Topology-preserving rigid transformation of 2D digital images

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

We provide conditions under which 2D digital images, considered in the two most common digital topology models (namely, dual adjacency and well-composedness), preserve their topological properties under rigid transformation. This study, that is developed in a discrete framework, leads to the proposal of efficient preprocessing strategies that ensure the topological invariance of images under further rigid transformation. These results and methods are proved to be valid for various kinds of images (binary, grey-level, label), thus providing a generic set of tools, that can be used in particular in the context of image registration and warping.

Mots clés: image preprocessing; registration; warping; topology; digital images; rigid transformation

Domaines: Traitement des images [eess.IV]; Topologie géométrique [math.GT]

Phuc Ngo, Nicolas Passat, Yukiko Kenmochi, Hugues Talbot. Topology-preserving rigid transformation of 2D digital images. IEEE Transactions on Image Processing, 2014, 23 (2), pp.885-897. ⟨10.1109/TIP.2013.2295751⟩. ⟨hal-00795054v2⟩