Distances defined by neighborhood sequences

Masafumi Yamashita, Toshihide Ibaraki

Research output: Contribution to journalArticlepeer-review

90 Citations (Scopus)


This paper investigates general properties of distance functions defined over digitized space. We assume that a distance between two points is defined as the length of a shortest path connecting them in the underlying graph which is defined by a given neighborhood sequence. Many typical distance functions can be described in this form, but there are cases in which given neighborhood sequence do not define distance functions. We first derive a necessary and sufficient condition for a neighborhood sequence to define a distance function. We then discuss another important problem of estimating how tight such distances can approximate the Euclid distance from the view point of relative error and absolute error.

Original languageEnglish
Pages (from-to)237-246
Number of pages10
JournalPattern Recognition
Issue number3
Publication statusPublished - 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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