Equivalent sequential and parallel reductions in arbitrary binary pictures

Research output: Contribution to journalArticle

9 Citations (Scopus)


A reduction transforms a binary picture only by changing some black points to white ones, which is referred to as deletion. Sequential reductions traverse the black points of a picture, and consider a single point for possible deletion, while parallel reductions can delete a set of 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 yields a pair of equivalent parallel and sequential reductions. This paper introduces a class of equivalent deletion rules that allows us to establish a new sufficient condition for topology-preserving parallel reductions in arbitrary binary pictures. In addition we present a method of verifying that a deletion rule given by matching templates is equivalent, a necessary and sufficient condition for order-independent deletion rules, and a sufficient criterion for order-independent and translation-invariant parallel subfield-based algorithms.

Original languageEnglish
Article number1460009
JournalInternational Journal of Pattern Recognition and Artificial Intelligence
Issue number7
Publication statusPublished - Jan 1 2014


  • Digital topology
  • Discrete geometry
  • Order-independency
  • Thinning algorithms
  • Topology-preserving reductions

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

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