Distance functions in digital geometry
Information Sciences: an International Journal
Octagonal distances for digital pictures
Information Sciences: an International Journal
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
2D and 3D visibility in discrete geometry: an application to discrete geodesic paths
Pattern Recognition Letters - Special issue: Discrete geometry for computer imagery (DGCI'2002)
Characterization of digital circles in triangular grid
Pattern Recognition Letters
Analytical Honeycomb Geometry for Raster and Volume Graphics
The Computer Journal
Distances based on neighbourhood sequences in non-standard three-dimensional grids
Discrete Applied Mathematics
Weighted distances based on neighbourhood sequences
Pattern Recognition Letters
General neighborhood sequences in Zn
Discrete Applied Mathematics
Geometry of neighborhood sequences in hexagonal grid
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
On covering a digital disc with concentric circles in Z2
Theoretical Computer Science
Linear combination of weighted t-cost and chamfering weighted distances
Pattern Recognition Letters
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In this paper the nodes of the hexagonal grid are used as points. There are three types of neighbours on this grid, therefore neighbourhood sequences contain values 1, 2, 3. The grid is coordinatized by three coordinates in a symmetric way. Digital circles are classified based on digital distances using neighbourhood sequences. They can be triangle, hexagon, enneagon and dodecagon. Their corners and side-lengths are computed, such as their perimeters and areas. The radius of a digital disk is usually not well-defined, i.e., the same disk can have various radii according to the neighbourhood sequence used. Therefore the non-compactness ratio is used to measure the quality of approximation of the Euclidean circles. The best approximating neighbourhood sequence is presented. It is shown that the approximation can be improved using two neighbourhood sequences in parallel. Comparisons to other approximations are also shown.