Séminaire LIGM : Convergent geometric estimators with digital volume and surface integrals

Le prochain séminaire de l'équipe A3SI du LIGM (unité mixte de recherche de l'Université Paris Est) aura lieu le mardi 7 juin de 11h00 à 12h00, salle 260 (ESIEE Paris).

Convergent geometric estimators with digital volume and surface integrals
Jacques-Olivier Lachaud
LAMA, Université de Savoie

Résumé : This talk presents several methods to estimate geometric quantities on subsets of the digital space Z^d. We take an interest both on global geometric quantities like volume and area, and on local geometric quantities like normal and curvatures.  All presented methods have the common property to be multigrid convergent, i.e. the estimated quantities tend to their Euclidean counterpart on finer and finer digitizations of (smooth enough) Euclidean shapes. Furthermore, all methods rely on digital integrals, which approach either volume integrals or surface integrals along shape boundary. With such tools, we achieve multigrid convergent estimators of volume, moments and area in Z^d, of normals, curvature and curvature tensor in Z^2 and Z^3, and of covariance measure and normals in Z^d even with Hausdorff noise.