Using this operator, binary image thinning is typically performed by applying in
parallel rotated versions of the structuring element B. A widely used structuring
element is that shown in Figure 7.7(A). Figure 7.8 illustrates the difference be-
tween the result using thinning(.) operator (B) (B is as shown in Figure 7.7(A))
and the morphological skeleton (C) of a binary image (A).
Q ? O--O--O 0--0 Z O -- O Q
o o ~ O-O ~. ~- " "
o o o , ....... o ~ ~., "
~ .
o o " e, ~ ~, o,~, .:~, •-
0 Z
" '-0 " _~: ; q~ ~. ~.~ ~ ._.
" " ~" ,2 O~O--O--O~-O--O-O--O ~O
q~ O- o~
:; ,- ~
...... _
:~ O-O qD •-~: " - -
~: 6 :~, 2, ~ ~:, ~_-~,; ~ _. ~_
o o ,_ oi~ o ~
(A) (B) (C)
Figure 7.8
Morphological thinning versus skeleton. (A) F. (B) thinningB(F ).
(C) Morphological skeleton (Definition 7.11)
As a complement to these operators, the context of mathematical mor-
phology provides pruning operators to remove spurious branches from the final
thinned set. This is particularly useful when thinning noisy images so that re-
construction will be more symmetric and smoothed. Pruning is typically based
on the hit or miss operator to exploit conditions within the neighbourhood. This
clearly corresponds to using connectivity and crossing numbers and is equivalent
to the beautifying step mentioned earlier.
7.2.3 Minimum-Base Segment algorithm
In the discrete space, skeletonisation based on local width simply uses
pixels as border points and follows the borders of the component in directions
allowed by the connectivity relationship given in the current context. The algo-
rithm detailed in [151] shows some shortcomings which are overcome in [91].
The main advantage of such a discrete approach is that it creates pairs
of border pixels to form local width lines. These lines have been shown to be
optimal for local width measurements and therefore for analysing the image. An
example is illustrated in Figure 7.9 where the skeleton and dual width lines are
shown for a ribbon-like image.
7.3 Binary line images
Binary images are typically used in applications where the shapes of the
foreground components are meaningful. This is the case, for example, in images
Figure 7.9 Skeleton and local width measurement
representing an alphabet (e.g. characters and sign language) or a shape allowing
identification (e.g. fingerprint). What all these images have in common is that
their skeletons are almost as meaningful as the images themselves. By contrast,
it is not clear how to identify a blob-like shape from its skeleton without recon-
structing it. This is emphasised schematically in Figure 7.10, where images of
different types and their respective skeletons are presented.
Figure 7.10 Examples of images and their skeletons
Figure 7.10(C) shows a typical example of what we call a binary
image. It is a binary image composed of strokes where the width information
is irrelevant. The representation of such an image can accurately be done by
finding its skeleton. From this feature, the image can be interpreted without
the need for reconstruction. It is actually proven that such a representation is
more reliable than the image itself (e.g. for OCR applications). In this section,
we study the class of binary line images via the significance of their skeletons
(Section 7.3.1).
Remark 7.15"
In this study, we leave aside the case of half-tone pictures, which are a particular
class of binary images which tends to belong to the class of gray scale images.

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