Chlamydiae are obligate intracellular bacteria that propagate in the inclusion, a specific niche inside the host cell. The standard method for counting chlamydiae is the immunofluorescent staining and manual counting of chlamydial inclusions. High or medium throughput estimation of the reduction in chlamydia inclusions should be the basis of testing antichlamydial compounds and other drugs that positively or negatively influence chlamydial growth, yet low-throughput manual counting is the common approach. To overcome the time-consuming and subjective manual counting we developed an automatic inclusion counting system based on a commercially available DNA chip scanner. Fluorescently labeled inclusions are detected by the scanner, and the image is processed by ChlamyCount, a custom plugin of the ImageJ software environment. ChlamyCount was able to measure the inclusion counts over a one log dynamic range with high correlation to the theoretical counts. ChlamyCount was capable of accurately determining the minimum inhibitory concentration of the novel antimicrobial compound PCC00213 and the already known antichlamydial antibiotics moxifloxacin and tetracycline. ChlamyCount was also able to measure the chlamydial growth altering effect of drugs that influence host-bacterium interaction such as interferon-gamma, DEAE-dextran and cycloheximide. ChlamyCount is an easily adaptable system for testing antichlamydial antimicrobials and other compounds that influence Chlamydia-host interactions.

}, isbn = {0066-4804}, author = {Anita Bogdanov and Val{\'e}ria Endr{\'e}sz and Szabolcs Urb{\'a}n and Ildik{\'o} Lantos and Judit De{\'a}k and Katalin Buri{\'a}n and K {\"O}nder and Ferhan Ayaydin and P{\'e}ter Bal{\'a}zs and Dezs{\H o} P Vir{\'o}k} } @article {1170, title = {Local and global uncertainty in binary tomographic reconstruction}, journal = {COMPUTER VISION AND IMAGE UNDERSTANDING}, year = {2014}, note = {Art. No.: S1077-3142(14)00117-9doi: 10.1016/j.cviu.2014.05.006Article in Press}, month = {2014}, type = {Journal article}, abstract = {In binary tomography the goal is to reconstruct the innerstructure of homogeneous objects from their projections. This is usually required from a low number of projections, which are also likely to be affected by noise and measurement errors. In general, the distorted and incomplete projection data holds insufficient information for the correct reconstruction of the original object. In this paper, we describe two methods for approximating the local uncertainty of the reconstructions, i.e., identifying how the information stored in the projections determine each part of the reconstructed image. These methods can measure the uncertainty of the reconstruction without any knowledge from the original object itself. Moreover, we provide a global uncertainty measure that can assess the information content of a projection set and predict the error to be expected in the reconstruction of a homogeneous object. We also give an experimental evaluation of our proposed methods, mention some of their possible applications, and describe how the uncertainty measure can be used to improve the performance of the DART reconstruction algorithm.

}, isbn = {1077-3142}, doi = {10.1016/j.cviu.2014.05.006}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and L{\'a}szl{\'o} G{\'a}bor Ny{\'u}l and Antal Nagy and P{\'e}ter Bal{\'a}zs} } @article {1165, title = {APPLICATION OF DNA CHIP SCANNING TECHNOLOGY FOR THE AUTOMATIC DETECTION OF CHLAMYDIA TRACHOMATIS AND CHLAMYDIA PNEUMONIAE INCLUSIONS}, journal = {ACTA MICROBIOLOGICA ET IMMUNOLOGICA HUNGARICA}, volume = {60}, year = {2013}, note = {doi: 10.1556/AMicr.60.2013.Suppl.1}, month = {2013}, pages = {173 - 174}, type = {Journal article}, isbn = {1217-8950} } @conference {940, title = {Bin{\'a}ris k{\'e}pek rekonstrukci{\'o}ja k{\'e}t vet{\"u}letb{\H o}l {\'e}s morfol{\'o}giai v{\'a}zb{\'o}l}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2013}, year = {2013}, month = {Jan 2013}, pages = {182 - 193}, publisher = {NJSZT-K{\'E}PAF}, organization = {NJSZT-K{\'E}PAF}, type = {Conference paper}, address = {Veszpr{\'e}m} } @conference {1157, title = {A comparison of heuristics for reconstructing hv-convex binary matrices from horizontal and vertical projections}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2013}, year = {2013}, month = {Jan 2013}, pages = {168 - 181}, publisher = {NJSZT-K{\'E}PAF}, organization = {NJSZT-K{\'E}PAF}, type = {Conference paper}, address = {Veszpr{\'e}m}, author = {Zolt{\'a}n Ozsv{\'a}r and P{\'e}ter Bal{\'a}zs}, editor = {L{\'a}szl{\'o} Cz{\'u}ni} } @article {1161, title = {Complexity results for reconstructing binary images with disjoint components from horizontal and vertical projections}, journal = {DISCRETE APPLIED MATHEMATICS}, volume = {161}, year = {2013}, note = {UT: 000322689900002ScopusID: 84874628675doi: 10.1016/j.dam.2013.02.004}, month = {2013}, pages = {2224 - 2235}, type = {Journal article}, isbn = {0166-218X}, author = {P{\'e}ter Bal{\'a}zs} } @inbook {1163, title = {Directional Convexity Measure for Binary Tomography}, booktitle = {Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications}, year = {2013}, note = {ScopusID: 84893169866doi: 10.1007/978-3-642-41827-3_2}, month = {2013}, pages = {9 - 16}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Berlin; Heidelberg}, abstract = {There is an increasing demand for a new measure of convexity fordiscrete sets for various applications. For example, the well- known measures for h-, v-, and hv-convexity of discrete sets in binary tomography pose rigorous criteria to be satisfied. Currently, there is no commonly accepted, unified view on what type of discrete sets should be considered nearly hv-convex, or to what extent a given discrete set can be considered convex, in case it does not satisfy the strict conditions. We propose a novel directional convexity measure for discrete sets based on various properties of the configuration of 0s and 1s in the set. It can be supported by proper theory, is easy to compute, and according to our experiments, it behaves intuitively. We expect it to become a useful alternative to other convexity measures in situations where the classical definitions cannot be used.

}, doi = {10.1007/978-3-642-41827-3_2}, url = {http://link.springer.com/chapter/10.1007\%2F978-3-642-41827-3_2}, author = {Tam{\'a}s S{\'a}muel Tasi and L{\'a}szl{\'o} G{\'a}bor Ny{\'u}l and P{\'e}ter Bal{\'a}zs}, editor = {Gabriella Sanniti di Baja and Jose Ruiz-Shulcloper} } @article {1156, title = {Dynamic angle selection in binary tomography}, journal = {COMPUTER VISION AND IMAGE UNDERSTANDING}, volume = {117}, year = {2013}, note = {UT: 000315556800002ScopusID: 84871533054doi: 10.1016/j.cviu.2012.07.005}, month = {2013}, pages = {306 - 318}, type = {Journal article}, abstract = {In this paper, we present an algorithm for the dynamic selection of projection angles in binary tomography. Based on the information present in projections that have already been measured, a new projection angle is computed, which aims to maximize the information gained by adding this projection to the set of measurements. The optimization model used for angle selection is based on a characterization of solutions of the binary reconstruction problem, and a related definition of information gain. From this formal model, an algorithm is obtained by several approximation steps. Results from a series of simulation experiments demonstrate that the proposed angle selection scheme is indeed capable of finding angles for which the reconstructed image is much more accurate than for the standard angle selection scheme. {\textcopyright} 2012 Elsevier Inc. All rights reserved.

}, isbn = {1077-3142}, doi = {10.1016/j.cviu.2012.07.005}, author = {Joost K Batenburg and Willem Jan Palenstijn and P{\'e}ter Bal{\'a}zs and Jan Sijbers} } @article {1162, title = {An empirical study of reconstructing hv-convex binary matrices from horizontal and vertical projections}, journal = {ACTA CYBERNETICA-SZEGED}, volume = {21}, year = {2013}, month = {2013}, pages = {149 - 163}, type = {Journal article}, abstract = {The reconstruction of hv-convex binary matrices (or equivalently, binary images) from their horizontal and vertical projections is proved to be NP-hard. In this paper we take a closer look at the difficulty of the problem. We investigate different heuristic reconstruction algorithms of the class, and compare them from the viewpoint of running-time and reconstruction quality. Using a large set of test images of different sizes and with varying number of components, we show that the reconstruction quality can depend not only on the size of the image, but on the number and location of its components, too. We also reveal that the reconstruction time can also be affected by the number of the so-called switching components present in the image.

\

}, isbn = {0324-721X}, author = {Zolt{\'a}n Ozsv{\'a}r and P{\'e}ter Bal{\'a}zs} } @conference {1159, title = {Gradiens m{\'o}dszerek automatikus s{\'u}lyoz{\'a}s{\'a}n alapul{\'o} diszkr{\'e}t tomogr{\'a}fiai elj{\'a}r{\'a}s}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2013}, year = {2013}, month = {Jan 2013}, pages = {210 - 223}, publisher = {NJSZT-K{\'E}PAF}, organization = {NJSZT-K{\'E}PAF}, type = {Conference paper}, address = {Veszpr{\'e}m}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy}, editor = {L{\'a}szl{\'o} Cz{\'u}ni} } @inbook {1151, title = {Local uncertainty in binary tomographic reconstruction}, booktitle = {Proceedings of the IASTED International Conference on Signal Processing, Pattern Recognition and Applications (SPPRA 2013)}, year = {2013}, note = {ScopusID: 84876584488doi: 10.2316/P.2013.798-067}, month = {Feb 2013}, pages = {490 - 496}, publisher = {IASTED - Acta Press}, organization = {IASTED - Acta Press}, type = {Conference paper}, address = {Calgary}, abstract = {We describe a new approach for the uncertainty problem arisingin the field of discrete tomography, when the low number of projections does not hold enough information for an accurate, and reliable reconstruction. In this case the lack of information results in uncertain parts on the reconstructed image which are not determined by the projections and cannot be reliably reconstructed without additional information. We provide a method that can approximate this local uncertainty of reconstructions, and show how each pixel of the reconstructed image is determined by a set of given projections. We also give experimental results for validating our approach.

}, doi = {10.2316/P.2013.798-067}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and L{\'a}szl{\'o} G{\'a}bor Ny{\'u}l and Antal Nagy and P{\'e}ter Bal{\'a}zs}, editor = {Martin Kampel} } @mastersthesis {1169, title = {Prior Information, Machine Learning, and Direction Dependency in Binary Tomography}, year = {2013}, month = {2013}, school = {University of Szeged}, type = {Thesis}, address = {Szeged, Hungary}, author = {P{\'e}ter Bal{\'a}zs} } @inbook {1167, title = {Reconstruction and Enumeration of hv-Convex Polyominoes with Given Horizontal Projection}, booktitle = {Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications (CIARP)}, series = {Lecture Notes in Computer Science}, number = {8258}, year = {2013}, note = {ScopusID: 84893181366doi: 10.1007/978-3-642-41822-8_13}, month = {Nov 2013}, pages = {100 - 107}, publisher = {Springer}, organization = {Springer}, type = {Conference paper}, address = {Heidelberg; London; New York}, isbn = {978-3-642-41821-1}, doi = {10.1007/978-3-642-41822-8_13}, author = {Norbert Hantos and P{\'e}ter Bal{\'a}zs}, editor = {Jose Ruiz-Shulcloper and Gabriella Sanniti di Baja} } @article {1160, title = {The reconstruction of polyominoes from horizontal and vertical projections and morphological skeleton is NP-complete}, journal = {FUNDAMENTA INFORMATICAE}, volume = {125}, year = {2013}, note = {UT: 000322028300009ScopusID: 84881495517doi: 10.3233/FI-2013-868}, month = {2013}, pages = {343 - 359}, type = {Journal article}, isbn = {0169-2968}, author = {Norbert Hantos and P{\'e}ter Bal{\'a}zs} } @inbook {1166, title = {Restoration of blurred binary images using discrete tomography}, booktitle = {Advanced Concepts for Intelligent Vision Systems (ACIVS)}, series = {Lecture Notes in Computer Science}, number = {8192}, year = {2013}, note = {ScopusID: 84890864720doi: 10.1007/978-3-319-02895-8_8}, month = {2013}, pages = {80 - 90}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Berlin; Heidelberg; New York; London; Paris; Tokyo}, abstract = {Enhancement of degraded images of binary shapes is an important task in many image processing applications, *e.g.* to provide appropriate image quality for optical character recognition. Although many image restoration methods can be found in the literature, most of them are developed for grayscale images. In this paper we propose a novel binary image restoration algorithm. As a first step, it restores the projections of the shape using 1-dimensional deconvolution, then reconstructs the image from these projections using a discrete tomography technique. The method does not require any parameter setting or prior knowledge like an estimation of the signal-to-noise ratio. Numerical experiments on a synthetic dataset show that the proposed algorithm is robust to the level of the noise. The efficiency of the method has also been demonstrated on real out-of-focus alphanumeric images.

\

}, isbn = {978-3-319-02894-1}, doi = { 10.1007/978-3-319-02895-8_8}, author = {Jozsef Nemeth and P{\'e}ter Bal{\'a}zs}, editor = {Jacques Blanc-Talon and Andrzej Kasinski and Wilfried Philips and Dan Popescu and Paul Scheunders} } @conference {1164, title = {A uniqueness result for reconstructing hv-convex polyominoes from horizontal and vertical projections and morphological skeleton}, booktitle = {Proceedings of International Symposium on Image and Signal Processing and Analysis (ISPA)}, year = {2013}, month = {Sep 2013}, pages = {788 - 793}, publisher = {IEEE}, organization = {IEEE}, type = {Conference paper}, address = {Trieste}, abstract = {In this article we study the uniqueness of the reconstruction in a special class of 4-connected hv-convex images, using two projections and the so-called morphological skeleton. Generally, if just the two projections are given, there can be exponentially many hv-convex 4-connected images satisfying them. Knowing the morphological skeleton in addition, we can reduce the number of solutions. In the studied class, the images are defined by two parameters. We show that the uniqueness of their reconstruction depends only on the values of those parameters.

\

}, doi = {10.1109/ISPA.2013.6703845}, author = {Norbert Hantos and P{\'e}ter Bal{\'a}zs}, editor = {Giovanni Ramponi and Sven Lon{\v c}ari{\'c} and Alberto Carini and Karen Egiazarian} } @article {1144, title = {Artificial intelligence methods in discrete tomography}, year = {2012}, month = {June 2012}, pages = {16}, publisher = {University Szeged, Institute of Informatics}, type = {Abstract}, address = {Szeged}, abstract = {Tomography is an imaging procedure to examine the internal structure of objects. The crosssection

images are constructed with the aid of the object{\textquoteright}s projections. It is often necessary to

minimize the number of those projections to avoid the damage or destruction of the examined

object, since in most cases the projections are made by destructive rays.

Sometimes the number of available projections are so small that conventional methods cannot

provide satisfactory results. In these cases Discrete Tomograpy can provide acceptable solutions,

but it can only be used with the assumption the object is made of only a few materials,

thus only a small number of intensity values appear in the reconstructed cross-section image.

Although there are a lot of discrete tomographic reconstruction algorithms, only a few papers

deal with the determination of intensity values of the image, in advance. In our work we

try to fill this gap by using different learning methods. During the learning and classification

we used the projection values as input arguments.

In the second part of our talk we concentrate on Binary Tomography (a special kind of Discrete

Tomography)where it is supposed that the object is composed of onematerial. Thus, there

can be only two intensities on the cross-section image - one for the object points and one for

the background. Here, we compared our earlier presented binary tomographic evolutionary

reconstruction algorithm to two others. We present the details of the above-mentioned reconstruction

method and our experimental results. This paper is based on our previous works.

In binary tomography, the goal is to reconstruct binary images from a small set of their projections. However, especially when only two projections are used, the task can be extremely underdetermined. In this paper, we show how to reduce ambiguity by using the morphological skeleton of the image as a priori. Three different variants of our method based on Simulated Annealing are tested using artificial binary images, and compared by reconstruction time and error. {\textcopyright} 2012 Springer-Verlag.

}, doi = {10.1007/978-3-642-34732-0_20}, author = {Norbert Hantos and P{\'e}ter Bal{\'a}zs and K{\'a}lm{\'a}n Pal{\'a}gyi}, editor = {Reneta P Barneva and Valentin E Brimkov and Jake K Aggarwal} } @conference {1145, title = {Binary tomography using two projections and morphological skeleton}, booktitle = {Conference of PhD Students in Computer Science}, volume = {Volume of Extended Abstracts}, year = {2012}, month = {June 2012}, pages = {20}, publisher = {Univ Szeged Institute of Informatics}, organization = {Univ Szeged Institute of Informatics}, address = {Szeged} } @inbook {1133, title = {A central reconstruction based strategy for selecting projection angles in binary tomography}, booktitle = {Image Analysis and Recognition}, series = {Lecture Notes in Computer Science}, number = {7324}, year = {2012}, note = {ScopusID: 84864128031doi: 10.1007/978-3-642-31295-3_45}, month = {June 2012}, pages = {382 - 391}, publisher = {Springer}, organization = {Springer}, type = {Conference paper}, address = {Berlin; Heidelberg; New York; London; Paris; Tokyo}, abstract = {In this paper we propose a novel strategy for selecting projection angles in binary tomography which yields significantly more accurate reconstructions than others. In contrast with previous works which are of experimental nature, the method we present is based on theoretical observations. We report on experiments for different phantom images to show the effectiveness and roboustness of our procedure. The practically important case of noisy projections is also studied. {\textcopyright} 2012 Springer-Verlag.

}, doi = {10.1007/978-3-642-31295-3_45}, author = {P{\'e}ter Bal{\'a}zs and Joost K Batenburg}, editor = {Aur{\'e}lio Campilho and Mohamed Kamel} } @conference {1152, title = {Chlamydia inkl{\'u}zi{\'o}k automatiz{\'a}lt sz{\'a}mol{\'a}sa fluoreszcens DNS-chip szkenner seg{\'\i}ts{\'e}g{\'e}vel}, booktitle = {11. Cserh{\'a}ti Istv{\'a}n Eml{\'e}k{\"u}l{\'e}s : Fiatalok Tudom{\'a}nyos F{\'o}ruma}, year = {2012}, month = {2012.11.23}, pages = {37}, publisher = {SZTE {\'A}OK II. sz. Belgy{\'o}gy{\'a}szati Klinika {\'e}s Kardiol{\'o}giai K{\"o}zpont}, organization = {SZTE {\'A}OK II. sz. Belgy{\'o}gy{\'a}szati Klinika {\'e}s Kardiol{\'o}giai K{\"o}zpont}, address = {Szeged} } @article {1146, title = {Empirical studies of reconstructing hv-convex binary matrices from horizontal and vertical projections}, year = {2012}, month = {June 2012}, pages = {44}, publisher = {University of Szeged, Institute of Informatics}, type = {Abstract}, address = {Szeged}, author = {Zolt{\'a}n Ozsv{\'a}r and P{\'e}ter Bal{\'a}zs} } @inbook {1149, title = {An energy minimization reconstruction algorithm for multivalued discrete tomography}, booktitle = {Computational Modelling of Objects Represented in Images: Fundamentals, Methods and Applications III}, year = {2012}, month = {2012}, pages = {179 - 185}, publisher = {CRC Press - Taylor and Frances Group}, organization = {CRC Press - Taylor and Frances Group}, type = {Conference paper}, address = {London}, abstract = {We propose a new algorithm for multivalued discrete tomography, that reconstructs images from few projections by approximating the minimum of a suitably constructed energy function with a deterministic optimization method. We also compare the proposed algorithm to other reconstruction techniques on software phantom images, in order to prove its applicability.

}, doi = {10.1201/b12753-1}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy}, editor = {Paolo Di Giamberardino and Daniela Iacoviello and Renato M Natal Jorge and Joao Manuel R S Taveres} } @article {1147, title = {Extracting geometrical features of discrete images from their projections}, year = {2012}, month = {June 2012}, pages = {52}, publisher = {University of Szeged, Institute of Informatics}, type = {Abstract}, address = {Szeged}, author = {Tam{\'a}s S{\'a}muel Tasi and P{\'e}ter Bal{\'a}zs} } @inbook {1131, title = {Machine learning as a preprocessing phase in discrete tomography}, booktitle = {Applications of Discrete Geometry and Mathematical Morphology (WADGMM)}, series = {Lecture Notes in Computer Science}, number = {7346}, year = {2012}, note = {ScopusID: 84865454250doi: 10.1007/978-3-642-32313-3_8}, month = {Aug 2012}, pages = {109 - 124}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Berlin; Heidelberg; New York; London; Paris; Tokyo}, abstract = {In this paper we investigate for two well-known machine learning methods, decision trees and neural networks, how they classify discrete images from their projections. As an example, we present classification results when the task is to guess the number of intensity values of the discrete image. Machine learning can be used in Discrete Tomography as a preprocessing step in order to choose the proper reconstruction algorithm or - with the aid of the knowledge acquired - to improve its accuracy. We also show how to design new evolutionary reconstruction methods that can exploit the information gained by machine learning classifiers. {\textcopyright} 2012 Springer-Verlag.

}, doi = {10.1007/978-3-642-32313-3_8}, author = {Mih{\'a}ly Gara and Tam{\'a}s S{\'a}muel Tasi and P{\'e}ter Bal{\'a}zs}, editor = {Ullrich K{\"o}the and Annick Montanvert and Pierre Soille} } @article {1148, title = {A novel optimization-based reconstruction algorithm for multivalued discrete tomography}, year = {2012}, month = {June 2012}, pages = {57}, publisher = {University of Szeged, Institute of Informatics}, type = {Abstract}, address = {Szeged}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy} } @conference {1155, title = {An optimization-based reconstruction algorithm for multivalued discrete tomography}, booktitle = {Veszpr{\'e}m Optimization Conference: Advanced Algorithms (Vocal)}, year = {2012}, month = {Dec 2012}, pages = {39 - 40}, publisher = {University of Pannonia}, organization = {University of Pannonia}, type = {Conference paper}, address = {Veszpr{\'e}m}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy} } @conference {1132, title = {Perimeter estimation of some discrete sets from horizontal and vertical projections}, booktitle = {IASTED International Conference on Signal Processing, Pattern Recognition and Applications (SPPRA)}, year = {2012}, note = {ScopusID: 84864772360doi: 10.2316/P.2012.778-017}, month = {June 2012}, pages = {174 - 181}, publisher = {IASTED ACTA Press}, organization = {IASTED ACTA Press}, type = {Conference paper}, address = {Crete, Greek}, abstract = {In this paper, we design neural networks to estimate the perimeter of simple and more complex discrete sets from their horizontal and vertical projections. The information extracted this way can be useful to simplify the problem of reconstructing the discrete set from its projections, which task is in focus of discrete tomography. Beside presenting experimental results with neural networks, we also reveal some statistical properties of the perimeter of the studied discrete sets.

}, doi = {10.2316/P.2012.778-017}, author = {Tam{\'a}s S{\'a}muel Tasi and M Heged{\H u}s and P{\'e}ter Bal{\'a}zs}, editor = {M Petrou and A D Sappa and A G Triantafyllidis} } @conference {1154, title = {Solving binary tomography from morphological skeleton via optimization}, booktitle = {Veszpr{\'e}m Optimization Conference: Advanced Algorithms (VOCAL)}, year = {2012}, month = {Dec 2012}, pages = {42}, publisher = {University of Pannonia}, organization = {University of Pannonia}, type = {Conference paper}, address = {Veszpr{\'e}m}, author = {Norbert Hantos and P{\'e}ter Bal{\'a}zs and K{\'a}lm{\'a}n Pal{\'a}gyi} } @conference {1128, title = {Bin{\'a}ris tomogr{\'a}fiai rekonstrukci{\'o} objektum alap{\'u} evol{\'u}ci{\'o}s algoritmussal}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2011}, year = {2011}, month = {Jan 2011}, pages = {117 - 127}, publisher = {NJSZT}, organization = {NJSZT}, type = {Conference paper}, address = {Szeged} } @article {1127, title = {Direction-dependency of binary tomographic reconstruction algorithms}, journal = {GRAPHICAL MODELS}, volume = {73}, year = {2011}, note = {UT: 000296999100028ScopusID: 80054709026doi: 10.1016/j.gmod.2011.06.006}, month = {Nov 2011}, pages = {365 - 375}, type = {Journal article}, abstract = {In this work we study the relation between the quality of a binary tomographic reconstruction and the choice of angles of the projections. We conduct experiments on a set of software phantoms by reconstructing them from different projection sets using three different discrete tomography reconstruction algorithms, and compare the accuracy of the corresponding reconstructions with suitable approaches. To validate our results for possible real-world applications, we conduct the experiments by adding random noise of different characteristics to the simulated projection data, and by applying small topological changes on the phantom images as well. In addition, we also discuss some consequences of the angle-selection dependency and possible practical applications arising from the field of non-destructive testing, too.

}, isbn = {1524-0703}, doi = {10.1016/j.gmod.2011.06.006}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy} } @book {1150, title = {K{\'e}prekonstrukci{\'o}}, year = {2011}, month = {2011}, publisher = {Typotex Kiad{\'o}}, organization = {Typotex Kiad{\'o}}, type = {Book}, address = {Budapest} } @conference {1129, title = {Medi{\'a}nsz{\H u}r{\'e}s alkalmaz{\'a}sa algebrai rekonstrukci{\'o}s m{\'o}dszerekben}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2011}, year = {2011}, month = {Jan 2011}, pages = {106 - 116}, publisher = {NJSZT}, organization = {NJSZT}, type = {Conference paper}, address = {Szeged}, author = {Norbert Hantos and P{\'e}ter Bal{\'a}zs}, editor = {Zoltan Kato and K{\'a}lm{\'a}n Pal{\'a}gyi} } @article {1334, title = {Projection selection dependency in binary tomography}, journal = {ACTA CYBERNETICA-SZEGED}, volume = {20}, year = {2011}, note = {ScopusID: 79960679541}, month = {2011}, pages = {167 - 187}, publisher = {University of Szeged, Institute of Informatics}, type = {Journal article}, address = {Szeged}, abstract = {It has already been shown that the choice of projection angles can significantly influence the quality of reconstructions in discrete tomography. In this contribution we summarize and extend the previous results by explaining and demonstrating tile effects of projection selection dependency, in a set of experimental software tests. We perform reconstructions of software phantoms, by using different binary tomography reconstruction algorithms, from different equiangular and non-equiangular projections sets, under various conditions (i.e., when the objects to be reconstructed undergo slight topological changes, or the projection data is affected by noise) and compare the results with suitable approaches. Based on our observations, we reveal regularities in the resulting data and discuss possible consequences of such projection selection dependency in binary tomography.

\

}, isbn = {0324-721X}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy} } @conference {1173, title = {Tehets{\'e}ggondoz{\'o} program a Szegedi Tudom{\'a}nyegyetem Informatikai Tansz{\'e}kcsoport BSc szakjain}, booktitle = {Informatika a fels{\H o}oktat{\'a}sban 2011 konferencia}, year = {2011}, month = {Aug 2011}, pages = {905 - 912}, publisher = {Debreceni Egyetem Informatikai Kar}, organization = {Debreceni Egyetem Informatikai Kar}, type = {Conference paper}, address = {Debrecen}, author = {P{\'e}ter Bal{\'a}zs and Zolt{\'a}n L N{\'e}meth}, editor = {L{\'a}szl{\'o} Cser and Mikl{\'o}s Herdon} } @conference {1130, title = {Vet{\"u}leti ir{\'a}nyf{\"u}gg{\H o}s{\'e}g a bin{\'a}ris tomogr{\'a}fi{\'a}ban}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2011}, year = {2011}, month = {Jan 2011}, pages = {92 - 105}, publisher = {NJSZT}, organization = {NJSZT}, type = {Conference paper}, address = {Szeged}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy}, editor = {Zoltan Kato and K{\'a}lm{\'a}n Pal{\'a}gyi} } @conference {1121, title = {Binary tomographic reconstruction with an object-based evolutionary algorithm}, booktitle = {Conference of PhD Students in Computer Science. Volume of Extended Abstracts}, year = {2010}, month = {June 2010}, pages = {31}, publisher = {University of Szeged}, organization = {University of Szeged}, type = {Abstract}, address = {Szeged}, author = {Mih{\'a}ly Gara and P{\'e}ter Bal{\'a}zs} } @inbook {1110, title = {Direction-dependency of a binary tomographic reconstruction algorithm}, booktitle = {Computational Modeling of Objects Represented in Images}, series = {Lecture Notes in Computer Science}, number = {6026}, year = {2010}, note = {UT: 000279020400022ScopusID: 77952365308doi: 10.1007/978-3-642-12712-0_22}, month = {May 2010}, pages = {242 - 253}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Buffalo, NY, USA}, abstract = {We study how the quality of an image reconstructed by a binary tomographic algorithm depends on the direction of the observed object in the scanner, if only a few projections are available. To do so we conduct experiments on a set of software phantoms by reconstructing them form different projection sets using an algorithm based on D.C. programming (a method for minimizing the difference of convex functions), and compare the accuracy of the corresponding reconstructions by two suitable approaches. Based on the experiments, we discuss consequences on applications arising from the field of non-destructive testing, as well.

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}, isbn = {978-3-642-12711-3}, doi = {10.1007/978-3-642-12712-0_22}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy}, editor = {Reneta P Barneva and Valentin E Brimkov and Herbert A Hauptman and Renato M Natal Jorge and Jo{\~a}o Manuel R S Tavares} } @inbook {1119, title = {Image enhancement by median filters in algebraic reconstruction methods: an experimental study}, booktitle = {Advances in Visual Computing}, series = {Lecture Notes in Computer Science}, number = {6455}, year = {2010}, note = {UT: 000290358400035ScopusID: 78650793785doi: 10.1007/978-3-642-17277-9_35}, month = {Nov-Dec 2010}, pages = {339 - 348}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Las Vegas, NV, USA}, abstract = {Algebraic methods for image reconstruction provide good solutions even if only few projections are available. However, they can create noisy images if the number of iterations or the computational time is limited. In this paper, we show how to decrease the effect of noise by using median filters during the iterations. We present an extensive study by applying filters of different sizes and in various times of the reconstruction process. Also, our test images are of different structural complexity. Our study concentrates on the ART and its discrete variant DART reconstruction methods.

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}, isbn = {978-3-642-17276-2}, doi = {10.1007/978-3-642-17277-9_35}, author = {Norbert Hantos and P{\'e}ter Bal{\'a}zs}, editor = {George Bebis and Richard Boyle and Bahram Parvin and Darko Koracin and Ronald Chung and Riad Hammound and Muhammad Hussain and Tan Kar-Han and Roger Crawfis and Daniel Thalmann and David Kao and Lisa Avila} } @inbook {1125, title = {Machine learning for supporting binary tomographic reconstruction}, booktitle = {Workshop on Applications of Discrete Geometry in Mathematical Morphology}, series = {Lecture Notes in Computer Science}, year = {2010}, month = {Aug 2010}, pages = {101 - 105}, publisher = {Springer}, organization = {Springer}, type = {Conference paper}, address = {Istambul, Turkey}, author = {P{\'e}ter Bal{\'a}zs and Mih{\'a}ly Gara and Tam{\'a}s S{\'a}muel Tasi}, editor = {Ullrich K{\"o}the and Annick Montanvert and Pierre Soille} } @conference {1122, title = {Median filtering in algebraic reconstruction methods}, booktitle = {Conference of PhD Students in Computer Science. Volume of Extended Abstracts.}, year = {2010}, month = {June 2010}, pages = {36}, publisher = {University of Szeged}, organization = {University of Szeged}, type = {Abstract}, address = {Szeged, Hungary} } @conference {1124, title = {Object rotation effects on binary tomographic reconstruction}, booktitle = {Conference of PhD Students in Computer Science. Volume of Extended Abstracts}, year = {2010}, month = {June 2010}, pages = {76}, publisher = {University of Szeged}, organization = {University of Szeged}, type = {Abstract}, address = {Szeged, Hungary}, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy} } @conference {1123, title = {Obtaining geometrical properties of binary images from two projections using neural networks}, booktitle = {Conference of PhD Students in Computer Science. Volume of Extended Abstracts}, year = {2010}, month = {June 2010}, pages = {69}, publisher = {University of Szeged}, organization = {University of Szeged}, type = {Abstract}, address = {Szeged, Hungary}, author = {Tam{\'a}s S{\'a}muel Tasi and P{\'e}ter Bal{\'a}zs} } @inbook {1333, title = {Projection selection algorithms for discrete tomography}, booktitle = {Advanced Concepts for Intelligent Vision Systems}, year = {2010}, note = {UT: 000287941400037ScopusID: 78650892305doi: 10.1007/978-3-642-17688-3_37}, month = {Dec 2010}, pages = {390 - 401}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Sydney, Australia }, author = {L{\'a}szl{\'o} G{\'a}bor Varga and P{\'e}ter Bal{\'a}zs and Antal Nagy}, editor = {Jacques Blanc-Talon and Don Bone and Wilfried Philips and Dan Popescu and Paul Scheunders} } @article {1105, title = {A benchmark set for the reconstruction of hv-convex discrete sets}, journal = {DISCRETE APPLIED MATHEMATICS}, volume = {157}, year = {2009}, note = {UT: 000271375400009ScopusID: 70249142878doi: 10.1016/j.dam.2009.02.019}, month = {Aug 2009}, pages = {3447 - 3456}, publisher = {Elsevier}, type = {Journal article}, isbn = {0166-218X}, doi = {10.1016/j.dam.2009.02.019}, author = {P{\'e}ter Bal{\'a}zs} } @conference {1117, title = {D{\"o}nt{\'e}si f{\'a}kon alapul{\'o} el{\H o}feldolgoz{\'a}s a bin{\'a}ris tomogr{\'a}fi{\'a}ban}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2009}, year = {2009}, note = {8 pages}, month = {Jan 2009}, pages = {nincs sz{\'a}moz{\'a}s}, publisher = {Akaprint}, organization = {Akaprint}, type = {Conference paper}, address = {Budapest} } @inbook {1135, title = {An evolutionary approach for object-based image reconstruction using learnt priors}, booktitle = {Image Analysis}, series = {Lecture Notes in Computer Science}, number = {5575}, year = {2009}, note = {UT: 000268661000053ScopusID: 70350650400doi: 10.1007/978-3-642-02230-2_53}, month = {June 2009}, pages = {520 - 529}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, type = {Conference paper}, address = {Oslo, Norway}, abstract = {In this paper we present a novel algorithm for reconstructingbinary images containing objects which can be described by some parameters. In particular, we investigate the problem of reconstructing binary images representing disks from four projections. We develop a genetic algorithm for this and similar problems. We also discuss how prior information on the number of disks can be incorporated into the reconstruction in order to obtain more accurate images. In addition, we present a method to exploit such kind of knowledge from the projections themselves. Experiments on artificial data are also conducted. {\textcopyright} 2009 Springer Berlin Heidelberg.

}, isbn = {978-3-642-02229-6}, doi = {10.1007/978-3-642-02230-2_53}, author = {P{\'e}ter Bal{\'a}zs and Mih{\'a}ly Gara}, editor = {Arnt-Borre Salberg and Jon Yngve Hardeberg and Robert Jenssen} } @article {1106, title = {Learning connectedness and convexity of binary images from their projections}, journal = {PURE MATHEMATICS AND APPLICATIONS}, volume = {20}, year = {2009}, month = {2009}, pages = {27 - 48}, type = {Journal article}, isbn = {1218-4586}, author = {Mih{\'a}ly Gara and Tam{\'a}s S{\'a}muel Tasi and P{\'e}ter Bal{\'a}zs} } @conference {1118, title = {Neutron tomography with prior information}, booktitle = {5th Conference on Applied Inverse Problems}, volume = {Abstracts}, year = {2009}, month = {July 2009}, pages = {38}, type = {Conference paper} } @conference {1116, title = {Reconstruction of binary images with disjoint components from horizontal and vertical projections}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2009}, year = {2009}, note = {8 pages}, month = {Jan 2009}, publisher = {Akaprint}, organization = {Akaprint}, type = {Conference paper}, address = {Budapest} } @inbook {1134, title = {Reconstruction of canonical hv-convex discrete sets from horizontal and vertical projections}, booktitle = {Combinatorial Image Analysis}, number = {5852}, year = {2009}, note = {UT: 000279344100022ScopusID: 78650444641doi: 10.1007/978-3-642-10210-3_22}, month = {Nov 2009}, pages = {280 - 288}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Berlin; Heidelberg; New York; London; Paris; Tokyo}, abstract = {The problem of reconstructing some special hv-convex discretesets from their two orthogonal projections is considered. In general, the problem is known to be NP-hard, but it is solvable in polynomial time if the discrete set to be reconstructed is also 8-connected. In this paper, we define an intermediate class - the class of hv-convex canonical discrete sets - and give a constructive proof that the above problem remains computationally tractable for this class, too. We also discuss some further theoretical consequences and present experimental results as well. {\textcopyright} Springer-Verlag Berlin Heidelberg 2009.

}, isbn = {978-3-642-10208-0}, doi = {10.1007/978-3-642-10210-3_22}, author = {P{\'e}ter Bal{\'a}zs}, editor = {Petra Wiederhold and Reneta P Barneva} } @article {1102, title = {On the ambiguity of reconstructing hv-convex binary matrices with decomposable configurations}, journal = {ACTA CYBERNETICA-SZEGED}, volume = {18}, year = {2008}, note = {ScopusID: 47749139604}, month = {2008}, pages = {367 - 377}, publisher = {University of Szeged}, type = {Journal article}, address = {Szeged, Hungary}, abstract = {`Reconstructing binary matrices from their row, column, diagonal, and antidiagonal sums (also called projections) plays a central role in discrete tomography. One of the main difficulties in this task is that in certain cases the projections do not uniquely determine the binary matrix. This can yield an extremely large number of (sometimes very different) solutions. This ambiguity can be reduced by having some prior knowledge about the matrix to be reconstructed. The main challenge here is to find classes of binary matrices where ambiguity is drastically reduced or even completely eliminated. The goal of this paper is to study the class of $hv$-convex matrices which have decomposable configurations from the viewpoint of ambiguity. First, we give a negative result in the case of three projections. Then, we present a heuristic for the reconstruction using four projections and analyze its performance in quality and running time.`

In binary tomography, several algorithms are known for reconstructing binary images having some geometrical properties from their projections. In order to choose the appropriate reconstruction algorithm it is necessary to have a priori information of the image to be reconstructed. In this way we can improve the speed and reduce the ambiguity of the reconstruction. Our work is concerned with the problem of retrieving geometrical information from the projections themselves. We investigate whether it is possible to determine geometric features of binary images if only their projections are known. Most of the reconstruction algorithms based on geometrical information suppose $hv$-convexity or connectedness about the image to be reconstructed. We investigate those properties in detail, and also the task of separating 4- and 8-connected images. We suggest decision trees for the classification, and show some preliminary experimental results of applying them for the class of $hv$-convex and connected discrete sets. ` `

We present a general framework for reconstructing binary images with disjoint components from the horizontal and vertical projections. We develop a backtracking algorithm that works for binary images having components from an arbitrary class. Thus, a priori knowledge about the components of the image to be reconstructed can be incorporated into the reconstruction process. In addition, we show how to extend the algorithm to obtain a branch-and-bound scheme useful to reconstruct images satisfying some further properties (for example similarity to a model image) as much as possible. Experimental results are also presented.

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}, isbn = {0218-6543}, doi = {10.1142/S0218654308001142 }, author = {P{\'e}ter Bal{\'a}zs} } @article {1103, title = {A framework for generating some discrete sets with disjoint components by using uniform distributions}, journal = {THEORETICAL COMPUTER SCIENCE}, volume = {406}, year = {2008}, note = {UT: 000260289400004ScopusID: 51549107301doi: 10.1016/j.tcs.2008.06.010}, month = {Oct 2008}, pages = {15 - 23}, publisher = {Elsevier}, type = {Journal article}, isbn = {0304-3975}, doi = {10.1016/j.tcs.2008.06.010}, author = {P{\'e}ter Bal{\'a}zs} } @inbook {1172, title = {A k{\'e}pfeldolgoz{\'a}s kutat{\'a}sa a Szegedi Tudom{\'a}nyegyetemen}, booktitle = {Informatika a fels{\H o}oktat{\'a}sban 2008}, year = {2008}, note = {Art. No.: E62}, month = {2008///}, publisher = {Debreceni Egyetem Informatikai Kar}, organization = {Debreceni Egyetem Informatikai Kar}, address = {Debrecen}, abstract = {A digit{\'a}lis k{\'e}pfeldolgoz{\'a}s kutat{\'a}s{\'a}nak a Szegedi Tudom{\'a}nyegyetemTerm{\'e}szettudom{\'a}nyi {\'e}s Informatikai Kar{\'a}n, az Informatikai Tansz{\'e}kcsoport K{\'e}pfeldolgoz{\'a}s {\'e}s Sz{\'a}m{\'\i}t{\'o}g{\'e}pes Grafika Tansz{\'e}k{\'e}n k{\"o}zel n{\'e}gy {\'e}vtizedes hagyom{\'a}nya van. A Tansz{\'e}k valamennyi munkat{\'a}rsa nemzetk{\"o}zileg elismert kutat{\'o}munk{\'a}t folytat, melyet m{\'a}r t{\"o}bb sz{\'a}z rangos publik{\'a}ci{\'o} f{\'e}mjelez. Sz{\'a}mos, a k{\'e}pfeldolgoz{\'a}s kutat{\'a}s{\'a}ban vezet{\H o} egyetemmel {\'e}s kutat{\'o}int{\'e}zettel {\'e}p{\'\i}tett{\"u}nk ki szoros kapcsolatot {\'e}s folytattunk eredm{\'e}nyes kutat{\'o}munk{\'a}t, akt{\'\i}v r{\'e}sztvev{\H o}i vagyunk a hazai {\'e}s a nemzetk{\"o}zi tudom{\'a}nyos k{\"o}z{\'e}letnek. A legfontosabb, jelenleg is foly{\'o} kutat{\'a}saink: orvosi k{\'e}pek feldolgoz{\'a}sa, diszkr{\'e}t tomogr{\'a}fia, k{\'e}pszegment{\'a}l{\'a}s, t{\'e}rinformatika, t{\'a}v{\'e}rz{\'e}kel{\'e}s, k{\'e}pregisztr{\'a}ci{\'o}, v{\'a}zkijel{\"o}l{\'e}s, m{\H u}t{\'e}ti tervez{\'e}s. }, url = {http://www.agr.unideb.hu/if2008/kiadvany/papers/E62.pdf} } @inbook {1138, title = {On the number of hv-convex discrete sets}, booktitle = {Combinatorial Image Analysis}, series = {Lecture Notes in Computer Science}, number = {4958}, year = {2008}, note = {UT: 000254600100010ScopusID: 70249110264doi: 10.1007/978-3-540-78275-9_10}, month = {Apr 2008}, pages = {112 - 123}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Buffalo, NY, USA}, abstract = {One of the basic problems in discrete tomography is thereconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfills some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. The class of hv-convex discrete sets and its subclasses have a well-developed theory. Several reconstruction algorithms as well as some complexity results are known for those classes. The key to achieve polynomial-time reconstruction of an hv- convex discrete set is to have the additional assumption that the set is connected as well. This paper collects several statistics on hv-convex discrete sets, which are of great importance in the analysis of algorithms for reconstructing such kind of discrete sets. {\textcopyright} 2008 Springer-Verlag Berlin Heidelberg.

}, isbn = {978-3-540-78274-2}, doi = {10.1007/978-3-540-78275-9_10}, author = {P{\'e}ter Bal{\'a}zs}, editor = {Valentin E Brimkov and Reneta P Barneva and Herbert A Hauptman} } @inbook {1137, title = {Reconstruction of binary images with few disjoint components from two projections}, booktitle = {Advances in Visual Computing}, series = {Lecture Notes in Computer Science}, number = {5359}, year = {2008}, note = {UT: 000262709700114ScopusID: 70149090157doi: 10.1007/978-3-540-89646-3_114}, month = {Dec 2008}, pages = {1147 - 1156}, publisher = {Springer Verlag}, organization = {Springer Verlag}, type = {Conference paper}, address = {Las Vegas, NV, USA}, abstract = {We present a general framework for reconstructing binary imageswith few disjoint components from the horizontal and vertical projections. We develop a backtracking algorithm that works for binary images having components from an arbitrary class. Thus, a priori information about the components of the image to be reconstructed can be incorporated into the reconstruction process. In addition, we can keep control over the number of components which can increase the speed and accuracy of the reconstruction. Experimental results are also presented. {\textcopyright} 2008 Springer Berlin Heidelberg.

}, isbn = {978-3-540-89645-6}, issn = {0302-9743}, doi = {10.1007/978-3-540-89646-3_114}, author = {P{\'e}ter Bal{\'a}zs}, editor = {George Bebis and Richard Boyle and Bahram Parvin and Darko Koracin and Paolo Remagnino and Fatih Porikli and J{\"o}rg Peters and James Klosowski and Laura Arns and Yu Ka Chun and Theresa-Marie Rhyne and Laura Monroe} } @mastersthesis {1107, title = {Binary Tomography Using Geometrical Priors: Uniqueness and Reconstruction Results}, year = {2007}, month = {2007}, school = {University of Szeged}, type = {PhD thesis}, address = {Szeged, Hungary}, author = {P{\'e}ter Bal{\'a}zs} } @inbook {1142, title = {Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components}, booktitle = {ADVANCES IN DISCRETE TOMOGRAPHY AND ITS APPLICATIONS}, series = {Applied and Numerical Harmonic Analysis}, year = {2007}, note = {UT: 000271523600010doi: 10.1007/978-0-8176-4543-4_8}, month = {2007}, pages = {153 - 173}, publisher = {Birkhauser Boston}, organization = {Birkhauser Boston}, type = {Book chapter}, address = {Cambridge}, abstract = {The reconstruction of discrete sets from their projections is a frequently studied field in discrete tomography with applications in electron microscopy, image processing, radiology, and so on. Several efficient reconstruction algorithms have been developed for certain classes of discrete sets having some good geometrical properties. On the other hand, it has been shown that the reconstruction under certain circumstances can be very time-consuming, even NP-hard. In this chapter we show how prior information that the set to be reconstructed consists of several components can be exploited in order to facilitate the reconstruction. We present some general techniques to decompose a discrete set into components knowing only its projections and thus reduce the reconstruction of a general discrete set to the reconstruction of single components, which is usually a simpler task.

}, isbn = {978-0-8176-3614-2}, doi = {10.1007/978-0-8176-4543-4_8}, author = {P{\'e}ter Bal{\'a}zs}, editor = {G{\'a}bor T Herman and Attila Kuba} } @article {1101, title = {A decomposition technique for reconstructing discrete sets from four projections}, journal = {IMAGE AND VISION COMPUTING}, volume = {25}, year = {2007}, note = {UT: 000249047200009ScopusID: 34447547739doi: 10.1016/j.imavis.2006.06.015}, month = {Oct 2007}, pages = {1609 - 1619}, publisher = {Elsevier}, type = {Journal article}, abstract = {The reconstruction of discrete sets from four projections is in general an NP-hard problem. In this paper we study the class of decomposable discrete sets and give an efficient reconstruction algorithm for this class using four projections. It is also shown that an arbitrary discrete set which is Q-convex along the horizontal and vertical directions and consists of several components is decomposable. As a consequence of decomposability we get that in a subclass of *hv*-convex discrete sets the reconstruction from four projections can also be solved in polynomial time. Possible extensions of our method are also discussed.

One of the basic problems in discrete tomography is thereconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfils some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. Since the reconstruction from two projections in the class of so-called hv-convex sets is NP-hard this class is suitable to test the efficiency of newly developed reconstruction algorithms. However, until now no method was known to generate sets of this class from uniform random distribution and thus only ad hoc comparison of several reconstruction techniques was possible. In this paper we first describe a method to generate some special hv-convex discrete sets from uniform random distribution. Moreover, we show that the developed generation technique can easily be adapted to other classes of discrete sets, even for the whole class of hv- convexes. Several statistics are also presented which are of great importance in the analysis of algorithms for reconstructing hv-convex sets. {\textcopyright} Springer-Verlag Berlin Heidelberg 2007.

}, isbn = {978-3-540-73039-2}, issn = {0302-9743}, doi = {10.1007/978-3-540-73040-8_35}, author = {P{\'e}ter Bal{\'a}zs}, editor = {Bjarne Kj{\ae}r Ersb{\o}ll and Kim Steenstrup Pedersen} } @inbook {1143, title = {Reconstructing some hv-convex binary images from three or four projections}, booktitle = {Proccedings of the 5th International Symposium on Image and Signal Processing and Analysis}, year = {2007}, note = {UT: 000253387900025ScopusID: 7949129892doi: 10.1109/ISPA.2007.4383678}, month = {Sep 2007}, pages = {136 - 140}, publisher = {IEEE}, organization = {IEEE}, type = {Conference paper}, address = {Istanbul, Turkey}, abstract = {The reconstruction of binary images from their projections is animportant problem in discrete tomography. The main challenge in this task is that in certain cases the projections do not uniquely determine the binary image. This can yield an extremely large number of (sometimes very different) solutions. Moreover, under certain circumstances the reconstruction becomes NP-hard. A commonly used technique to reduce ambiguity and to avoid intractability is to suppose that the image to be reconstructed arises from a certain class of images having some geometrical properties. This paper studies the reconstruction problem in the class of hv-convex images having their components in so-called decomposable configurations. First, we give a negative result showing that there can be exponentially many images of the above class having the same three projections. Then, we present a heuristic that uses four projections to reconstruct an hv-convex image with decomposable configuration. We also analyze the performance of our heuristic from the viewpoints of accuracy and running time.

}, isbn = {978-953-184-116-0 }, doi = {10.1109/ISPA.2007.4383678 }, author = {P{\'e}ter Bal{\'a}zs}, editor = {M Petrou and T Saramaki and Aytul Ercil and Sven Lon{\v c}ari{\'c}} } @conference {1114, title = {Uniform generation of hv-convex discrete sets}, booktitle = {A K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}g{\'a}nak konferenci{\'a}ja - K{\'E}PAF 2007}, year = {2007}, month = {Jan 2007}, pages = {63 - 70}, publisher = {K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}ga}, organization = {K{\'e}pfeldolgoz{\'o}k {\'e}s Alakfelismer{\H o}k T{\'a}rsas{\'a}ga}, type = {Conference paper}, address = {Debrecen} } @conference {1113, title = {On the ambiguity of reconstructing decomposable hv-convex binary matrices}, booktitle = {Conference of PhD Students in Computer Science}, volume = {Volume of Extenden Abstracts}, year = {2006}, month = {June 2006}, pages = {17} } @inbook {1140, title = {The number of line-convex directed polyominoes having the same orthogonal projections}, booktitle = {Discrete Geometry for Computer Imagery}, year = {2006}, note = {UT: 000241649600007ScopusID: 33845210215}, month = {2006///}, pages = {77 - 85}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, address = {Berlin, Heidelberg}, abstract = {The number of line-convex directed polyominoes with givenhorizontal and vertical projections is studied. It is proven that diagonally convex directed polyominoes are uniquely determined by their orthogonal projections. The proof of this result is algorithmical. As a counterpart, we show that ambiguity can be exponential if antidiagonal convexity is assumed about the polyomino. Then, the results are generalised to polyominoes having convexity property along arbitrary lines. {\textcopyright} Springer-Verlag Berlin Heidelberg 2006.

} } @article {1100, title = {Reconstruction of 8-connected but not 4-connected hv-convex discrete sets}, journal = {DISCRETE APPLIED MATHEMATICS}, volume = {147}, year = {2005}, note = {UT: 000228118600002ScopusID: 14744285148doi: 10.1016/j.dam.2004.09.009}, month = {2005///}, pages = {149 - 168}, isbn = {0166-218X} } @inbook {1141, title = {Reconstruction of decomposable discrete sets from four projections}, booktitle = {Discrete Geometry for Computer Imagery}, year = {2005}, note = {UT: 000229183900010ScopusID: 24344465865}, month = {2005///}, pages = {104 - 114}, publisher = {Springer Verlag}, organization = {Springer Verlag}, address = {Berlin; Heidelberg; New York; London; Paris; Tokyo}, abstract = {In this paper we introduce the class of decomposable discretesets and give a polynomial algorithm for reconstructing discrete sets of this class from four projections. It is also shown that the class of decomposable discrete sets is more general than the class S'8 of hv-convex 8-but not 4-connected discrete sets which was studied in [3]. As a consequence we also get that the reconstruction from four projections in S'8can be solved in O(mn) time. {\textcopyright} Springer-Verlag Berlin Heidelberg 2005.

} } @article {1109, title = {Reconstruction of discrete sets from four projections: strong decomposability}, journal = {ELECTRONIC NOTES IN DISCRETE MATHEMATICS}, volume = {20}, year = {2005}, note = {ScopusID: 34247130130doi: 10.1016/j.endm.2005.05.072}, month = {2005///}, pages = {329 - 345}, isbn = {1571-0653} } @conference {1112, title = {Reconstruction of discrete sets from four projections: Decomposable cases}, booktitle = {Conference of PhD Students in Computer Science}, volume = {Volume of Extended Abstracts}, year = {2004}, month = {July 2004}, pages = {22} } @inbook {1108, title = {A fast algorithm for reconstructing hv-convex 8-connected but not 4-connected discrete sets}, booktitle = {Discrete Geometry for Computer Imagery}, year = {2003}, note = {UT: 000187499600037ScopusID: 0242460250}, month = {2003///}, pages = {388 - 397}, publisher = {Springer Verlag}, organization = {Springer Verlag}, address = {Berlin; Heidelberg; New York; London; Paris; Tokyo} } @conference {1111, title = {A fast algorithm for reconstructing hv-convex 8-connected but not 4-connected discrete sets}, booktitle = {Conference of PhD Students in Computer Science}, volume = {Volume of Extended Abstracts}, year = {2002}, month = {July 2002}, pages = {19} }