A comparative study of Voronoi algorithm construction in thinning

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.