Digital Signal Processing Reference
In-Depth Information
Fig. 4.7 a
Original image.
b
Histogram corresponding to
a
.
c
Histogram equalized image.
d
Histogram corresponding to
c
image is illustrated in the Fig.
4.7
. Note that the value of the mass function for the
background color is made zero in the histogram plot.
4.2.6 Histogram Specification
It is possible to obtain the transformation
Y
=
g
(
X
)
for the arbitrary cumulative dis-
tribution functions
F
Y
(
(instead of uniform distribution as mentioned in histogram
equalization) as described below. This is known as histogram specification.
y
)
1. Identify the transfer function
Z
that maps the random variable
X
to
intermediate random variable
Z
, such that
F
Z
(
=
g
1
(
X
)
z
)
=
z
.
2. Identify the transfer function
Z
that maps the random variable
Y
to
intermediate random variable
Z
, such that
F
Z
(
=
g
2
(
Y
)
z
)
=
z
.
3. Given the arbitrary value of the matrix
α
, identify the corresponding value for
Z
using
Z
=
g
1
(
X
)
.(say
β
).
g
−
1
2
4. Using the function
Y
.
5. Repeat this for all values in the original image matrix described by the random
variable
X
to obtain the image matrix described by the random variable
Y
,us-
ing the intermediate random variole
Z
. Thus the histogram equalized image is
obtained.
=
(
Z
)
, identify the value of
Y
corresponding to
Z
=
β
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