Discrete linear objects in dimension n: the standard model

Eric Andres (1)

1 SIC - SIGNAL-IMAGE-COMMUNICATION

A new analytical description model, called the standard model, for the discretization of Euclidean linear objects (point, m-flat, m-simplex) in dimension n is proposed. The objects are defined analytically by inequalities. This allows a global definition independent of the number of discrete points. A method is provided to compute the analytical description for a given linear object. A discrete standard model has many properties in common with the supercover model from which it derives. However, contrary to supercover objects, a standard object does not have bubbles. A standard object is (n-1)-connected, tunnel-free and bubble-free. The standard model is geometrically consistent. The standard model is well suited for modelling applications.

Mots clés: digitization; dimension n; discrete geometry; m-flat; simplex

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Géométrie algorithmique [cs.CG]; Modélisation et simulation; Synthèse d'image et réalité virtuelle [cs.GR]

Eric Andres. Discrete linear objects in dimension n: the standard model. Graphical Models, 2003, 65 (1-3), pp.92 - 111. ⟨10.1016/S1524-0703(03)00004-3⟩. ⟨hal-00354729⟩