Image Processing Reference
In-Depth Information
Re (gw(t))
Im (gw(t))
t
t
(a) Real part
(b) Imaginary part
Figure 2.22
An example Gabor wavelet
a 2D form aimed to be optimal in terms of spatial and spectral resolution. These 2D Gabor
wavelets are given by
2
2
( -
xx
) + ( -
yy
)
0
0
-
1
2
2
σ
-
j
2
f
((
xx
-
)cos(
)+(
yy
-
)sin(
))
(2.45)
gw
2D(
x y
, ) =
e
e
0
0
0
σπ
where
x
0
,
y
0
control position,
f
0
controls the frequency of modulation along either axis, and
θ controls the
direction
(orientation) of the wavelet (as implicit in a two-dimensional
system). Naturally, the shape of the area imposed by the 2D Gaussian function could be
elliptical if different variances were allowed along the
x
and
y
axes (the frequency can also
be modulated differently along each axis). Figure
2.23
, of an example 2D Gabor wavelet,
shows that the real and imaginary parts are even and odd functions, respectively; again,
different values for
f
0
and σ control the frequency and envelope's spread respectively, the
extra parameter θ
controls rotation.
Re(Gabor_wavelet)
Im(Gabor_wavelet)
(a) Real part
(b) Imaginary part
Figure 2.23
Example two-dimensional Gabor wavelet
