Page 147 -

Chapter 3 ■ Digital Morphology 121

count := 0;
loop
count := #a + count;
b := (a--L1) + (a--L2) + (a--L3) + (a--L4);
exit whenb=0;
a:= b;
end;
message ˝ Number of 8 regions is ˝; message count; message;
end;

This program counts eight regions in Figure 3.22e, which is correct for
8-connected regions. It also counts two regions in Figure 3.11a, which is also
correct. The algorithm for 4-connected regions is the same but uses different
structuring elements.

3.4 Grey-Level Morphology

The use of multiple grey levels introduces an enormous complication, both
conceptually and computationally. A pixel can now have any integer value, so
the nice picture of an image being a set disappears. There is also some question
about what dilation, for example, should mean for a grey-level image. Rather
than being strictly mathematical here, we will take a more intuitive approach,
in the hope that the result will make sense.
Consider the image of a line in Figure 3.23a.

(a) (b) (c) (d)
Figure 3.23: Grey-scale dilation. (a) A bi-level image of a line. (b) Binary dilation of (a)
by simple. (c) A grey-scale image of a line; background is 0, and the line pixels have the
value 20. (d) This is what the grey line should look like after a dilation.

This is a bi-level image, and the dilation of this image by the simple
structuring element can be computed (Figure 3.23b). Now imagine that instead
of having levels 0 and 1, the pixels in the line have the value 20 and the
background is 0. What should a dilation of this new image by simple look