Edge Detection Using Cellular Automata - Cellular Automata in Image Processing and Geometry - page 85

Slatnia et al. [41] assigned rotational symmetric patterns the same rule, but they
were not training symmetric state transition rules as was done in [3]. Inspired by
Rosin's work [32], they instead used genetic algorithms to train only a single power-
ful rule, that is, the central cell changes its state only when its Moore neighbourhood
matches a specific pixel pattern. Interestingly, they got an optimal rule which was
the same as that proposed by Wongthanavasu and Sadananda [45]. Again, they com-
pared their results with Canny's, and claimed that they had better results, although
this is not obvious from the figures they provided.
Ya n g et al. [46] proposed a CA approach for a specialised form of edge detection.
Instead of using binary state transition rules to evolve the CA, they complicated the
algorithm by introducing more state values. Their method consists of two steps. The
first step sets the state value of each pixel. It uses the Prewitt operator, rotating in
eight angles (from 0 ⓦ with interval 45 ⓦ , numbered as direction 1 to 8), to compute
eight direction values for each pixel, and takes the direction number (called the lo-
cation coordinate in their paper) with maximal direction value as the state value
(called the characteristic vector). The state value is changed to 16 if the maximal
direction value is less than 3. The second step evolves the CA based on the states
(represented by values in 1

8, or 16) in the neighbourhood of each cell. The differ-
ences of the state values between the central cell and its neighbours are calculated,
and the number of neighbours with differences 0, 1, or 7 is counted. If the number is
not equal to 2, the state of the central cell is changed to 16. After several iterations,
the pixels with state values other than 16 are classified as edge pixels. One iteration
of the algorithm will result in reasonable edge detection results. More iterations will
delete irregular edges, and only the edges of the objects that are strictly rectangular
survive.
In fact, we can simply describe Yang et al. 's algorithm by binary state transition
rules also in two steps. The first step performs only one iteration with the rule that if
three contiguous neighbours of a central pixel have the value 1 and the other three
contiguous neighbours symmetric to them about the central pixel have the value 0,
then the central pixel keeps its state (either as edge or non-edge), otherwise it is
non-edge. The second step performs several iterations based on the rule that an edge
pixel remains as edge if exactly two pixels in its von Neumann neighbourhood are
edge pixels, and all the other pixels in its Moore neighbourhood are non-edge.
It should be mentioned that most of the proposed CA-based binary image edge
detection methods were compared against Canny's method. This is inappropriate
because Canny's method was not designed specifically for binary image edge detec-
tion, but rather for grey-scale image edge detection. In fact, Canny's method is not
poorer than the above-mentioned methods even when dealing with binary images.
Another issue is that, from an image processing perspective, detecting bound-
aries in binary images is a relatively trivial task, and is not generally considered to
be a research problem. In comparison, detecting edges in intensity images (which
often also involves estimating edge magnitude and orientation as well) still regularly
generates many papers in high ranking journals and conferences in the field of image
processing/computer vision.

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