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Binary Tomography

This paper provides an introduction to binary tomography, discussing the basic idea, computerized tomography, and discrete tomography. It explores various algorithms such as simulated annealing, linear relaxation, and branch and bound, along with their applications. The paper also presents our solutions, including the star section algorithm, evolutionary algorithm for 2D and 3D objects, modified Kaczmarz algorithm, and greedy algorithm. Reconstruction results for different projections and noise levels are shown, highlighting the efficacy of these algorithms. Future avenues of research are suggested, including the use of circular directed growing, 3D implementation, and automatic parameter adjustment.

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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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