Image Processing Reference
In-Depth Information
f
(
n
,
m
)
EMAP (
n
,
m
)
T
= 0.4
(a)
(b)
FIGURE 2.27
(a) Original LENA image and (b) edge map of LENA image.
G
(
n, m
) ¼j
G
x
(
n, m
)jþj
G
y
(
n, m
)j
(
2
:
95
)
to 1 bit using the threshold T
1 G
(
n, m
)
T
0 G
(
n, m
) >
T
EMAP(
n, m
) ¼
(
2
:
96
)
The result of applying the above edge detection algorithm to the LENA image is
shown in Figure 2.27b.
2.6.1 D
ESIGN OF
2-D FIR F
ILTERS
Two-dimensional FIR
filters can be designed to have zero-phase response. Zero-
phase
filters introduce no phase distortion. The necessary and suf
cient condition for
2-D FIR
filters to have zero-phase response is that the
filter impulse response be
symmetric with respect to the origin (center point), that is,
h
(
n
1
, n
2
) ¼
h
(
n
1
,
n
2
)
(
2
:
97
)
The
first step in designing 2-D FIR
filters using the window method is to compute the
desired
filter impulse response by inverting the desired frequency response using the
inverse Fourier transform, that is,
p
p
1
H
d
(
j
v
1
, j
v
2
)
e
j
(v
1
n
þv
2
n
2
)
dv
1
dv
2
h
d
(
n
1
, n
2
) ¼
(
2
:
98
)
4
p
2
p
p
Closed form solutions exist for the 2-D impulse response sequences of LP, HP,
and band-pass
filters for both rotationally symmetrical and nonsymmetrical
filters [5].
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