# Jean-Luc Toutant

• Discrete Applied Mathematics
• 2013
In this paper we provide an analytical description of various classes of digital circles, spheres and in some cases hyperspheres, defined in a morphological framework. The topological properties of these objects, especially the separation of the digital space, are discussed according to the shape of the structuring element. The proposed framework is generic(More)
• Discrete Applied Mathematics
• 2009
While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the 3-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector n, we provide algorithms either to determine whether a(More)
• DGCI
• 2009
While connected rational arithmetical discrete lines and connected rational arithmetical discrete planes are entirely characterized, only partial results exist for the irrational arithmetical discrete planes. In the present paper, we focus on the connectedness of irrational arithmetical discrete planes, namely the arithmetical discrete planes with a normal(More)
• DGCI
• 2006
While connected arithmetic discrete lines are entirely characterized by their arithmetic thickness, only partial results exist for arithmetic discrete hyperplanes in any dimension. In the present paper, we focus on 0-connected rational arithmetic discrete planes in Z. Thanks to an arithmetic reduction on a given integer vector n, we provide an algorithm(More)
In this paper we introduce a notion of digital implicit surface in arbitrary dimensions. The digital implicit surface is the result of a morphology inspired digitization of an implicit surface {x ∈ R : f(x) = 0} which is the boundary of a given closed subset of R, {x ∈ R : f(x) ≤ 0}. Under some constraints, the digital implicit surface has some interesting(More)
In the framework of arithmetic discrete geometry, a discrete object is provided with its own analytical definition corresponding to a discretization scheme. It can thus be considered as the equivalent, in a discrete space, of an euclidean object. Linear objects, namely lines and hyperplanes, have been widely studied under this assumption and are now deeply(More)