Tomography is an imaging procedure to examine the internal structure of objects. The crosssection

images are constructed with the aid of the object’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 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. © 2012 Springer-Verlag.

%B Applications of Discrete Geometry and Mathematical Morphology (WADGMM) %S Lecture Notes in Computer Science %I Springer Verlag %C Berlin; Heidelberg; New York; London; Paris; Tokyo %P 109 - 124 %8 Aug 2012 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-32313-3_8 %0 Conference Paper %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2011 %D 2011 %T Bináris tomográfiai rekonstrukció objektum alapú evolúciós algoritmussal %A Mihály Gara %A Péter Balázs %E Zoltan Kato %E Kálmán Palágyi %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2011 %I NJSZT %C Szeged %P 117 - 127 %8 Jan 2011 %G eng %9 Conference paper %0 Conference Paper %B Conference of PhD Students in Computer Science. Volume of Extended Abstracts %D 2010 %T Binary tomographic reconstruction with an object-based evolutionary algorithm %A Mihály Gara %A Péter Balázs %B Conference of PhD Students in Computer Science. Volume of Extended Abstracts %I University of Szeged %C Szeged %P 31 %8 June 2010 %G eng %9 Abstract %0 Book Section %B Workshop on Applications of Discrete Geometry in Mathematical Morphology %D 2010 %T Machine learning for supporting binary tomographic reconstruction %A Péter Balázs %A Mihály Gara %A Tamás Sámuel Tasi %E Ullrich Köthe %E Annick Montanvert %E Pierre Soille %B Workshop on Applications of Discrete Geometry in Mathematical Morphology %S Lecture Notes in Computer Science %I Springer %C Istambul, Turkey %P 101 - 105 %8 Aug 2010 %G eng %9 Conference paper %! LNCS %0 Conference Paper %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2009 %D 2009 %T Döntési fákon alapuló előfeldolgozás a bináris tomográfiában %A Mihály Gara %A Péter Balázs %E Dmitrij Chetverikov %E Tamas Sziranyi %B A Képfeldolgozók és Alakfelismerők Társaságának konferenciája - KÉPAF 2009 %I Akaprint %C Budapest %P nincs számozás %8 Jan 2009 %G hun %9 Conference paper %0 Book Section %B Image Analysis %D 2009 %T An evolutionary approach for object-based image reconstruction using learnt priors %A Péter Balázs %A Mihály Gara %E Arnt-Borre Salberg %E Jon Yngve Hardeberg %E Robert Jenssen %XIn 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. © 2009 Springer Berlin Heidelberg.

%B Image Analysis %S Lecture Notes in Computer Science %I Springer-Verlag %C Oslo, Norway %P 520 - 529 %8 June 2009 %@ 978-3-642-02229-6 %G eng %9 Conference paper %! LNCS %R 10.1007/978-3-642-02230-2_53 %0 Journal Article %J PURE MATHEMATICS AND APPLICATIONS %D 2009 %T Learning connectedness and convexity of binary images from their projections %A Mihály Gara %A Tamás Sámuel Tasi %A Péter Balázs %B PURE MATHEMATICS AND APPLICATIONS %V 20 %P 27 - 48 %8 2009 %@ 1218-4586 %G eng %N 1-2 %9 Journal article %! PU.M.A PURE MATH APPL %0 Generic %D 2009 %T Supervised Color Image Segmentation in a Markovian Framework %A Mihály Gara %A Zoltan Kato %XThis is the sample implementation of a Markov random field based color image segmentation algorithm described in the following paper: Zoltan Kato, Ting Chuen Pong, and John Chung Mong Lee. Color Image Segmentation and Parameter Estimation in a Markovian Framework. Pattern Recognition Letters, 22(3-4):309--321, March 2001. Note that the current demo program implements only a supervised version of the segmentation method described in the above paper (i.e. parameter values are learned interactively from representative regions selected by the user). Otherwise, the program implements exactly the color MRF model proposed in the paper. Images are automatically converted from RGB to the perceptually uniform CIE-L*u*v* color space before segmentation.

%8 2009/// %G eng %U http://www.inf.u-szeged.hu/~kato/software/colormrfdemo.html %0 Conference Paper %B Conference of PhD Students in Computer Science. Volume of Extended Abstracts %D 2008 %T Determination of geometric features of binary images from their projections by using decision trees %A Mihály Gara %A Péter Balázs %E Kálmán Palágyi %E Balázs Bánhelyi %E Tamás Gergely %E István Matievics %B Conference of PhD Students in Computer Science. Volume of Extended Abstracts %I University of Szeged %C Szeged, Hungary %P 26 %8 July 2008 %G eng %9 Abstract