A reduction operator transforms a binary picture only by changing some black points to white ones, which is referred to as deletion. Sequential reductions may delete just one point at a time, while parallel reductions can alter a set of points simultaneously. Two reductions are called equivalent if they produce the same result for each input picture. This work lays a bridge between the parallel and the sequential strategies. A class of deletion rules are proposed that provide 2D parallel reductions being equivalent to sequential reductions. Some new sufficient conditions for topology-preserving parallel reductions are also reported.

JF - Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications T3 - Lecture Notes in Computer Science PB - Springer CY - Berlin; Heidelberg SN - 978-3-642-41821-1 UR - http://link.springer.com/chapter/10.1007%2F978-3-642-41822-8_3 N1 - Lecture Notes in Computer Science, Vol. 8258 JO - Conference Paper 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 - CHAP T1 - Reconstruction and Enumeration of hv-Convex Polyominoes with Given Horizontal Projection T2 - Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications (CIARP) Y1 - 2013 A1 - Norbert Hantos A1 - Péter Balázs ED - Jose Ruiz-Shulcloper ED - Gabriella Sanniti di Baja JF - Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications (CIARP) T3 - Lecture Notes in Computer Science PB - Springer CY - Heidelberg; London; New York SN - 978-3-642-41821-1 N1 - ScopusID: 84893181366doi: 10.1007/978-3-642-41822-8_13 ER - TY - CHAP T1 - A fast algorithm for reconstructing hv-convex 8-connected but not 4-connected discrete sets T2 - Discrete Geometry for Computer Imagery Y1 - 2003 A1 - Péter Balázs A1 - Emese Balogh A1 - Attila Kuba ED - Ingela Nyström ED - Gabriella Sanniti di Baja ED - Stina Svensson JF - Discrete Geometry for Computer Imagery PB - Springer Verlag CY - Berlin; Heidelberg; New York; London; Paris; Tokyo N1 - UT: 000187499600037ScopusID: 0242460250 ER -