Quasi-regularity verification for 2D polygonal objects based on medial axis analysis

Phuc Ngo (1) , Nicolas Passat (2) , Yukiko Kenmochi (3)

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

Quasi-regularity has been proved to be a sufficient condition for simple-connectedness preservation during the digitization process of 2D continuous objects. The original definition of quasi-regularity relies on set-based morphological operations of erosion and dilation. With this definition, quasi-regularity is algorithmically difficult to assess. In this paper, we propose a tractable framework for quasi-regularity verification, especially designed for polygons. Our approach mainly relies on the computation and analysis of the medial axis of these objects, and determines their potential quasi-regularity, and thus their ability to undergo a digitization without alteration of their topological properties. The framework is applied in the context of topology-preserving rigid motions of digital objects.

Mots clés: quasi-regularity; polygonal objects; medial axis; topology preservation; rigid motion

Domaines: Topologie géométrique [math.GT]; Géométrie algorithmique [cs.CG]; Traitement des images [eess.IV]

Phuc Ngo, Nicolas Passat, Yukiko Kenmochi. Quasi-regularity verification for 2D polygonal objects based on medial axis analysis. International Conference on Image Processing (ICIP), Sep 2021, Anchorage, Alaska, United States. pp.1584-1588, ⟨10.1109/ICIP42928.2021.9506543⟩. ⟨hal-03121428⟩