Image Processing Reference
In-Depth Information
of Life to detect the edges. Unfortunately, their description is unclear. 1 Essentially
they are using the thresholding to do the majority of the work, and then the CA just
finds the boundaries in the binary image. Otsu's method [21] is used for threshold-
ing. The resulting pixel value 0 represents background, and 1 represents a potential
edge pixel. The cellular automaton rule used is totalistic, and (to the best of our
understanding given the inconsistencies of their description) is:
1,if
|
M c | =
5
v c =
v c ,if
|
M c | =
3
,
4
,
6
,
7
0
, otherwise.
|
|
where
is the number of edge pixels (value 1) in the Moore neighbourhood of
the central cell c (including c itself). Since the thresholding is global, it will miss
many edges and also find spurious edges!
Another method that first converts an intensity image to a binary image and then
uses CA to detect edges, was proposed by Qadir and Khan [29]. Although 2 512
possible rule sets exist for a CA with a Moore neighbourhood, there are only 512
linear rule sets among them. Qadir and Khan tested all the 512 linear rule sets,
and found that some of them showed no edge detection, some showed strong edge
detection, while the others showed weak detection. They compared their results
with Sobel's and Canny's, and claimed that their results are better, but this is not
obviously clear from their example images provided.
The state transition rules of the above-mentioned approaches are all specified
manually, and are not necessarily optimal. Some researchers tried to find optimal
rules for edge detection using genetic algorithms or evolutionary algorithms.
Kazar and Slatnia [14] used genetic algorithms to construct CA rules for edge
detection of intensity images. One novelty in their approach is that they do not use
pixel intensities as state values, but rather label different intensities in the Moore
neighbourhood of a central pixel, and take the labels as the state values. In this
way, they significantly reduced the possible number of neighbourhood patterns from
256 8
M c
5to8 8
5 for 256 greyscale images, and thus constructing state transition ta-
bles becomes computationally affordable.
Sato and Kanoh [36] introduced rule-changing cellular automata for edge detec-
tion, and used a form of genetic programming, namely gene expression program-
ming (GEP) - an evolutionary algorithm to optimise the CA rules. The idea of
rule-changing CA is to execute an array of transition rules R i for M i iterations in
sequence. Each rule R i is represented by a binary expression tree with the leaf nodes
being the pixel states in the Moore neighbourhood of a central pixel or the constants
0, 127, and -128, and the non-leaf nodes functions max
/
/
, saturated addition,
or saturated subtraction. GEP were used to optimise both R i and M i . Experiments
showed that better results are obtained using two rules (the rule-changing CA) than
()
,min
()
1
Diwakar et al. 's neighbourhood appears to contain the central pixel, which is not consis-
tent with the standard descriptions of Conway's Game of Life. Moreover, they describe
their system as implementing Wolfram's rule 124, which is however normally used to de-
scribe a one dimensional (rather than two dimensional) cellular automaton.
 
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