Digital Signal Processing Reference
In-Depth Information
To compensate for this shortage, Jerome Revaud proposes a new distance measure of
Zernike moments which takes both magnitude and phase into consideration [14]. With
reference to Revaud's improvement idea, this paper will improve the distance measure
of Pseudo-Zernike moments through the calculation of both magnitude and phase and
propose a new method for binary trademark image retrieval.
2
Improved Distance Measure of Zernike Moments
2.1
Zernike Moments
In recent years, Zernike moment has been used widely in pattern recognition and image
analysis as a shape descriptor. Zernike moments of a given image are calculated as
correlation values of the image with a set of orthogonal Zernike basis functions mapped
over a unit circle.
A basis function for Zernike moments is defined with the order of Zernike moments
n and a repetition m constrained by n with the following condition:
`
. In Eq. (1), (x, y) is the pixel value of
'
^
Q
P
_
Q
t
Q
!
P
Q
P
LV
HYHQ
θ
the image and
r
,
is the polar coordinate position.
V
(
x
,
y
)
V
(
r
,
T
)
R
(
r
)
exp (
im
T
)
(1)
nm
nm
nm
and
(
n
m
)
/
2
(
n
s
)!
¦
R
(
r
)
(
1
s
r
n
2
s
nm
(2)
§
·
§
·
n
m
n
m
s
0
¨
©
¸
¹
¨
©
¸
¹
s
!
u
s
!
u
s
!
2
2
Then a Zernike moment can be expressed as:
Q
S
³
³
=
I
U
T
5
U
H[S
LP
T
UGUG
T
(3)
QP
QP
S
2.2
Distance Measure of Zernike Moments[14]
Apparently,
n
Z
is a complex number. In a classical way, Euclidean distance is used for
computing distance between two Zernike moments, only taking the magnitude infor-
mation into consideration without the phase information. Let I and J be two different
images and
n
Z
represent Zernike moments of image
I
and
J
, the classical
distance measure can be simply expressed as:
I
nm
and
J
Z
¦¦
G
=
,
QP
=
-
QP
Q
P
'
(4)
=0V
