Inspired by binary tomography, we present a measure of directional convexity of binary images combining various properties of the configuration of 0s and 1s in the binary image. The measure can be supported by proper theory, is easy to compute, and as shown in our experiments, behaves intuitively. The measure can be useful in numerous applications of digital image processing and pattern recognition, and especially in binary tomography. We show in detail an application of this latter one, by providing a novel reconstruction algorithm for almost hv-convex binary images. We also present experimental results and mention some of the possible generalizations of the measure.

1 aBalázs, Péter1 aOzsvár, Zoltán1 aTasi, Tamás Sámuel1 aNyúl, László, G uhttp://www.inf.u-szeged.hu/en/publication/a-measure-of-directional-convexity-inspired-by-binary-tomography01468nas a2200169 4500008004100000245005600041210005600097260004600153300001100199520089100210100002501101700002801126700002001154700003101174700002601205856006701231 2013 eng d00aDirectional Convexity Measure for Binary Tomography0 aDirectional Convexity Measure for Binary Tomography aBerlin; HeidelbergbSpringer Verlagc2013 a9 - 163 aThere 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.

1 aTasi, Tamás Sámuel1 aNyúl, László, Gábor1 aBalázs, Péter1 aSanniti di Baja, Gabriella1 aRuiz-Shulcloper, Jose uhttp://link.springer.com/chapter/10.1007%2F978-3-642-41827-3_200552nas a2200121 4500008004100000245007800041210006900119260007000188300000700258100002500265700002000290856012000310 2012 eng d00aExtracting geometrical features of discrete images from their projections0 aExtracting geometrical features of discrete images from their pr aSzegedbUniversity of Szeged, Institute of InformaticscJune 2012 a521 aTasi, Tamás Sámuel1 aBalázs, Péter uhttp://www.inf.u-szeged.hu/en/publication/extracting-geometrical-features-of-discrete-images-from-their-projections01368nas a2200181 4500008004100000245006900041210006900110260008200179300001400261520067500275100001800950700002500968700002000993700002001013700002301033700001901056856011101075 2012 eng d00aMachine learning as a preprocessing phase in discrete tomography0 aMachine learning as a preprocessing phase in discrete tomography aBerlin; Heidelberg; New York; London; Paris; TokyobSpringer VerlagcAug 2012 a109 - 1243 aIn 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.

1 aGara, Mihály1 aTasi, Tamás Sámuel1 aBalázs, Péter1 aKöthe, Ullrich1 aMontanvert, Annick1 aSoille, Pierre uhttp://www.inf.u-szeged.hu/en/publication/machine-learning-as-a-preprocessing-phase-in-discrete-tomography01182nas a2200181 4500008004100000245008800041210006900129260004700198300001400245520049500259100002500754700001600779700002000795700001400815700001600829700002500845856013000870 2012 eng d00aPerimeter estimation of some discrete sets from horizontal and vertical projections0 aPerimeter estimation of some discrete sets from horizontal and v aCrete, GreekbIASTED ACTA PresscJune 2012 a174 - 1813 aIn 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.

1 aTasi, Tamás Sámuel1 aHegedűs, M1 aBalázs, Péter1 aPetrou, M1 aSappa, A, D1 aTriantafyllidis, A G uhttp://www.inf.u-szeged.hu/en/publication/perimeter-estimation-of-some-discrete-sets-from-horizontal-and-vertical-projections00642nas a2200169 4500008004100000245007000041210006900111260004100180300001400221100002000235700001800255700002500273700002000298700002300318700001900341856011200360 2010 eng d00aMachine learning for supporting binary tomographic reconstruction0 aMachine learning for supporting binary tomographic reconstructio aIstambul, TurkeybSpringercAug 2010 a101 - 1051 aBalázs, Péter1 aGara, Mihály1 aTasi, Tamás Sámuel1 aKöthe, Ullrich1 aMontanvert, Annick1 aSoille, Pierre uhttp://www.inf.u-szeged.hu/en/publication/machine-learning-for-supporting-binary-tomographic-reconstruction00573nas a2200121 4500008004100000245009700041210006900138260005300207300000700260100002500267700002000292856013900312 2010 eng d00aObtaining geometrical properties of binary images from two projections using neural networks0 aObtaining geometrical properties of binary images from two proje aSzeged, HungarybUniversity of SzegedcJune 2010 a691 aTasi, Tamás Sámuel1 aBalázs, Péter uhttp://www.inf.u-szeged.hu/en/publication/obtaining-geometrical-properties-of-binary-images-from-two-projections-using-neural-networks00577nas a2200157 4500008004100000020001400041245008100055210006900136260000900205300001200214490000700226100001800233700002500251700002000276856012300296 2009 eng d a1218-458600aLearning connectedness and convexity of binary images from their projections0 aLearning connectedness and convexity of binary images from their c2009 a27 - 480 v201 aGara, Mihály1 aTasi, Tamás Sámuel1 aBalázs, Péter uhttp://www.inf.u-szeged.hu/en/publication/learning-connectedness-and-convexity-of-binary-images-from-their-projections