Edge Detection Using Cellular Automata - Cellular Automata in Image Processing and Geometry - page 90

Cloud models are the extension of fuzzy models, which combine fuzziness and
randomness into the transformation between the qualitative linguistic description
and the quantitative numerical values. Zhang et al. [47] combined a cloud model
and cellular automata in edge detection. They used the direction information, the
neighbour edge intensity, and the width of the neighbour edge isolation as the input
to a cloud reasoning system, which produces a binary edge map as the mark matrix.
The same CA rules as Chang et al. 's [5] are then used to link the edge pixels. Their
experiments showed that the proposed method can detect edges appropriately, but
the resulting edges are wide.

5.4.1 A Simple Edge Linking Scheme

To link disconnected thin edges using cellular automata, we propose a simple four-
step method whose input is a thresholded edge map. Some of the rules are based on
the 3

3 neighbourhood.
In addition to the two states of the initial image, two more states are introduced, to
represent the ends of open curves and 'T'-junctions. These extra states enable us
to use a 1D rather than 2D neighbourhood at times. The rules use X , the crossing
number at a pixel which is the number of transitions from white to black and vice
versa when the pixel's eight neighbours are traversed in a circular fashion.
Essentially, each iteration of the CA extends open end points of edge curves by
one pixel. Any further extension is terminated if the end point touches an existing
edge (i.e. the point becomes a junction). After completing the extension of edges,
those that did not reach an existing edge, i.e. end points at the end of open curves,
are contracted back to their initial length.
Using the 3

× 3 Moore neighbourhood, while other rules use just a 1 ×

3 neighbourhood, edges can be extended in the eight principal
directions (0 ⓦ ,45 ⓦ , ...). If a larger neighbourhood were used, then not only could
more orientations be used, but curved extensions could also be accommodated.

×

1. detect end points (one iteration):
if p = edge and X =2then p = end
2. extend open ends ( n iterations):

a. detect junctions (one iteration):
if p = end and X =6then p = junction
b. extend open ends (one iteration):
if p = end and number of non-background = 1
and any of the 1D patterns in figure 5.1 match then update

3. contract open ends ( n iterations):
if p = end or junction and number of non-background = 1
then p = non-edge
4. relabel pixels:
if p

= non-edge then p = edge