On 2D constrained discrete rigid transformations

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

Rigid transformations are involved in a wide range of digital image processing applications. In such a context, they are generally considered as continuous processes, followed by a digitization of the results. Recently, rigid transformations on Z^2 have been alternatively formulated as a fully discrete process. Following this paradigm, we investigate –from a combinatorial point of view– the effects of pixel-invariance constraints on such transformations. In particular we describe the impact of these constraints on both the combi-natorial structure of the transformation space and the algorithm leading to its generation.

Mots clés: combinatorial structure; rigid transformation; discrete geometry; pixel-invariance constraints; image processing

Domaines: Traitement des images [eess.IV]

Phuc Ngo, Yukiko Kenmochi, Nicolas Passat, Hugues Talbot. On 2D constrained discrete rigid transformations. Annals of Mathematics and Artificial Intelligence, 2015, Annals of Mathematics and Artificial Intelligence, 75 (1-2), pp.163-193. ⟨10.1007/s10472-014-9406-x⟩. ⟨hal-00838184v2⟩