Graphics Reference
In-Depth Information
ablockofsizeb
b, a two-dimensional discrete Fourier transform can be expressed
as
b
−
x
=
b
−
y
=
b
ux
b
vy
b
F
(
u,v
)=
f
(
x, y
)
exp
−
i
π
+
(
.
)
where i
. Because the image intensity is real-valued, the
Fourier transform issymmetrical about the center. Because of this symmetry, almost
half of the FFT calculation is redundant. herefore, the feature in the frequency do-
main consists of
=
−
,u,v
=
,
, b
−
with dimension b
F
u,v
ifb is of the power
.
(
)
+
Space-Frequency Domain: Gabor Filter Banks of Local Blocks
Human vision has demonstrated its superior capacity to detect the boundaries of
desiredobjects.hevisionmodelbaseduponthepreviousworkofthisauthorandhis
collaborators is described in Chen et al. (
,
a), although similar approaches
can be applied too. A neuroimage or distance map is constructed by convolving the
observed image with a bank of specific frequency and orientation bands, such as
a bank of Gabor functions. he general form of a Gabor function is given by
a
a
g
(
x, y
)=
exp
−[(
x
−
x
)
+(
y
−
y
)
]
π
exp
−
πi
[
u
(
x
−
x
)+
v
(
y
−
y
)]
(
.
)
and its Fourier transform is
π
(
u
−
u
)
+
(
v
−
v
)
G
u,v
exp
(
)=
−
a
b
exp
−
πi
[
x
(
u
−
u
)+
y
(
v
−
v
)]
(
.
)
Each local block is convolved with a bank of Gabor filters with different orientations
and frequencies. he so-called G-vector is employed as the feature vector at pixel
(
I, J
)
, which is computed by
G
V
(
I, J
)=
g
pk
(
I, J
)
, g
nk
(
I, J
)
; k
=
,
, r
(
.
)
where g
pk
are the summations of the positive and negative values
for the neuroimage that is the convoluted image with the kth Gabor filter. hus, the
dimension of the feature vector is
r in the space-frequency domain. For instance,
abankofr
(
I, J
)
and g
nk
(
I, J
)
=
=
Gabor filters aredesigned with three scales of center frequen-
, and b
whenb
cies, where
,
=
=
, as well as eight orientations of
angles,
,
,
,
,
,
,
and
.
On the other hand, statistical distributions can be used to model speckle noise
in ultrasound images. Suppose the intensities are independently and identically dis-
tributed as Rayleigh and related distributions (Burckhardt,
; Goodman,
).
hese different types of features can be combined with active contour models (i.e.,
