Topology-preserving conditions for 2D digital images under rigid transformations

Phuc Ngo (1) , Nicolas Passat (2) , Yukiko Kenmochi (1) , Hugues Talbot (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804

In the continuous domain 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 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 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 geometry; discrete topology; simple point; DRT graph.; DRT graph

Domains: Image Processing [eess.IV]

Phuc Ngo, Nicolas Passat, Yukiko Kenmochi, Hugues Talbot. Topology-preserving conditions for 2D digital images under rigid transformations. Journal of Mathematical Imaging and Vision, 2014, 49 (2), pp.418-433. ⟨10.1007/s10851-013-0474-z⟩. ⟨hal-00838183v1⟩