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Chapter 3 ■ Digital Morphology 87

(a) (b) (c)

(d)
Figure 3.1: (a) A collection of pixels consisting of four 4-connected regions. (b) Adding
a pixel seems to connect the regions, but does not; now there are five 4-connected
regions. (c) Three 8-connected regions, showing the diagonal connections allowed for
8-regions. There are five 4-regions in this image. (d) Setting one pixel to black (the grey
one) connects all regions together.

Digital morphology uses the geometry of small connected sets of pixels to
accomplish tasks that are useful in processing regions within images. Morphol-
ogy can count and mark connected regions in images, can fill in small holes,
and can smooth boundaries. These are important functions for some kinds
of vision processing, and some form of morphological processing is nearly
always one step in the process of locating and recognizing objects in images.

3.3 Elements of Digital Morphology—Binary
Operations

As has been explained, most morphological operations are defined on bi-level
images — that is, images that consist of either black or white pixels only. These
will be called binary morphological operators to distinguish them from the less
common grey-level morphological operations described in Section 3.2. For the
purpose of beginning the discussion, consider the image seen in Figure 3.2a.
The set of black pixels form a square object.