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.

}, doi = {10.3233/FI-2015-1269}, author = {P{\'e}ter Bal{\'a}zs and Zolt{\'a}n Ozsv{\'a}r and Tam{\'a}s S{\'a}muel Tasi and L{\'a}szl{\'o} G Ny{\'u}l} } @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 {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} } @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} } @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 {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} } @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} }