by Klette, R
Abstract:
A wide variety of algorithms and methods in computer graphics and digital image processing is based on point grids Zm defined by regular orthogonal grids in m-dimensional real space Rm, and on the metrics that may be defined on Zm, for m ≥ 2. In this paper, half-norms ∥ · ∥l, metrics δl, and point products 〈·, ·〉l are introduced characterizing different m-dimensional metric grid point spaces, for 0 <- l < m. Furthermore, grid point ditizations in m-dimensional space are defined and grid intersection digitizations for hyperplanes are analyzed. It is shown that digital straight lines (according to grid intersection digitizations) are special digital curves which may be uniquely recognized by m -1 projections into the 2-dimensional point grid Z2. © 1985.
Reference:
The m-dimensional grid point space (Klette, R), In Computer Vision, Graphics and Image Processing, volume 30, 1985.
Bibtex Entry:
@article{klette1985thespace,
author = "Klette, R",
journal = "Computer Vision, Graphics and Image Processing",
pages = "1--12",
title = "The m-dimensional grid point space",
volume = "30",
year = "1985",
abstract = "A wide variety of algorithms and methods in computer graphics and digital image processing is based on point grids Zm defined by regular orthogonal grids in m-dimensional real space Rm, and on the metrics that may be defined on Zm, for m ≥ 2. In this paper, half-norms ∥ · ∥l, metrics δl, and point products 〈·, ·〉l are introduced characterizing different m-dimensional metric grid point spaces, for 0 <- l < m. Furthermore, grid point ditizations in m-dimensional space are defined and grid intersection digitizations for hyperplanes are analyzed. It is shown that digital straight lines (according to grid intersection digitizations) are special digital curves which may be uniquely recognized by m -1 projections into the 2-dimensional point grid Z2. © 1985.",
doi = "10.1016/0734-189X(85)90014-3",
issn = "0734-189X",
issue = "1",
language = "eng",
pii = "0734-189X(85)90014-3",
}