A Novel Method of Skeletonization of Complex Shapes Based on Bisectors

Abstract

The mathematical skeleton of a complex form has been essential for a variety of scientific fields and of great interest to many researchers for decades. It is based on several concepts such as the reconstruction of forms and image processing. This paper aims to develop a novel mathematical algorithm to approximate the skeleton of a non-polygonal shape and to compare it to the most used methods. The mathematical technique of skeletonization is used as a reference to validate and compare the proposed method to the most used ones. The crux of the proposed technique is to Cartesianize the shape (polygonize in 2D), then skeletonize it. Moreover, this novel method is grounded upon the construction of bisectors on the simplex of the corresponding Cartesianized shape. Python is used to implement the algorithm proposed and test it on multiple shapes. The comparison of the results generated by the proposed algorithm and the Python predefined function skeletonize() shows that the proposed method is more effective and could be adjusted through the rate of Cartesianization of the target shape. The major contributions of this novel technique include the mitigation of some issues of existing methods, simplification, and optimization of the processing performance mainly in terms of algorithm complexity.