Fixpoints of Iterated Reductions with Equivalent Deletion Rules

  • Kálmán PalágyiEmail author
  • Gábor Németh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11255)


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.


Digital geometry and topology Equivalent reduction Thinning 



This research was supported by the project “Integrated program for training new generation of scientists in the fields of computer science”, no EFOP-3.6.3-VEKOP-16-2017-0002. The project has been supported by the European Union and co-funded by the European Social Fund.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Image Processing and Computer GraphicsUniversity of SzegedSzegedHungary

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