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New Directions in Discrete Tomography and Its Applications in Neutron Radiography

Key members: 
Attila Kuba
Kálmán Palágyi
Antal Nagy
Péter Balázs
Zoltán Kiss
Lajos Rodek
Founded by: 
Hungarian Scientific Research Fund (OTKA)
Partners: 

KFKI Atomic Research Institute (Márton Balaskó)

Related projects: 
Lifetime from: 
2005
Lifetime to: 
2008
Short description: 
New approaches in Discrete Tomography are investigated. Studies are concentrating on absorbed projections, fan-beam geometry, new geometrical properties of discrete sets. Besides, new application fields (such as neutron radiography) are studied.
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: 
Herman GT, Kuba A. Advances in Discrete Tomography and Its Applications. Birkhauser; 2007.
Barcucci E, Frosini A, Kuba A, Nagy A, Rinaldi S, Samal M, et al. Emission discrete tomography. In: Herman G T, Kuba A, editors. ADVANCES IN DISCRETE TOMOGRAPHY AND ITS APPLICATIONS. Cambridge: Birkhauser Boston; 2007. 3. p. 333-366p. (Applied and Numerical Harmonic Analysis ).
Baumann J, Kiss Z, Krimmel S, Kuba A, Nagy A, Rodek L, et al. Discrete Tomography Methods for Nondestructive Testing. In: Herman G T, Kuba A, editors. Advances in Discrete Tomography and Its Applications. Birkhauser; 2007. 3. p. 303-332p. (Applied and Numerical Harmonic Analysis ).
Kiss Z, Rodek L, Kuba A. Image reconstruction and correction methods in neutron and X-ray tomography. Acta Cybernetica. 2006;17:557-587.
Nagy A, Kuba A. Parameter settings for reconstructing binary matrices from fan-beam projections. CIT JOURNAL OF COMPUTING AND INFORMATION TECHNOLOGY. 2006;14(2):100-110.
Kuba A, Nivat M. A sufficient condition for non-uniqueness in binary tomography with absorption. Theoretical Computer Science. 2005;346:335-357.
Kuba A, Ruskó L, Rodek L, Kiss Z. Preliminary studies of discrete tomography in neutron imaging. IEEE Transactions on Nuclear Science. 2005;52:380-385.
Balázs P. Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components. In: Herman G T, Kuba A, editors. ADVANCES IN DISCRETE TOMOGRAPHY AND ITS APPLICATIONS. Cambridge: Birkhauser Boston; 2007. 1. p. 153-173p. (Applied and Numerical Harmonic Analysis).
Balázs P. A decomposition technique for reconstructing discrete sets from four projections. IMAGE AND VISION COMPUTING. 2007;25(10):1609-1619.
Balázs P. Generation and empirical investigation of hv-Convex discrete sets. In: Ersbøll BKjær, Pedersen KSteenstrup, editors. Image Analysis. Aalborg, Denmark: Springer Verlag; 2007. 3. p. 344-353p. (Lecture Notes in Computer Science).
Balázs P. The number of line-convex directed polyominoes having the same orthogonal projections. In: Kuba A, Nyúl LGábor, Palágyi K, editors. Discrete Geometry for Computer Imagery. Berlin, Heidelberg: Springer-Verlag; 2006. 7. p. 77-85p.
Balaskó M, Kuba A, Nagy A, Kiss Z, Rodek L, Ruskó L. Neutron-, gamma- and X-ray three-dimensional computed tomography at the Budapest research reactor site. NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A- ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT. 2005;542(1-3):22-27.
Balaskó M, Sváb E, Kuba A, Kiss Z, Rodek L, Nagy A. Pipe corrosion and deposit study using neutron- and gamma- radiation sources. NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A- ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT. 2005;542(1-3):302-308.
Kiss Z, Rodek L, Nagy A, Kuba A, Balaskó M. Reconstruction of pixel-based and geometric objects by discrete tomography. Simulation and physical experiments. ELECTRONIC NOTES IN DISCRETE MATHEMATICS. 2005;20:475-491.
Kuba A, Rodek L, Kiss Z, Ruskó L, Balaskó M, Nagy A. Discrete tomography in neutron radiography. NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A- ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT. 2005;542(1-3):376-382.
Weber S, Nagy A, Schulle T, Schnorr C, Kuba A. A benchmark evaluation of large-scale optimization approaches to binary tomography. In: Kuba A, Nyúl LGábor, Palágyi K, editors. Discrete Geometry for Computer Imagery. Berlin; Heidelberg: Springer-Verlag; 2006. 1. p. 146-156p.
Balázs P. A framework for generating some discrete sets with disjoint components by using uniform distributions. THEORETICAL COMPUTER SCIENCE. 2008;406(1-2):15-23.
Balázs P. On the ambiguity of reconstructing hv-convex binary matrices with decomposable configurations. ACTA CYBERNETICA-SZEGED. 2008;18(3):367-377.
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Balázs P. On the number of hv-convex discrete sets. In: Brimkov VE, Barneva RP, Hauptman HA, editors. Combinatorial Image Analysis. Buffalo, NY, USA: Springer Verlag; 2008. 1. p. 112-123p. (Lecture Notes in Computer Science).
Balázs P. Reconstruction of binary images with few disjoint components from two projections. In: Bebis G, Boyle R, Parvin B, Koracin D, Remagnino P, Porikli F et al., editors. Advances in Visual Computing. Las Vegas, NV, USA: Springer Verlag; 2008. 1. p. 1147-1156p. (Lecture Notes in Computer Science).
Balázs P, Gara M. Decision trees in binary tomography for supporting the reconstruction of hv-convex connected images. In: Proceedings of the Advanced Concepts for Intelligent Vision Systems. Vol 5259. Juan-les-Pins, France: Springer; 2008. 4. p. 433-443p. (Lecture Notes in Computer Science; vol 5259).
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Kategória: 
Tomography - Discrete Tomography