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Binary Tomography

17 th Summer School on Image Processing Debrecen, Hungary 2009. Binary Tomography . Introduction. Basic idea Computerized tomography Discrete tomography Binary tomography Applications. Problem description. Projections. Reconstruction. Known algorithms. Simulated annealing

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Binary Tomography

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  1. 17th Summer School on Image Processing Debrecen, Hungary 2009 BinaryTomography

  2. Introduction • Basic idea • Computerized tomography • Discrete tomography • Binary tomography • Applications

  3. Problem description Projections Reconstruction

  4. Known algorithms • Simulated annealing • Linear relaxation • Branch and bound • SPG based method • Maximum flow problem • Neural networks • Convex-concave regularization • ...

  5. Our solutions • Simple solution • Star section algorithm for 2 and 4 projections • Evolutionary algorithm for 2D and 3D objects • Modified Kaczmarz algorithm

  6. Simple solution • Greedy algorithm Orginal image Reconstructions

  7. Star section algorithm • Maximum value of projections • Cross shape growing

  8. 2 projections - results

  9. 2 projections - results

  10. 2 projections - results

  11. 4 projections - results

  12. 4 projections - results

  13. 4 projections - results

  14. 4 projections - results

  15. Evolutionary algorithm for 2D • Population • Mutation • Crossover • Fitness • Prototype based representation of shapes

  16. 2D results 25% noise 10% noise Noisless

  17. 2D results

  18. Evolutionary algorithm for 3D

  19. Modified Kaczmarz algorithm • Linear system • r(i) is chosen from the set {1,2,...,m} at random, with probability proportional to

  20. Results

  21. Results

  22. Results

  23. Results

  24. Summary

  25. The avenue of future researches • Star section algorithm • Using circular directed growing instead of sectional • 3D implementation • Evolutionary algorithm • Automatic parameter adjustment • Applying algorithm to other shapes • Randomize Kaczmarz algorithm • Improving boundary reconstruction method

  26. A - team

  27. Thank You for Your Patiance

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