### Abstract

the Voronoi Diagram (VD) is defined as a rediscovered mathematical concept from the 19th century. It is one of the most fundamental and useful constructions, defined by irregular lattices. The objectives are: i) to study three construction algorithms of VD, which are the divide-and-conquer algorithm, the half-plane intersection algorithm, and the incremental algorithm; ii) to apply the three VD algorithms chosen in (i) on thinning of Arabic handwriting; and iii) to compare the three algorithms of VD to find out the fastest and best in construction. The study is proven in practice, whereby all three algorithms can obtain the skeleton in the same number of points, but in the construction of VD, a different number of vertices are obtained. Three stages are done. The first stage includes edge detection, contour tracing, and sampling; in the second stage, the VD is constructed using the three algorithms which were chosen before. In the final stage, the medial axis is extracted by only the VD while vertices, which are located within the text boundaries, are kept and joined. The dataset used in this work consists of 569 handwritten Arabic images of Tunisian town names. All the handwritten images are in the binary image form. By using sampling interval R = 4, the experimental results are proven. 481 of the generator points were obtained. 1362 vertices were obtained by a divide-and-conquer algorithm. It took 0.013307 seconds, compared with a half-plane intersection algorithm. For the 1401 vertices obtained, it took 0.019313 seconds, while, in the incremental algorithm, these 1401 vertices were obtained in 0.38502 seconds. Through the results obtained, the divide-and-conquer algorithm is faster than the half-plane intersection and incremental algorithms in the construction of VD.

Original language | English |
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Title of host publication | Proceedings of the 2011 International Conference on Electrical Engineering and Informatics, ICEEI 2011 |

DOIs | |

Publication status | Published - 2011 |

Event | 2011 International Conference on Electrical Engineering and Informatics, ICEEI 2011 - Bandung Duration: 17 Jul 2011 → 19 Jul 2011 |

### Other

Other | 2011 International Conference on Electrical Engineering and Informatics, ICEEI 2011 |
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City | Bandung |

Period | 17/7/11 → 19/7/11 |

### Fingerprint

### Keywords

- Handwritten word
- OCR
- VD Thinning
- Voronoi Diagram

### ASJC Scopus subject areas

- Information Systems
- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2011 International Conference on Electrical Engineering and Informatics, ICEEI 2011*[6021658] https://doi.org/10.1109/ICEEI.2011.6021658

**A comparative study of Voronoi algorithm construction in thinning.** / Mady, Ali M M; Omar, Khairuddin.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2011 International Conference on Electrical Engineering and Informatics, ICEEI 2011.*, 6021658, 2011 International Conference on Electrical Engineering and Informatics, ICEEI 2011, Bandung, 17/7/11. https://doi.org/10.1109/ICEEI.2011.6021658

}

TY - GEN

T1 - A comparative study of Voronoi algorithm construction in thinning

AU - Mady, Ali M M

AU - Omar, Khairuddin

PY - 2011

Y1 - 2011

N2 - the Voronoi Diagram (VD) is defined as a rediscovered mathematical concept from the 19th century. It is one of the most fundamental and useful constructions, defined by irregular lattices. The objectives are: i) to study three construction algorithms of VD, which are the divide-and-conquer algorithm, the half-plane intersection algorithm, and the incremental algorithm; ii) to apply the three VD algorithms chosen in (i) on thinning of Arabic handwriting; and iii) to compare the three algorithms of VD to find out the fastest and best in construction. The study is proven in practice, whereby all three algorithms can obtain the skeleton in the same number of points, but in the construction of VD, a different number of vertices are obtained. Three stages are done. The first stage includes edge detection, contour tracing, and sampling; in the second stage, the VD is constructed using the three algorithms which were chosen before. In the final stage, the medial axis is extracted by only the VD while vertices, which are located within the text boundaries, are kept and joined. The dataset used in this work consists of 569 handwritten Arabic images of Tunisian town names. All the handwritten images are in the binary image form. By using sampling interval R = 4, the experimental results are proven. 481 of the generator points were obtained. 1362 vertices were obtained by a divide-and-conquer algorithm. It took 0.013307 seconds, compared with a half-plane intersection algorithm. For the 1401 vertices obtained, it took 0.019313 seconds, while, in the incremental algorithm, these 1401 vertices were obtained in 0.38502 seconds. Through the results obtained, the divide-and-conquer algorithm is faster than the half-plane intersection and incremental algorithms in the construction of VD.

AB - the Voronoi Diagram (VD) is defined as a rediscovered mathematical concept from the 19th century. It is one of the most fundamental and useful constructions, defined by irregular lattices. The objectives are: i) to study three construction algorithms of VD, which are the divide-and-conquer algorithm, the half-plane intersection algorithm, and the incremental algorithm; ii) to apply the three VD algorithms chosen in (i) on thinning of Arabic handwriting; and iii) to compare the three algorithms of VD to find out the fastest and best in construction. The study is proven in practice, whereby all three algorithms can obtain the skeleton in the same number of points, but in the construction of VD, a different number of vertices are obtained. Three stages are done. The first stage includes edge detection, contour tracing, and sampling; in the second stage, the VD is constructed using the three algorithms which were chosen before. In the final stage, the medial axis is extracted by only the VD while vertices, which are located within the text boundaries, are kept and joined. The dataset used in this work consists of 569 handwritten Arabic images of Tunisian town names. All the handwritten images are in the binary image form. By using sampling interval R = 4, the experimental results are proven. 481 of the generator points were obtained. 1362 vertices were obtained by a divide-and-conquer algorithm. It took 0.013307 seconds, compared with a half-plane intersection algorithm. For the 1401 vertices obtained, it took 0.019313 seconds, while, in the incremental algorithm, these 1401 vertices were obtained in 0.38502 seconds. Through the results obtained, the divide-and-conquer algorithm is faster than the half-plane intersection and incremental algorithms in the construction of VD.

KW - Handwritten word

KW - OCR

KW - VD Thinning

KW - Voronoi Diagram

UR - http://www.scopus.com/inward/record.url?scp=80054011203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054011203&partnerID=8YFLogxK

U2 - 10.1109/ICEEI.2011.6021658

DO - 10.1109/ICEEI.2011.6021658

M3 - Conference contribution

SN - 9781457707520

BT - Proceedings of the 2011 International Conference on Electrical Engineering and Informatics, ICEEI 2011

ER -