On the computational complexity of reconstructing lattice sets from their x-rays
Discrete Mathematics
On the comptational complexity of determining polyatomic structures by X-rays
Theoretical Computer Science
Reconstructing polyatomic structures from discrete X-rays: NP-completeness proof for three atoms
Theoretical Computer Science
A solvable case of image reconstruction in discrete tomography
Discrete Applied Mathematics
Reconstruction of binary matrices under fixed size neighborhood constraints
Theoretical Computer Science
Solving the two color problem: an heuristic algorithm
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Approximating bicolored images from discrete projections
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Solving Multicolor Discrete Tomography Problems by Using Prior Knowledge
Fundamenta Informaticae - Strategies for Tomography
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In the field of Discrete Tomography, the 2-color problem consists in determining a matrix whose elements are of two different types, starting from its horizontal and vertical projections. It is known that the one color problem has a polynomial time reconstruction algorithm, while, with k ≥ 2, the k-color problem is NP-complete. Thus, the 2-color problem constitutes an interesting example of a problem just in the frontier between hard and easy problems. In this paper we define a linear time algorithm to solve a set of its instances, where some values of the horizontal and vertical projections are constant, while the others are upper bounded by a positive number proportional to the dimension of the problem. Our algorithm relies on classical studies for the solution of the one color problem.