Institute of Informatics
Acta Cybernetica
Past Issues
Volume 16, Number 1, 2003
Velocity and Distance of Neighbourhood Sequences
# Velocity and Distance of Neighbourhood Sequences

**András Hajdu and Lajos Hajdu**

### Abstract (in LaTeX format)

Das et al. \cite{nseq} defined the notion of periodic neighbourhood sequences. They also %%@ introduced a natural ordering relation $\sqsupseteq^*$ for such sequences. Fazekas et al. %%@ \cite{genseq} generalized the concept of neighbourhood sequences, by dropping periodicity. %%@ They also extended the ordering to these generalized neighbourhood sequences. The relation %%@ $\sqsupseteq^*$ 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.

**Keywords: ** digital geometry, neighbourhood sequences, distance, metric.

### Full text

Available electronic editions: PDF.

### DOI

DOI is not available for this article.

### BibTeX entry
`
@article{Hajdu:2003:ActaCybernetica,`

author = {Andr{\'a}s Hajdu and Lajos Hajdu},

title = {Velocity and Distance of Neighbourhood Sequences},

journal = {Acta Cybernetica},

year = {2003},

volume = {16},

number = {1},

pages = {133--145},

abstract = {Das et al. \cite{nseq} defined the notion of periodic neighbourhood sequences. They also %%@ introduced a natural ordering relation $\sqsupseteq^*$ for such sequences. Fazekas et al. %%@ \cite{genseq} generalized the concept of neighbourhood sequences, by dropping periodicity. %%@ They also extended the ordering to these generalized neighbourhood sequences. The relation %%@ $\sqsupseteq^*$ 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.},

keywords = {digital geometry, neighbourhood sequences, distance, metric}

}