Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Generating convex polyominoes at random
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
Genetic algorithms + data structures = evolution programs (3rd ed.)
Genetic algorithms + data structures = evolution programs (3rd ed.)
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
The discrete Radon transform and its approximate inversion via linear programming
Discrete Applied Mathematics
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
New ideas in optimization
Tabu Search
A decomposition technique for reconstructing discrete sets from four projections
Image and Vision Computing
A genetic algorithm for discrete tomography reconstruction
Genetic Programming and Evolvable Machines
Analysis on the strip-based projection model for discrete tomography
Discrete Applied Mathematics
Theoretical Computer Science
A benchmark set for the reconstruction of hv-convex discrete sets
Discrete Applied Mathematics
A memetic algorithm for binary image reconstruction
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
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One of the main problems in discrete tomography is the reconstruction of binary matrices from their projections in a small number of directions. In this paper we consider a new algorithmic approach for reconstructing binary matrices from only two projections. This problem is usually underdetermined and the number of solutions can be very large. We present an evolutionary algorithm for finding the reconstruction which maximises an evaluation function, representing the "quality" of the reconstruction, and show that the algorithm can be successfully applied to a wide range of evaluation functions. We discuss the necessity of a problem-specific representation and tailored search-operators for obtaining satisfactory results. Our new search-operators can also be used in other discrete tomography algorithms.