Image Processing Reference
In-Depth Information
8.3.1 Template-Based Edge Detection
This method is an extension of fuzzy divergence-based edge detector [4]. For
edge detection, a set of 16 fuzzy templates, each of size 3 × 3, representing the
edge profiles of different types, are used:
0
0
0
ba
ba
ba
aaa
aab
ab
b
b
bbb
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
000
0
00
000
bbb
aaa
⎣
⎦
⎣
⎦
⎣
⎦
⎣
⎦
baa
ba
b
ba
ba
ba
a
b
⎡
⎤
⎡
0
0
0
⎤
⎡
0
0
0
⎤
⎡
000
⎤
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
a
b
bbb
aaa
0
00
a
b
⎣
⎦
⎣
⎦
⎣
⎦
⎣
⎦
⎡
aaa
bbb
⎤
⎡
ab
ab
ab
0
0
0
⎤
⎡
000 0
⎤
⎡
aab
ab
ab
⎤
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
aaa
bbb
0
0
000
⎣
⎦
⎣
⎦
⎣
⎦
⎣
⎦
bbb
aaa
b
0
0
0
a
b
000
0
00
0
b
ba
baa
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
b
a
ab
aab
000
b
a
⎣
⎦
⎣
⎦
⎣
⎦
⎣
⎦
A set of sixteen 3 × 3 templates.
The choice of templates is crucial, which reflects the type and direction
of edges. The templates are the examples of the edges, which are also the
images.
a
,
b
and 0 represent the pixels of the edge templates, where the values
of
a
and
b
are chosen by the trial-and-error method. The best combination is
a
= 0.3,
b
= 0.8, and with these values, the edge-detected results are better.
Sixteen templates are considered to be optimum for edge detection.
The size of the templates is less than the size of the image. The centre of
each template is placed at each pixel position (
i
,
j
) over a normalized image.
The intuitionistic fuzzy divergence (
IFD
) measure at each pixel position (
i
,
j
)
in the image, where the template was centred,
IFD
(
i
,
j
), is computed between
the image window (same size as that of the template) and the template using
the max-min relationship, as given in the following equation [5]:
(8.1)
IFDi j
(,)max[min(
=
IFD AB
( , ]
r
N
'
r
= 9' is the number of elements in the square template (3
2
= 9)
N
is the total number of templates
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