### Abstract

In the field of pattern recognition, many researchers adopt the definition that distance between two points x and y on digitized space is the length of the shortest path from x to y determined by a specific sequence of neighborhood forms. The diamond distance and various octagonal distances are typical examples of these kinds of distances. However, not necessarily every sequence of neighborhood forms does define a distance function. Thus, in this paper, we present a necessary and sufficient condition for a sequence of neighborhood forms to define a distance function. Two applications of this condition are also presented.

Original language | English |
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Pages (from-to) | 509-513 |

Number of pages | 5 |

Journal | Pattern Recognition |

Volume | 17 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jan 1 1984 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Pattern Recognition*,

*17*(5), 509-513. https://doi.org/10.1016/0031-3203(84)90048-7

**Distance functions defined by variable neighborhood sequences.** / Yamashita, Masafumi; Honda, Namio.

Research output: Contribution to journal › Article

*Pattern Recognition*, vol. 17, no. 5, pp. 509-513. https://doi.org/10.1016/0031-3203(84)90048-7

}

TY - JOUR

T1 - Distance functions defined by variable neighborhood sequences

AU - Yamashita, Masafumi

AU - Honda, Namio

PY - 1984/1/1

Y1 - 1984/1/1

N2 - In the field of pattern recognition, many researchers adopt the definition that distance between two points x and y on digitized space is the length of the shortest path from x to y determined by a specific sequence of neighborhood forms. The diamond distance and various octagonal distances are typical examples of these kinds of distances. However, not necessarily every sequence of neighborhood forms does define a distance function. Thus, in this paper, we present a necessary and sufficient condition for a sequence of neighborhood forms to define a distance function. Two applications of this condition are also presented.

AB - In the field of pattern recognition, many researchers adopt the definition that distance between two points x and y on digitized space is the length of the shortest path from x to y determined by a specific sequence of neighborhood forms. The diamond distance and various octagonal distances are typical examples of these kinds of distances. However, not necessarily every sequence of neighborhood forms does define a distance function. Thus, in this paper, we present a necessary and sufficient condition for a sequence of neighborhood forms to define a distance function. Two applications of this condition are also presented.

UR - http://www.scopus.com/inward/record.url?scp=0021644150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021644150&partnerID=8YFLogxK

U2 - 10.1016/0031-3203(84)90048-7

DO - 10.1016/0031-3203(84)90048-7

M3 - Article

AN - SCOPUS:0021644150

VL - 17

SP - 509

EP - 513

JO - Pattern Recognition

JF - Pattern Recognition

SN - 0031-3203

IS - 5

ER -