Leonid Mestetskiy (Moscow State University, Russia)
Medial representation of object shape (skeleton and radial function) is a powerful and widely used tool for image shape analysis. Originally, the concept of skeleton was denoted for continuous objects: the skeleton of a closed region in Euclidean plane is a locus of centers of maximum empty circles in this region. And radial function is defined in every skeleton point and is equal to the radius of inscribed circle centered in this point. However, this concept became the most popular in shape analysis and classification of discrete bitmap digital images. Therefore, the need to generalize the concept of the skeleton for discrete images was raised.
In principle, we can formulate two approaches to extend the concept of the skeleton to discrete images. The first approach, which is the most popular because of ease of implementation, will be called discrete. It consists in a morphological transformation of the original image (Figure a) and construction new image (Figure b), which can be regarded as a skeleton. In this new bitmap medial axis represented by discrete lines one pixel wide. We can say it is a digital image of the skeleton. The discrete approach is implemented in different ways: based on distance maps, thinning etc.
Another approach, which we call continuous, consists of:
- approximation of a discrete object by the polygonal geometrical figure in terms of a continuous geometry (Figure c);
- construction of line segment Voronoi diagram for sides of this figure;
- extract a continuous skeleton of discrete objects from Voronoi diagram (Figure d);
- construction of continuous medial representation as a set of fat Bezier curves.
We present the full implementation of the continuous approach. We propose an original method to obtain continuous skeleton and radial function and represent it as a planar graph whose edges are described by straight lines and quadratic Bezier curves.