operations, and the best running time [S. Brunetti, A. Daurat, A. Kuba, Fast filling operations used in the reconstruction of convex lattice sets, in: Proc. of DGCI 2006, in: Lecture Notes in Comp. Sci., vol. 4245, 2006, pp. 98-109] is O(N^2logN) time, where N is the size of projections. In this paper we improve this result by providing an implementation of the filling operations in O(N^2). As a consequence, we reduce the time-complexity of the reconstruction algorithms for many classes of lattice sets having some convexity properties. In particular, the reconstruction of convex lattice sets satisfying the conditions of Gardner-Gritzmann [R.J. Gardner, P. Gritzmann, Discrete tomography: Determination of finite sets by X-rays, Trans. Amer. Math. Soc. 349 (1997) 2271-2295] can be performed in O(N^4)-time.