The number of convex polyominoes reconstructible from their orthogonal projections
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
On the precise number of (0,1)-matrices in U(R,S)
Discrete Mathematics
On the computational complexity of reconstructing lattice sets from their x-rays
Discrete Mathematics
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
New ideas in optimization
Principles of computerized tomographic imaging
Principles of computerized tomographic imaging
Stability and instability in discrete tomography
Digital and image geometry
An introduction to periodical discrete sets from a tomographical perspective
Theoretical Computer Science
A Network Flow Algorithm for Reconstructing Binary Images from Discrete X-rays
Journal of Mathematical Imaging and Vision
A genetic algorithm for discrete tomography reconstruction
Genetic Programming and Evolvable Machines
An evolutionary algorithm for discrete tomography
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Reconstruction of 8-connected but not 4-connected hv-convex discrete sets
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
A memetic algorithm for binary image reconstruction
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
A memetic island model for discrete tomography reconstruction
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
An island strategy for memetic discrete tomography reconstruction
Information Sciences: an International Journal
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Discrete tomography deals with the reconstruction of images from very few projections, which is, in the general case, an NP-hard problem. This paper describes a new memetic reconstruction algorithm. It generates a set of initial images by network flows, related to two of the input projections, and lets them evolve towards a possible solution, by using crossover and mutation. Switch and compactness operators improve the quality of the reconstructed images during each generation, while the selection of the best images addresses the evolution to an optimal result. One of the most important issues in discrete tomography is known as the stability problem and it is tackled here, in the case of noisy projections, along four directions. Extensive experiments have been carried out to evaluate the robustness of the new methodology. A comparison with the output of two other evolutionary algorithms and a generalized version of a deterministic method shows the effectiveness of our new algorithm.