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Table 5.1 Comparison of image processing by the method of mathematical morphology and by
Belousov-Zhabotinsky reaction-diffusion media
Mathematical morphology
Chemical reaction-diffusion medium
Numerical method of image processing based
on nonlinear transformations of their
shape
Image processing of the chemical reaction-dif-
fusion medium based on nonlinear dynamic
mechanisms
Object processing—an image represented by
a set of pixels
Object processing—an image entered as a sin-
gle entity in the medium
Sequential pixel by pixel image processing by
a digital computer
Parallel image processing simultaneously at all
its points by a distributed chemical
environment
Different modes of image processing based
on the structural elements of arbitrary
shape
A single circular structural element used almost
exclusively
“Dilation” and “erosion”—the basic opera-
tions of image processing
The two basic operations—“open” and
“close”—involve joint application of ele-
mentary operations
“Contour (+)” and “contour (
)”—the basic
operations of image processing
Operations “open” and “close” can be reduced
to the joint application of these elementary
operations
Virtually all processing operations of black-
and-white images can be performed
Virtually all processing operations of black-
and-white images can be performed
A large number of gray-scale image
processing operations can be performed
A large number of gray-scale image processing
operations equivalent to the operations of
mathematical morphology can be performed
Zhabotinsky medium should be carefully chosen. On the other hand, as a result of
the highly complex behavior of the medium, new opportunities to discriminate
information about the structure of the image emerge that are too difficult if not
impossible to obtain by the method of mathematical morphology.
In general, there is no doubt that reaction-diffusion media (and in particular the
Belousov-Zhabotinsky media) allow for obtaining information about the structure
of the image safely and fairly easy.
5.2.2.2 Vibrational Mode
Evolution of images in a medium of the Belousov-Zhabotinsky type functioning in
the vibrational mode turns out to be much more complex compared to the excitable
regime. Great opportunities for a detailed analysis arise in the case of halftone
image processing. In this case, a positive halftone image is first converted into a
negative black-and-white image. After that, in a general case, contour enhancement
of individual fragments takes place, and then the image is converted to the original
gray-scale image. The duration of each phase of this evolution and the information
obtained about the structural features of the image may vary depending on the
contrast of the original image (Fig.
5.13
). When a negative form of the image
appears, its gray-scale fragments, the blackening of which varies from point to
