# AN OPTIMIZED ALGORITHM FOR COMPUTING THE VORONOI SKELETON

## DOI:

https://doi.org/10.47839/ijc.19.4.1987## Keywords:

Voronoi diagram, Voronoi graph, skeleton, polygon, shape simplification, heuristic, optimization## Abstract

The skeleton-based representation is widely used in such fields as computer graphics, computer vision and image processing. Therefore, efficient algorithms for computing planar skeletons are of high relevance. In this paper, we propose an optimized algorithm for computing the Voronoi skeleton of a planar object with holes, which is represented by a set of polygons. Such skeleton allows us to use efficiently the properties of the underlying Voronoi diagram data structure. It was shown that the complexity of the proposed Voronoi-based skeletonization algorithm is *O*(*N* log *N*), where *N* is the number of polygon’s vertices. We have also proposed theoretically justified optimization heuristic based on polygon/polyline simplification algorithms. In order to evaluate and prove the efficiency of the heuristic, a series of computational experiments were conducted involving the polygons obtained from MPEG 7 CE-Shape-1 dataset. We have measured the execution time of the skeletonization algorithm, computational overheads related to the introduced heuristics and also the influence of the heuristic onto accuracy of the resulting skeleton. As a result, we have established the criteria, which allow us to choose the optimal heuristics for our skeletonization algorithm depending on the system’s requirements.

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*International Journal of Computing*,

*19*(4), 542-554. https://doi.org/10.47839/ijc.19.4.1987

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