Medial Axis LUT Computation for Chamfer Norms Using H-Polytopes

International audienceChamfer distances are discrete distances based on the propagation of local distances, or weights defined in a mask. The medial axis, i.e. the centers of the maximal disks (disks which are not contained in any other disk), is a powerful tool for shape representation and analysis. The extraction of maximal disks is performed in the general case with comparison tests involving look-up tables representing the covering relation of disks in a local neighborhood. Although look-up table values can be computed efficiently, the computation of the look-up table neighborhood tend to be very time-consuming. By using polytope descriptions of the chamfer disks, the necessary operations to extract the look-up tables are greatly reduced

Medial Axis Lookup Table and Test Neighborhood Computation for 3D Chamfer Norms

International audienceChamfer distances are discrete distances based on the propagation of local distances, or weights defined in a mask. The medial axis, i.e. the centers of the maximal disks (disks which are not contained in any other disk), is a powerful tool for shape representation and analysis. The extraction of maximal disks is performed in the general case with comparison tests involving look-up tables representing the covering relation of disks in a local neighborhood. Although look-up table values can be computed efficiently, the computation of the look-up table neighborhood tend to be very time-consuming. By using polytope descriptions of the chamfer disks, the necessary operations to extract the look-up tables are greatly reduced

Farey Sequences and the Planar Euclidean Medial Axis Test Mask

Abstract. The Euclidean test mask T (r) is the minimum neighbourhood sufficient to detect the Euclidean Medial Axis of any discrete shape whose inner radius does not exceed r. We establish a link between T (r) and the well-known Farey sequences, which allows us to propose two new algorithms. The first one computes T (r) in time O(r 4 ) and space O(r 2 ). The second one computes for any vector − → v the smallest r for which − → v ∈ T (r), in time O(r 3 ) and constant space

Projections et distances discrètes

Le travail se situe dans le domaine de la géométrie discrète. La tomographie discrète sera abordée sous l'angle de ses liens avec la théorie de l'information, illustrés par l'application de la transformation Mojette et de la "Finite Radon Transform" au codage redondant d'information pour la transmission et le stockage distribué. Les distances discrètes seront exposées selon les points de vue théorique (avec une nouvelle classe de distances construites par des chemins à poids variables) et algorithmique (transformation en distance, axe médian, granulométrie) en particulier par des méthodes en un balayage d'image (en "streaming"). Le lien avec les séquences d'entiers non-décroissantes et l'inverse de Lambek-Moser sera mis en avant