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.

VL - 141 IS - 2-3 ER - TY - CHAP T1 - Directional Convexity Measure for Binary Tomography T2 - Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications Y1 - 2013 A1 - Tamás Sámuel Tasi A1 - László Gábor Nyúl A1 - Péter Balázs ED - Gabriella Sanniti di Baja ED - Jose Ruiz-Shulcloper AB -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.

JF - Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications PB - Springer Verlag CY - Berlin; Heidelberg UR - http://link.springer.com/chapter/10.1007%2F978-3-642-41827-3_2 N1 - ScopusID: 84893169866doi: 10.1007/978-3-642-41827-3_2 ER - TY - Generic T1 - Extracting geometrical features of discrete images from their projections Y1 - 2012 A1 - Tamás Sámuel Tasi A1 - Péter Balázs JF - Conference of PhD students in computer science. Volume of Extended Abstracts. PB - University of Szeged, Institute of Informatics CY - Szeged ER - TY - CHAP T1 - Machine learning as a preprocessing phase in discrete tomography T2 - Applications of Discrete Geometry and Mathematical Morphology (WADGMM) Y1 - 2012 A1 - Mihály Gara A1 - Tamás Sámuel Tasi A1 - Péter Balázs ED - Ullrich Köthe ED - Annick Montanvert ED - Pierre Soille AB -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.

JF - Applications of Discrete Geometry and Mathematical Morphology (WADGMM) T3 - Lecture Notes in Computer Science PB - Springer Verlag CY - Berlin; Heidelberg; New York; London; Paris; Tokyo N1 - ScopusID: 84865454250doi: 10.1007/978-3-642-32313-3_8 JO - LNCS ER - TY - CONF T1 - Perimeter estimation of some discrete sets from horizontal and vertical projections T2 - IASTED International Conference on Signal Processing, Pattern Recognition and Applications (SPPRA) Y1 - 2012 A1 - Tamás Sámuel Tasi A1 - M Hegedűs A1 - Péter Balázs ED - M Petrou ED - A D Sappa ED - A G Triantafyllidis AB -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.

JF - IASTED International Conference on Signal Processing, Pattern Recognition and Applications (SPPRA) PB - IASTED ACTA Press CY - Crete, Greek N1 - ScopusID: 84864772360doi: 10.2316/P.2012.778-017 ER - TY - CHAP T1 - Machine learning for supporting binary tomographic reconstruction T2 - Workshop on Applications of Discrete Geometry in Mathematical Morphology Y1 - 2010 A1 - Péter Balázs A1 - Mihály Gara A1 - Tamás Sámuel Tasi ED - Ullrich Köthe ED - Annick Montanvert ED - Pierre Soille JF - Workshop on Applications of Discrete Geometry in Mathematical Morphology T3 - Lecture Notes in Computer Science PB - Springer CY - Istambul, Turkey JO - LNCS ER - TY - CONF T1 - Obtaining geometrical properties of binary images from two projections using neural networks T2 - Conference of PhD Students in Computer Science. Volume of Extended Abstracts Y1 - 2010 A1 - Tamás Sámuel Tasi A1 - Péter Balázs JF - Conference of PhD Students in Computer Science. Volume of Extended Abstracts PB - University of Szeged CY - Szeged, Hungary ER - TY - JOUR T1 - Learning connectedness and convexity of binary images from their projections JF - PURE MATHEMATICS AND APPLICATIONS Y1 - 2009 A1 - Mihály Gara A1 - Tamás Sámuel Tasi A1 - Péter Balázs VL - 20 SN - 1218-4586 IS - 1-2 JO - PU.M.A PURE MATH APPL ER -