Name
Abstract | ||
|---|---|---|
A digital discrete hyperplane in Z(d) is defined by a normal vector v, a shift mu, and a thickness theta. The set of thicknesses theta for which the hyperplane is connected is a right unbounded interval of R+. Its lower bound, called the connecting thickness of v with shift mu, may be computed by means of the fully subtractive algorithm. A careful study of the behaviour of this algorithm allows us to give exhaustive results about the connectedness of the hyperplane at the connecting thickness in the case mu = 0. We show that it is connected if and only if the sequence of vectors computed by the algorithm reaches in finite time a specific set of vectors which has been shown to be Lebesgue negligible by Kraaikamp & Meester. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/978-3-319-09955-2_1 | DISCRETE GEOMETRY FOR COMPUTER IMAGERY, DGCI 2014 |
Keywords | Field | DocType |
discrete hyperplane, connectedness, connecting thickness, fully subtractive algorithm | Discrete mathematics,Subtractive color,Combinatorics,Social connectedness,Upper and lower bounds,Half-space,Facet (geometry),Hyperplane,Normal,Mathematics,Lebesgue integration | Conference |
Volume | ISSN | Citations |
8668 | 0302-9743 | 3 |
PageRank | References | Authors |
0.43 | 5 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Eric Domenjoud | 1 | 79 | 8.67 |
| X. Provençal | 2 | 49 | 3.31 |
| Laurent Vuillon | 3 | 186 | 26.63 |