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Binary Image Skeleton - Continuous Approach

In this paper we propose a building technique of a correct model of continuous skeleton for discrete binary image. Our approach is based on approximation of each connected object in an image by a polygonal figure. Figure boundary consists of closed paths of minimal perimeter which separate points of foreground and background. Figure skeleton is constructed as a locus of centers of maximal inscribed circles. In order to build a so-called skeletal base from figure skeleton, we cut unnecessary noise from it. It is shown, that the constructed continuous skeleton exists and is unique for each binary image. This continuous skeleton has the following advantages: it has a strict mathematical description, it is stable to noise, and it also has broad capabilities of form transformations and shape comparison of objects. The proposed approach gives a substantial advantage in the speed of skeleton construction in comparison with various discrete methods, including those in which parallel calculations are used. This advantage is demonstrated on real images of big size.