Convexity-preserving rigid motions of 2D digital objects

Phuc Ngo (1, 2) , Yukiko Kenmochi (3) , Isabelle Debled-Rennesson (1, 2) , Nicolas Passat (4)

1 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery
3 LIGM - Laboratoire d'Informatique Gaspard-Monge
4 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804

Rigid motions on R^2 are isometric and thus preserve the geometry and topology of objects. However, this important property is generally lost when considering digital objects defined on Z^2 , due to the digitization process from R^2 to Z^2. In this article, we focus on the convexity property of digital objects, and propose an approach for rigid motions of digital objects which preserves this convexity. The method is extended to non-convex objects, based on the concavity tree representation.

Mots clés: half-plane representation; concavity tree; digital convexity; digital rigid motion; quasi-regularity

Domaines: Traitement des images [eess.IV]; Géométrie algorithmique [cs.CG]; Mathématique discrète [cs.DM]

Phuc Ngo, Yukiko Kenmochi, Isabelle Debled-Rennesson, Nicolas Passat. Convexity-preserving rigid motions of 2D digital objects. Discrete Geometry for Computer Imagery (DGCI), 2017, Vienna, Austria. pp.69-81, ⟨10.1007/978-3-319-66272-5_7⟩. ⟨hal-01565028⟩