### Abstract

The decomposition of a polygon into simpler components plays an important role in syntactic pattern recognition and image processing. A new decompostion is proposed and termed the relative neighbor decomposition (RND). The lune of two vertices p//i, p//j of a polygon P, denoted by LUNE (p//i, p//j) is defined as the intersection of two circles with radius equal to d(p//i, p//j) centered at p//i and p//j, where d denotes Euclidean distance. The RND consists of the polygon P together with a subset of its diagonals. Two vertices p//i,p//j are joined by a diagonal if (a) p//i and p//j are visible to each other and (b) no other visible vertex of p//i or p//j lies inside LUNE (p//i,p//j). It is shown that the RND is planar, i. e. , no two diagonals intersect.

Original language | English (US) |
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Pages | 20-28 |

Number of pages | 9 |

State | Published - Jan 1 2017 |

Event | Proc Annu Allerton Conf Commun Control Comput 18th - Monticello, IL, USA Duration: Oct 8 1980 → Oct 11 1980 |

### Other

Other | Proc Annu Allerton Conf Commun Control Comput 18th |
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City | Monticello, IL, USA |

Period | 10/8/80 → 10/11/80 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*DECOMPOSING A SIMPLE POLYGON WITH THE RELATIVE NEIGHBORHOOD GRAPH.*. 20-28. Paper presented at Proc Annu Allerton Conf Commun Control Comput 18th, Monticello, IL, USA, .

**DECOMPOSING A SIMPLE POLYGON WITH THE RELATIVE NEIGHBORHOOD GRAPH.** / Toussaint, Godfried.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - DECOMPOSING A SIMPLE POLYGON WITH THE RELATIVE NEIGHBORHOOD GRAPH.

AU - Toussaint, Godfried

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The decomposition of a polygon into simpler components plays an important role in syntactic pattern recognition and image processing. A new decompostion is proposed and termed the relative neighbor decomposition (RND). The lune of two vertices p//i, p//j of a polygon P, denoted by LUNE (p//i, p//j) is defined as the intersection of two circles with radius equal to d(p//i, p//j) centered at p//i and p//j, where d denotes Euclidean distance. The RND consists of the polygon P together with a subset of its diagonals. Two vertices p//i,p//j are joined by a diagonal if (a) p//i and p//j are visible to each other and (b) no other visible vertex of p//i or p//j lies inside LUNE (p//i,p//j). It is shown that the RND is planar, i. e. , no two diagonals intersect.

AB - The decomposition of a polygon into simpler components plays an important role in syntactic pattern recognition and image processing. A new decompostion is proposed and termed the relative neighbor decomposition (RND). The lune of two vertices p//i, p//j of a polygon P, denoted by LUNE (p//i, p//j) is defined as the intersection of two circles with radius equal to d(p//i, p//j) centered at p//i and p//j, where d denotes Euclidean distance. The RND consists of the polygon P together with a subset of its diagonals. Two vertices p//i,p//j are joined by a diagonal if (a) p//i and p//j are visible to each other and (b) no other visible vertex of p//i or p//j lies inside LUNE (p//i,p//j). It is shown that the RND is planar, i. e. , no two diagonals intersect.

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M3 - Paper

SP - 20

EP - 28

ER -