Sufficient Conditions for Topological Invariance of 2D Images under Rigid Transformations

  • Phuc Ngo
  • Yukiko Kenmochi
  • Nicolas Passat
  • Hugues Talbot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)


In ℝ2, rigid transformations are topology-preserving operations. However, this property is generally no longer true when considering digital images instead of continuous ones, due to digitization effects. In this article, we investigate this issue by studying discrete rigid transformations (DRTs) on ℤ2. More precisely, we define conditions under which digital images preserve their topological properties under any arbitrary DRTs. Based on the recently introduced notion of DRT graph and the classical notion of simple point, we first identify a family of local patterns that authorize topological invariance under DRTs. These patterns are then involved in a local analysis process that guarantees topological invariance of whole digital images in linear time.


2D digital image discrete rigid transformation topology simple point DRT graph Eulerian model 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Phuc Ngo
    • 1
  • Yukiko Kenmochi
    • 1
  • Nicolas Passat
    • 2
  • Hugues Talbot
    • 1
  1. 1.LIGM, UPEMLV-ESIEE-CNRSUniversité Paris-EstFrance
  2. 2.CReSTICUniversité de ReimsFrance

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