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New Directions in Discrete Tomography and Its Applications in Neutron Radiography

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: 
Advances in Discrete Tomography and Its Applications, Herman, Gábor T., and Kuba Attila , Advances in Discrete Tomography and Its Applications, 2007, Number Applied and Numerical Harmonic Analysis, (2007)
Emission discrete tomography., Barcucci, Elena, Frosini Andrea, Kuba Attila, Nagy Antal, Rinaldi Simone, Samal Martin, and Zopf Steffen , ADVANCES IN DISCRETE TOMOGRAPHY AND ITS APPLICATIONS, 2007, Cambridge, p.333 - 366, (2007)
Image reconstruction and correction methods in neutron and X-ray tomography, Kiss, Zoltán, Rodek Lajos, and Kuba Attila , Acta Cybernetica, Volume 17, Szeged, Hungary, p.557-587, (2006)
Parameter settings for reconstructing binary matrices from fan-beam projections., Nagy, Antal, and Kuba Attila , CIT JOURNAL OF COMPUTING AND INFORMATION TECHNOLOGY, 2006, Volume 14, Issue 2, p.100 - 110, (2006)
A sufficient condition for non-uniqueness in binary tomography with absorption, Kuba, Attila, and Nivat Maurice , Theoretical Computer Science, 2005, Volume 346, p.335-357, (2005)
Preliminary studies of discrete tomography in neutron imaging, Kuba, Atila, Ruskó László, Rodek Lajos, and Kiss Zoltán , IEEE Transactions on Nuclear Science, 2005, Volume 52, p.380-385, (2005)
Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components, Balázs, Péter , ADVANCES IN DISCRETE TOMOGRAPHY AND ITS APPLICATIONS, 2007, Cambridge, p.153 - 173, (2007)
A decomposition technique for reconstructing discrete sets from four projections, Balázs, Péter , IMAGE AND VISION COMPUTING, Oct 2007, Volume 25, Issue 10, p.1609 - 1619, (2007)
Generation and empirical investigation of hv-Convex discrete sets, Balázs, Péter , Image Analysis, June 2007, Number 4522, Aalborg, Denmark, p.344 - 353, (2007)
The number of line-convex directed polyominoes having the same orthogonal projections, Balázs, Péter , Discrete Geometry for Computer Imagery, 2006///, Berlin, Heidelberg, p.77 - 85, (2006)
Neutron-, gamma- and X-ray three-dimensional computed tomography at the Budapest research reactor site., Balaskó, Márton, Kuba Attila, Nagy Antal, Kiss Zoltán, Rodek Lajos, and Ruskó László , NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A- ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT, 2005, Volume 542, Issue 1-3, p.22 - 27, (2005)
Pipe corrosion and deposit study using neutron- and gamma- radiation sources., Balaskó, Márton, Sváb Erzsébet, Kuba Attila, Kiss Zoltán, Rodek Lajos, and Nagy Antal , NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A- ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT, 2005, Volume 542, Issue 1-3, p.302 - 308, (2005)
Discrete tomography in neutron radiography, Kuba, Attila, Rodek Lajos, Kiss Zoltán, Ruskó László, Balaskó Márton, and Nagy Antal , NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A- ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT, 2005, Volume 542, Issue 1-3, p.376 - 382, (2005)
A benchmark evaluation of large-scale optimization approaches to binary tomography, Weber, Stefan, Nagy Antal, Schulle Thomas, Schnorr Christoph, and Kuba Attila , Discrete Geometry for Computer Imagery, 2006, Berlin; Heidelberg, p.146 - 156, (2006)
A framework for generating some discrete sets with disjoint components by using uniform distributions, Balázs, Péter , THEORETICAL COMPUTER SCIENCE, Oct 2008, Volume 406, Issue 1-2, p.15 - 23, (2008)
On the ambiguity of reconstructing hv-convex binary matrices with decomposable configurations, Balázs, Péter , ACTA CYBERNETICA-SZEGED, 2008, Volume 18, Issue 3, Szeged, Hungary, p.367 - 377, (2008)
Citekey 1305 not found
On the number of hv-convex discrete sets, Balázs, Péter , Combinatorial Image Analysis, Apr 2008, Number 4958, Buffalo, NY, USA, p.112 - 123, (2008)
Reconstruction of binary images with few disjoint components from two projections, Balázs, Péter , Advances in Visual Computing, Dec 2008, Number 5359, Las Vegas, NV, USA, p.1147 - 1156, (2008)
Decision trees in binary tomography for supporting the reconstruction of hv-convex connected images, Balázs, Péter, and Gara Mihály , Proceedings of the Advanced Concepts for Intelligent Vision Systems, Oct 2008, Volume 5259, Number 5259, Juan-les-Pins, France, p.433-443, (2008)
Citekey 1345 not found
Kategória: 
Tomography - Discrete Tomography