Image Processing Reference
In-Depth Information
9.5 Fuzzy Morphology in Image Processing
Morphological operators transform the original image into another image
of certain shape and size, also known as structuring element. Mathematical
morphology provides an approach to analyse the geometric characteristics
of images and has been widely used in image edge detection, segmentation,
noise suppression and so on. Fuzzy mathematical morphology extends the
binary morphological operators to grey-level images. In binary morphology,
fuzzy erosion, dilation, opening and closing are present. In a similar way in
fuzzy morphological operations, union operation is replaced by a maximum
operation and intersection operation is replaced by a minimum operation.
Morphological operators are used to find the morphological gradient or to
denoise the image. The effect of erosion and dilation operations is better for
finding the image edge by taking the difference between the dilated image
and eroded image, but they do not perform well in noisy images. As opposed
to erosion and dilation, opening and closing operations perform better in
denoising the images.
Techniques for mathematical morphology using fuzzy set and intuitionis-
tic fuzzy set on medical images are discussed.
9.5.1 Edge Detection
The image is initially fuzzified to have the values between [0, 1]. The
structuring element selected is
086086 086
086 1 086
086086 086
.
.
.
⎡
⎤
⎢
⎢
⎢
⎥
⎥
⎥
.
.
.
.
.
⎣
⎦
From Lukasiewicz's definition, the
t
-norm and
t
-conorm are
TAB
(,)max(,
=
0
A B
+ −
1
)
*
(,)min(,
TAB
=
1
A B
+
)
where
A
is an image
B
is a structuring element
From the definition of dilation and erosion,
DAB
(,) up
=
i By xAy
(
−
),()
⎣
⎦
yS
∈
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