A graph, non-tree representation of the topology of a gray scale image
Peter Saveliev · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
The paper provides a method of graph representation of gray scale images. For binary images, it is generally recognized that not only connected components must be captured, but also the holes. For gray scale images, there are two kinds of "connected components" - dark regions surrounded by lighter areas and light regions surrounded by darker areas. These regions are the lower and upper level sets of the gray level function, respectively. The proposed method represents the hierarchy of these sets, and the topology of the image, by means of a graph. This graph contains the well-known inclusion trees, but it is not a tree in general. Two standard topological tools are used. The first tool is cell decomposition: the image is represented as a combination of pixels as well as edges and vertices. The second tool is cycles: both the connected components and the holes are captured by circular sequences of edges.