Directional Convexity Measure for Binary Tomography

  • Tamás Sámuel Tasi
  • László G. Nyúl
  • Péter Balázs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8259)

Abstract

There is an increasing demand for a new measure of convexity for discrete 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.

Keywords

Binary Tomography Discrete Geometry Convexity Measure 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tamás Sámuel Tasi
    • 1
  • László G. Nyúl
    • 1
  • Péter Balázs
    • 1
  1. 1.Department of Image Processing and Computer GraphicsUniversity of SzegedSzegedHungary

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