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.
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