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Fig. 5.11 Initial basic operations of mathematical morphology by the Belousov-Zhabotinsky
medium
image being processed into the medium. The results of the pilot to perform these
operations are in good agreement with numerical simulations of these operations.
It is easy to see that these operations are equivalent to the operations “dilation”
and “erosion” in mathematical morphology. Naturally, they do not coincide
completely. The evolution of an image in a reaction-diffusion medium corresponds
in some sense to a particular case in which the transforming structural element of
mathematical morphology has the form of a circle. In this approximation the
reaction-diffusion medium easily reproduces the major operations of mathematical
morphology “open” and “close.” Figure
5.11
shows the execution of these opera-
tions on simple images using mathematical morphology and the evolution of these
images in a reaction-diffusion medium. In both cases the results of image
processing are virtually identical, and the reaction-diffusion medium behaves as
though it were simulating the process of performing these operations.
In view of the similarity between the initial operations performed by the method
of mathematical morphology and by the reaction-diffusion media, these media
provide an opportunity to execute all operations practically used for image
processing. Figure
5.10
shows an operation of determining the shape of a complex
figure when features of the image small enough compared with the size and shape of
the figure are excluded and the basic characteristics of its shape become apparent.
The thinning of the image elements is shown in the same figure. Different directions
of motion of contours of the individual image fragments lead to the medium
eliminating or conversely magnifying specific details of the image.
Implementation by the reaction-diffusion medium of the operations “open” and
“close” allows for more complex operations over images. Figure
5.12
shows the
