A Memetic Algorithm for Binary Image Reconstruction

This paper deals with a memetic algorithm for the reconstruction of binary images, by using their projections along four directions. The algorithm generates by network flows a set of initial images according to two of the input projections and lets them evolve toward a solution that can be optimal or close to the optimum. Switch and compactness operators improve the quality of the reconstructed images which belong to a given generation, while the selection of the best image addresses the evolution to an optimal output.

[1]  G. Herman,et al.  Discrete tomography : foundations, algorithms, and applications , 1999 .

[2]  Andrea Frosini,et al.  An introduction to periodical discrete sets from a tomographical perspective , 2005, Theor. Comput. Sci..

[3]  Marek Chrobak,et al.  Reconstructing hv-Convex Polyominoes from Orthogonal Projections , 1999, Inf. Process. Lett..

[4]  H. Ryser Combinatorial Properties of Matrices of Zeros and Ones , 1957, Canadian Journal of Mathematics.

[5]  Gabor T. Herman,et al.  Binary Tomography Using Gibbs Priors , 1999 .

[6]  Peter Gritzmann,et al.  On the computational complexity of reconstructing lattice sets from their X-rays , 1999, Discret. Math..

[7]  Kees Joost Batenburg,et al.  An evolutionary algorithm for discrete tomography , 2005, Discret. Appl. Math..

[8]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[9]  Bernd Freisleben,et al.  Fitness landscape analysis and memetic algorithms for the quadratic assignment problem , 2000, IEEE Trans. Evol. Comput..

[10]  M. Nivat,et al.  Medians of polyominoes: A property for reconstruction , 1998 .

[11]  T. Yung Kong,et al.  Tomographic Equivalence and Switching Operations , 1999 .

[12]  Attila Kuba,et al.  The reconstruction of two-directionally connected binary patterns from their two orthogonal projections , 1983 .

[13]  Bernd Freisleben,et al.  Memetic Algorithms and the Fitness Landscape of the Graph Bi-Partitioning Problem , 1998, PPSN.

[14]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[15]  Pablo Moscato,et al.  On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts : Towards Memetic Algorithms , 1989 .

[16]  D. Gale A theorem on flows in networks , 1957 .

[17]  Zhi Zhou,et al.  A novel memetic algorithm with random multi-local-search: a case study of TSP , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[18]  V. Di Gesù,et al.  The stability problem and noisy projections in discrete tomography , 2004, J. Vis. Lang. Comput..

[19]  Fuzhen Zhang,et al.  On the precise number of (0, 1)-matrices in U(R, R) , 1998, Discret. Math..

[20]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[21]  Richard P. Anstee,et al.  The network flows approach for matrices with given row and column sums , 1983, Discret. Math..