### Abstract

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 language | English |
---|---|

Pages (from-to) | 237-246 |

Number of pages | 10 |

Journal | Pattern Recognition |

Volume | 19 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1986 |

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Pattern Recognition*,

*19*(3), 237-246. https://doi.org/10.1016/0031-3203(86)90014-2

**Distances defined by neighborhood sequences.** / Yamashita, Masafumi; Ibaraki, Toshihide.

Research output: Contribution to journal › Article

*Pattern Recognition*, vol. 19, no. 3, pp. 237-246. https://doi.org/10.1016/0031-3203(86)90014-2

}

TY - JOUR

T1 - Distances defined by neighborhood sequences

AU - Yamashita, Masafumi

AU - Ibaraki, Toshihide

PY - 1986

Y1 - 1986

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0022594088&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022594088&partnerID=8YFLogxK

U2 - 10.1016/0031-3203(86)90014-2

DO - 10.1016/0031-3203(86)90014-2

M3 - Article

AN - SCOPUS:0022594088

VL - 19

SP - 237

EP - 246

JO - Pattern Recognition

JF - Pattern Recognition

SN - 0031-3203

IS - 3

ER -