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New Directions in Discrete Tomography and Its Applications in Neutron Radiography

iconMembers: Attila Kuba, Kálmán Palágyi, Antal Nagy, Péter Balázs, Zoltán Kiss, Lajos Rodek
Funded byPartners:Related Projects:Lifetime: 2005 - 2008

Description

This project follows a former one that investigated the basic aspects of Discrete Tomography (DT). In this research several new problems of DT are studied, we are mainly focusing on the following fileds:

1. New Projection Geometries: We study the reconstruction in the so-called fan-beam projection model. Experiments are conducted to deteremine the optimal parameter values for this kind of problem.

2. New Geometrical Properties: We introduce classes of discrete sets defined by new geometrical properties (line-convexity, decomposability) in which the reconstruction can be performed in polynomial time. Uniqueness of the solution is also studied.

3. Emission Discrete Tomography: Existence, Uniqueness and Reconstruction problems are studied in case of absorbed projections.

4. Neutron and X-ray Tomography in Non-Destructive Testing (NDT): A new complex neutron-, gamma-, and X-ray three-dimensional computer tomography system suitable for experimental and industrial applications has been built at 10-MW Budapest research reactor site. A number of objects were investigated and tomographic projections were made. We study the optimal preprocessing steps and the optimal parameterization of pixel-based and geometry-based reconstruction methods to obtain DT reconstruction techniques that are suitable for practical applications in NDT. Pipe corrosions, damages of turbine blades, and other industrial objects are investigated.

5. Analysis of DT reconstruction algorithms: We performed a benchmark evaluation of large-scale optimization approaches to Binary Tomography. We also designed algorithms to generate discrete sets having some convexity and connectedness properties using uniform random distributions to compare the performance of several reconstruction algorithms. Implementing those generators we supply benchmark collections for the reconstruction of hv-convex discrete sets.

6. Exploiting structural features of images from their projections: We apply learning methods (especially, decisions trees) to obtain geometrical properties of binary images solely from their projections, in order to be able to choose the proper algorithm and its parameters that fit best to the given reconstruction task. Algorithms which wisely can use learnt priors are also developed.

As a part of the project we implemented some of our reconstruction algorithms in the DIRECT framework.

Publications

  1. Gabor T. Herman and Attila Kuba, editors. Advances in Discrete Tomography and Its Applications, Applied and Numerical Harmonic Analysis. Birkhauser, 2007.
  2. Elena Barcucci, Andrea Frosini, Attila Kuba, Antal Nagy, Simone Rinaldi, Martin Samal, and Steffen Zopf. Emission discrete tomography. In Gabor T. Herman and Attila Kuba, editors, Advances in Discrete Tomography and Its Applications, pages 333-366. Birkhauser, Boston, 2007.
  3. Joachim Baumann, Zoltán Kiss, Sven Krimmel, Attila Kuba, Antal Nagy, Lajos Rodek, Burkhard Schillinger, and Juergen Stephan. Discrete Tomography Methods for Nondestructive Testing. In Gabor T. Herman and Attila Kuba, editors, Advances in Discrete Tomography and Its Applications, pages 303-332. Birkhauser, Boston, 2007.
  4. Zoltán Kiss, Lajos Rodek, and Attila Kuba. Image reconstruction and correction methods in neutron and X-ray tomography. Acta Cybernetica, 17(3):557-587, 2006.
  5. Antal Nagy and Attila Kuba. Parameter settings for reconstructing binary matrices from fan-beam projections. Journal of Computing and Information Technology, 14(2):100-110, 2006.
  6. Attila Kuba and Maurice Nivat. A sufficient condition for non-uniqueness in binary tomography with absorption. Theoretical Computer Science, 346:335-357, November 2005.
  7. Attila Kuba, László Ruskó, Lajos Rodek, and Zoltán Kiss. Preliminary studies of discrete tomography in neutron imaging. IEEE Transactions on Nuclear Science, 52(1):380-385, February 2005.
  8. Péter Balázs. Decomposition algorithms for reconstructing discrete sets with disjoint components. In Gabor T. Herman and Attila Kuba, editors, Advances in Discrete Tomography and Its Applications, chapter 8, pages 153-173. Birkhauser, 2007.
  9. Péter Balázs. A decomposition technique for reconstructing discrete sets from four projections. Image and Vision Computing, 25:10:1609-1619, 2007.
  10. Péter Balázs. Generation and empirical investigation of hv-convex discrete sets. In Proceedings of the Scandinavian Conference on Image Analysis, volume 4522 of Lecture Notes in Computer Science, pages 344-353, 2007. Springer Verlag.
  11. Péter Balázs. The number of line-convex directed polyominoes having the same orthogonal projections. In Proceedings of the International Conference on Discrete Geometry for Computer Imagery, volume 4245 of Lecture Notes in Computer Science, pages 77-85, 2006. Springer Verlag.
  12. Márton Balaskó, Attila Kuba, Antal Nagy, Zoltán Kiss, Lajos Rodek, and László Ruskó. Neutron-, gamma- and X-ray three-dimensional computed tomography at the Budapest research reactor site. In Proceedings of the International Topical Meeting on Neutron Radiography, volume 542 of Nuclear Instruments and Methods in Physics Research, pages 22-27, April 2005.
  13. Márton Balaskó, Erzsébet Sváb, Attila Kuba, Zoltán Kiss, Lajos Rodek, and Antal Nagy. Pipe corrosion and deposit study using neutron- and gamma- radiation sources. In Proceedings of the International Topical Meeting on Neutron Radiography, volume 542 of Nuclear Instruments and Methods in Physics Research, pages 302-308, april 2005.
  14. Zoltán Kiss, Lajos Rodek, Antal Nagy, Attila Kuba, and Márton Balaskó. Reconstruction of pixel-based and geometric objects by discrete tomography. Simulation and physical experiments. In Proceedings of the Workshop on Discrete Tomography and its Applications, volume 20 of Electronic Notes in Discrete Mathematics, pages 475-491, July 2005.
  15. Attila Kuba, Lajos Rodek, Zoltán Kiss, László Ruskó, Antal Nagy, and Márton Balaskó. Discrete tomography in neutron radiography. In Proceedings of the International Topical Meeting on Neutron Radiography, volume 542 of Nuclear Instruments and Methods in Physics Research, pages 376-382, april 2005.
  16. Stefan Weber, Antal Nagy, Thomas Schüle, Christoph Schnörr, and Attila Kuba. A Benchmark Evaluation of Large-Scale Optimization Approaches to Binary Tomography. In Discrete Geometry for Computer Imagery, volume 4245/2006 of Lecture Notes in Computer Science, pages 146-156, 2006. Springer Verlag.
  17. Péter Balázs. A framework for generating some discrete sets with disjoint components by using uniform distributions. Theoretical Computer Science, 406:15-23, 2008.
  18. Péter Balázs. On the Ambiguity of Reconstructing hv-Convex Binary Matrices with Decomposable Configurations. Acta Cybernetica, 18(3):367-377, 2008.
  19. Márton Balaskó, Attila Kuba, Attila Tanács, Zoltán Kiss, Antal Nagy, and Burkhard Schillinger. Comparison Radiography and Tomography Possibilities of FRM-II (20 MW) and Budapest (10 MW) Research Reactor. In Proceedings of the Eight World Conference WCNR-8, pages 18-27, 2008.
  20. Márton Balaskó, Erzsébet Sváb, Zoltán Kiss, Attila Tanács, Antal Nagy, and Attila Kuba. Study of the Inner Structure of a Damaged Control Rod by Neutron and X-ray Radiography and Discrete Tomography. In Proceedings of the Eight World Conference WCNR-8, pages 294-303, 2008.
  21. Péter Balázs. On the number hv-convex discrete sets. In Proceedings of the International Workshop on Combinatorial Image Analysis, volume 4958 of Lecture Notes in Computer Science, pages 112-123, 2008. Springer Verlag.
  22. Péter Balázs. Reconstruction of binary images with few disjoint components from two projections. In Proceedings of the International Symposium on Visual Computing, volume 5359 of Lecture Notes in Computer Science, pages 1147-1156, December 2008. Springer Verlag.
  23. Péter Balázs and Mihály Gara. Decision trees in binary tomography for supporting the reconstruction of hv-convex connected images. In Proceedings of the Advanced Concepts for Intelligent Vision Systems, volume 5259 of Lecture Notes in Computer Science, pages 433-443, October 2008. Springer Verlag.
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