Distance functions in digital geometry
Information Sciences: an International Journal
Performance Analysis of k-ary n-cube Interconnection Networks
IEEE Transactions on Computers
Lattice of octagonal distances in digital geometry
Pattern Recognition Letters
On the rectangular grid representation of general CNN networks: Research Articles
International Journal of Circuit Theory and Applications - CNN Technology
Metrical neighborhood sequences in Zn
Pattern Recognition Letters
General neighborhood sequences in Zn
Discrete Applied Mathematics
Neighborhood sequences and their applications in the digital image processing
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
On the lattice structure of subsets of octagonal neighborhood sequences in Zn
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
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Das et al. [2] defined the notion of periodic neighbourhood sequences. They also introduced a natural ordering relation ⊒* for such sequences. Fazekas et al. [4] generalized the concept of neighbourhood sequences, by dropping periodicity. They also extended the ordering to these generalized neighbourhood sequences. The relation ⊒* has some unpleasant properties (e.g., it is not a complete ordering). In certain applications it can be useful to compare any two neighbourhood sequences. For this purpose, in the present paper we introduce a norm-like concept, called velocity, for neighbourhood sequences. This concept is in very close connection with the natural ordering relation. We also define a metric for neighbourhood sequences, and investigate its properties.