Journal of Mathematical Imaging and Vision

, Volume 49, Issue 2, pp 418–433

Topology-Preserving Conditions for 2D Digital Images Under Rigid Transformations

  • Phuc Ngo
  • Yukiko Kenmochi
  • Nicolas Passat
  • Hugues Talbot
Article

DOI: 10.1007/s10851-013-0474-z

Cite this article as:
Ngo, P., Kenmochi, Y., Passat, N. et al. J Math Imaging Vis (2014) 49: 418. doi:10.1007/s10851-013-0474-z

Abstract

In the continuous domain \(\mathbb{R}^{n}\), rigid transformations are topology-preserving operations. Due to digitization, this is not the case when considering digital images, i.e., images defined on \(\mathbb{Z}^{n}\). In this article, we begin to investigate this problem by studying conditions for digital images to preserve their topological properties under all rigid transformations on \(\mathbb{Z}^{2}\). Based on (i) the recently introduced notion of DRT graph, and (ii) the notion of simple point, we propose an algorithm for evaluating digital images topological invariance.

Keywords

Rigid transformation 2D digital image Discrete topology Simple point DRT graph 

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Phuc Ngo
    • 1
  • Yukiko Kenmochi
    • 1
  • Nicolas Passat
    • 2
  • Hugues Talbot
    • 1
  1. 1.LIGM, UPEMLV-ESIEE-CNRSUniversité Paris-EstParisFrance
  2. 2.CReSTICUniversité de Reims Champagne-ArdenneReimsFrance

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