Revisiting Digital Straight Segment Recognition

F. de Vieilleville (1) , Jacques-Olivier Lachaud (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

This paper presents new results about digital straight segments, their recognition and related properties. They come from the study of the arithmetically based recognition algorithm proposed by I. Debled-Rennesson and J.-P. Reveillès in 1995 [Debled95]. We indeed exhibit the relations describing the possible changes in the parameters of the digital straight segment under investigation. This description is achieved by considering new parameters on digital segments: instead of their arithmetic description, we examine the parameters related to their combinatoric description. As a result we have a better understanding of their evolution during recognition and analytical formulas to compute them. We also show how this evolution can be projected onto the Stern-Brocot tree. These new relations have interesting consequences on the geometry of digital curves. We show how they can for instance be used to bound the slope difference between consecutive maximal segments.

Mots clés: discrete geometry; digital straight segment recognition; stern-brocot tree; continued fraction; maximal segments

Domaines: Autre [cs.OH]; Traitement des images [eess.IV]; Mathématique discrète [cs.DM]

F. de Vieilleville, Jacques-Olivier Lachaud. Revisiting Digital Straight Segment Recognition. Proc. Int. Conf. Discrete Geometry for Computer Imagery (DGCI2006), Oct 2006, Szeged, Hungary. pp.355-366, ⟨10.1007/11907350_30⟩. ⟨hal-00308338⟩