ISSN:
1573-7683
Schlagwort(e):
Alexandroff space
;
computer graphics
;
connected ordered topological space
;
digital image
;
digital picture
;
digital space
;
digital topology
;
dimension
;
graph
;
locally finite space
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract Many applications of digital image processing now deal with three- and higher-dimensional images. One way to represent n-dimensional digital images is to use the specialization graphs of subspaces of the Alexandroff topological space ℤn (where ℤ denotes the integers with the Khalimsky line topology). In this paper the dimension of any such graph is defined in three ways, and the equivalence of the three definitions is established. Two of the definitions have a geometric basis and are closely related to the topological definition of inductive dimension; the third extends the Alexandroff dimension to graphs. Diagrams are given of graphs that are dimensionally correct discrete models of Euclidean spaces, n-dimensional spheres, a projective plane and a torus. New characterizations of n-dimensional (digital) surfaces are presented. Finally, the local structure of the space ℤn is analyzed, and it is shown that ℤn is an n-dimensional surface for all n≥1.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF00119834
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