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Chapter 3 ■ Digital Morphology 123

for instance, that dilation makes the small hole in the top of each key smaller,
whereas the erosion made them larger.

(a) (b) (c)
Figure 3.24: Grey-scale erosion and dilation. (a) Original. (b) Dilated by simple. (c) Eroded
by simple.

3.4.1 Opening and Closing

Opening and closing a grey-scale image is done in the same way as before,
except that the grey-scale erosion and dilation operators are used — that is,
an opening is a grey-scale erosion followed by a grey-scale dilation using the
same structuring element, and a closing is vice versa. However, intuitively it
is more useful to use a geometric model to see what is happening.
Consider a grey-level image to be a three-dimensional surface, where the
horizontal (x) and vertical (y) axes are as before, and the depth (z)axisisgiven
by the grey value of the pixel. A structuring element will also be a grey-level
image, and in particular consider one that is spherical such as:

00 0000 0000 0
00 1112 1110 0
01 1223 2211 0
01 2334 3321 0
01 2355 5321 0
02 3456 5432 0
01 2355 5321 0
01 2334 3321 0

01 1223 2211 0
00 1112 1110 0
00 0000 0000 0