### 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 defines a distance function. Thus, this paper presents a necessary and sufficient condition for a sequence of neighborhood form to define a distance function.

Original language | English |
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Pages (from-to) | 70-75 |

Number of pages | 6 |

Journal | Systems, computers, controls |

Volume | 15 |

Issue number | 5 |

Publication status | Published - Sep 1 1984 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Systems, computers, controls*,

*15*(5), 70-75.

**DISTANCE FUNCTIONS DEFINED BY VARIABLE NEIGHBORHOOD SEQUENCES.** / Yamashita, Masafumi; Honda, Namio.

Research output: Contribution to journal › Article

*Systems, computers, controls*, vol. 15, no. 5, pp. 70-75.

}

TY - JOUR

T1 - DISTANCE FUNCTIONS DEFINED BY VARIABLE NEIGHBORHOOD SEQUENCES.

AU - Yamashita, Masafumi

AU - Honda, Namio

PY - 1984/9/1

Y1 - 1984/9/1

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 defines a distance function. Thus, this paper presents a necessary and sufficient condition for a sequence of neighborhood form to define a distance function.

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 defines a distance function. Thus, this paper presents a necessary and sufficient condition for a sequence of neighborhood form to define a distance function.

UR - http://www.scopus.com/inward/record.url?scp=0021483920&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021483920&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0021483920

VL - 15

SP - 70

EP - 75

JO - Systems, computers, controls

JF - Systems, computers, controls

SN - 0096-8765

IS - 5

ER -