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Normes de chanfrein et axe médian dans le volume discret

Eric Remy 1
LSIS - Laboratoire des Sciences de l'Information et des Systèmes
Abstract : First, we present a class of discrete distances: the chamfer distances. We show that the properties of these functions depend on the geometry of the convex hull of the chamfer mask points used to define them. We present a method to construct regular chamfer masks which define discrete norms (verifying the homogeneity property). We obtain constraints and then optimize them, in order to find practical 3D examples of optimal chamfer norms (minimizing the error between the chamfer distance and the euclidean distance). Then, we define the medial axis of a shape, which is the set of centres of maximal balls inside this shape. We detail its computation from the distance map of the shape, by the method of the look-up tables. We present a method to determine the values of these look-up tables for any discrete distance in both 2D and 3D. Then, we present a method to compute and validate the test neighbourhood on which depends the local computation of the medial axis. Finally, we give several examples of look-up tables and neighbourhood obtained in the case of 3D chamfer norms, and in the case of the square of the euclidean distance.
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Submitted on : Thursday, April 6, 2017 - 2:28:21 PM
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  • HAL Id : tel-01502985, version 1


Eric Remy. Normes de chanfrein et axe médian dans le volume discret. Informatique [cs]. Université de la Méditerranée, 2001. Français. ⟨tel-01502985⟩



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