Convex shapes and convergence speed of discrete tangent estimators

Jacques-Olivier Lachaud (1) , François de Vieilleville (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Discrete geometric estimators aim at estimating geometric characteristics of a shape with only its digitization as input data. Such an estimator is multigrid convergent when its estimates tend toward the geometric characteristics of the shape as the digitization step h tends toward 0. This paper studies the multigrid convergence of tangent estimators based on maximal digital straight segment recognition. We show that such estimators are multigrid convergent for some family of convex shapes and that their speed of convergence is on average O(h^(2/3)). Experiments confirm this result and suggest that the bound is tight.

Mots clés: discrete geometry; discrete geometric estimators; tangent estimators; maximal segments; multigrid convergence; discrete convexity

Domaines: Autre [cs.OH]; Mathématique discrète [cs.DM]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Jacques-Olivier Lachaud, François de Vieilleville. Convex shapes and convergence speed of discrete tangent estimators. Proc. Int. Symposium on Visual Computing (ISVC2006), Nov 2006, Lake Tahoe, Nevada, United States. pp.688-697, ⟨10.1007/11919629⟩. ⟨hal-00308337⟩