Fixpoints of Iterated Reductions with Equivalent Deletion Rules

Kálmán Palágyi, Gábor Németh

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

Abstract

A reduction transforms a binary picture only by deleting some black points to white ones. Sequential reductions traverse the black points of a picture, and focus on the actually visited point for possible deletion, while parallel reductions delete all ‘deletable’ black points simultaneously. Two reductions are called equivalent if they produce the same result for each input picture. A deletion rule is said to be equivalent if it provides a pair of equivalent sequential and parallel reductions. Thinning and shrinking algorithms iterate reductions until no points are deleted. If a black point is not deleted in an iteration step, it is taken into consideration again in the next step. This work examine fixpoints of iterated reductions with equivalent deletion rules, i.e., ‘survival’ points whose rechecking is not needed in the remaining iterations.

Original languageEnglish
Title of host publicationCombinatorial Image Analysis - 19th International Workshop, IWCIA 2018, Proceedings
EditorsReneta P. Barneva, João Manuel R.S Tavares, Valentin E. Brimkov
PublisherSpringer Verlag
Pages17-27
Number of pages11
ISBN (Print)9783030052874
DOIs
Publication statusPublished - Jan 1 2018
Event19th International Workshop on Combinatorial Image Analysis, IWCIA 2018 - Porto, Portugal
Duration: Nov 22 2018Nov 24 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11255 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other19th International Workshop on Combinatorial Image Analysis, IWCIA 2018
CountryPortugal
CityPorto
Period11/22/1811/24/18

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Keywords

  • Digital geometry and topology
  • Equivalent reduction
  • Thinning

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Palágyi, K., & Németh, G. (2018). Fixpoints of Iterated Reductions with Equivalent Deletion Rules. In R. P. Barneva, J. M. R. S. Tavares, & V. E. Brimkov (Eds.), Combinatorial Image Analysis - 19th International Workshop, IWCIA 2018, Proceedings (pp. 17-27). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11255 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-05288-1_2