Image Processing Reference
In-Depth Information
using only one rule (the ordinary CA). The paper provided their optimal rules and
iterations
R
1
,
,
M
2
. Unfortunately, it seems that errors or typos existed in
R
1
because it is not a binary expression tree with two arguments for each function
as stated in their algorithm specification.
Priego
et al.
[27] describe an approach for edge detection from hyperspectral
(i.e. multi-band) images. Rather than input the hyperspectral values directly into
the CA, they first extract a set of features from each pixel's neighbourhood (first
the eight spectral angles are computed, and these are then described by their mean,
directional gradients and standard deviation). A genetic algorithm is then employed
to learn
M
M
1
and
R
2
20 rules, each consisting of a tuple mapping an instance of the six
feature elements to a real valued output value in the range
=
. Once the rules have
been learnt, the CA is run by applying at each pixel the closest matching rule (in
terms of its Euclidean distance to the six feature elements). The output at each pixel
is thresholded at 0.5 to produce a binary edge map.
Beside traditional CA approaches, cellular automata combined with other tech-
niques were also proposed for edge detection of intensity images.
Mirzaei
et al.
[20] used fuzzy cellular automata for edge detection. They de-
signed eight masks, each of which separates the Moore neighbourhood into two
groups. The average of the absolute state differences between the central pixel and
the pixels within each group is calculated, and then fuzzified into a fuzzy descrip-
tion of 'High' and 'Low'. Thirty-two fuzzy rules are used for fuzzy state transition,
and the resulting fuzzy description is defuzzified to produce an updated numerical
state. The authors claim that their method has better efficiency than the Robert and
Sobel edge detectors, and moreover that they have largely overcome detection errors
(missed edges and false edges). However, their published results do not support this
claim.
Chen and Yan [6] proposed an approach for edge detection which first uses a CA-
based diffusion model for image smoothing, and then detects the image edges by
finding the zero-crossings of the second order derivative of the image defined as the
difference between the smoothed and the original images divided by the diffusion
time. Experiments showed better results were obtained by the proposed method than
that by Laplacian of Gaussian, Laplacian, Canny, and Sobel operators. However, the
final results are heavily dependent on the suitable choice of the number of iterations
in the smoothing stage.
Other methods, including cellular neural networks [2, 17], fuzzy cellular neural
network [39], cellular learning automata [10], and cellular automata transformation
methods [24], all produced reasonable results, which shows that CA combined with
other techniques are promising tools for image edge detection.
Finally, we describe a method developed by one of this chapter's authors. In an
attempt to retain the simplicity of binary CA with the ability to process intensity (i.e.
non-binary) images, Rosin [34] applied threshold decomposition, a technique often
used in image processing. This involves decomposing a gray level image into the set
of binary images obtained by thresholding it at all possible gray levels. A single set
of two-state CA rules is learnt which is applied independently to each binary image.
[
0
,
1
]
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