Reconstruction of Binary Images Represented on Equilateral Triangular Grid Using Evolutionary Algorithms
In this paper we study the problem of reconstructing a binary hexagonal image represented on an equilateral triangular grid from its projections. We propose an evolutionary algorithm for reconstructing this images from its projections in three directions. We will consider three projections as the points in the grid are triangles and by the symmetry of the grid there are three natural directions. Genetic operators, e.g., crossover and mutation operators are defined, as well as an operator based on the switch operator from discrete tomography. We use a compactness operator to eliminate the isolated points of an image and improve the quality of the image. The initial population and the children images are generated using the network flow algorithm with some restrictions due to the equilateral triangular grid and point shape and type. Some artificial binary images were used to test the efficiency of the algorithm.
Keywordsdiscrete tomography triangular grid genetic algorithm memetic algorithm
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- 2.Batenburg, K.J.: Network Flow Algorithms for Discrete Tomography. PhD thesis (2006)Google Scholar
- 4.Bertsekas, D., Tseng, P.: RELAX-IV: a faster version of the RELAX code for solving minimum cost flow problems. LIDS Technical Report LIDS-P-2276, MIT (1994)Google Scholar
- 5.Bertsekas, D., Frangioni, A., Gentile, C.: Relax IV, The MCF Class Project (2004), http://www.di.unipi.it/di/groups/optimize/Software/MCF.html
- 7.Goldberg, D.E.: Genetic Algorithms in Search Optimization and Machine Learning. Addison Wesley (1989)Google Scholar
- 8.Lukic, T., Nagy, B.: Energy-minimization based Discrete Tomography Reconstruction Method for Images on Triangular Grid. In: 15th International Workshop on Combinatorial Image Analysis, IWCIA 2012 (accepted for publication, 2012)Google Scholar
- 9.Moisi, E., Nagy, B.: Discrete Tomography on the Triangular Grid: a Memetic Approach. In: 7th International Symposium on Image and Signal Processing and Analysis (ISPA 2011), Dubrovnik, Croatia, pp. 579–584 (2011)Google Scholar
- 10.Nagy, B.: Finding Shortest Path with Neighborhood Sequences in Triangular Grids. In: 2nd IEEE R8-EURASIP International Symposium on Image and Signal Processing and Analysis (ITI-ISPA 2001), Pula, Croatia, pp. 55–60 (2001)Google Scholar
- 14.Spears, W.M.: Evolutionary Algorithms: The Role of the Mutation and recombination. Springer (2000)Google Scholar