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.
Highlights
The skeletal representation of the planar object is essential for many problems of computer vision and pattern recognition, computer graphics and visualization [1]
We proposed an optimized algorithm for computing the Voronoi skeleton based on polygonal data
This topic is of relevance because of its direct relation to the optimization tasks in image processing and computer graphics
Summary
The skeletal representation of the planar object is essential for many problems of computer vision and pattern recognition, computer graphics and visualization [1]. Skeletons are widely used for shape matching [2, 3], optical character recognition [4] and image retrieval [2, 5]. In the biological image processing, skeletonization methods are extensively applied to extract the central line of thin objects. Based on the image data one can obtain the skeletal graph representing the retinal blood vessels topology [6, 7]. This technique is applied for segmenting the biological neurons [8] and for extracting thin subcellular structures [9, 10] based on microscopy data
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