Directional convexity measure for binary tomography

Tamás Sámuel Tasi, L. Nyúl, Péter Balázs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages9-16
Number of pages8
Volume8259 LNCS
EditionPART 2
DOIs
Publication statusPublished - 2013
Event18th Iberoamerican Congress on Pattern Recognition, CIARP 2013 - Havana, Cuba
Duration: Nov 20 2013Nov 23 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume8259 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other18th Iberoamerican Congress on Pattern Recognition, CIARP 2013
CountryCuba
CityHavana
Period11/20/1311/23/13

Fingerprint

Tomography
Convexity
Binary
Experiments
Configuration
Alternatives
Experiment

Keywords

  • Binary tomography
  • Convexity measure
  • Discrete geometry

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Tasi, T. S., Nyúl, L., & Balázs, P. (2013). Directional convexity measure for binary tomography. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 2 ed., Vol. 8259 LNCS, pp. 9-16). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8259 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-41827-3_2

Directional convexity measure for binary tomography. / Tasi, Tamás Sámuel; Nyúl, L.; Balázs, Péter.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8259 LNCS PART 2. ed. 2013. p. 9-16 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8259 LNCS, No. PART 2).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Tasi, TS, Nyúl, L & Balázs, P 2013, Directional convexity measure for binary tomography. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 2 edn, vol. 8259 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 8259 LNCS, pp. 9-16, 18th Iberoamerican Congress on Pattern Recognition, CIARP 2013, Havana, Cuba, 11/20/13. https://doi.org/10.1007/978-3-642-41827-3_2
Tasi TS, Nyúl L, Balázs P. Directional convexity measure for binary tomography. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 2 ed. Vol. 8259 LNCS. 2013. p. 9-16. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). https://doi.org/10.1007/978-3-642-41827-3_2
Tasi, Tamás Sámuel ; Nyúl, L. ; Balázs, Péter. / Directional convexity measure for binary tomography. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8259 LNCS PART 2. ed. 2013. pp. 9-16 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2).
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