Image Processing Reference
In-Depth Information
µ
(p,q,shape):= cmom
←
0
rows(shape)-1
1
rows(shape)
←
⋅
xc
(shape )
i0
i=0
rows(shape)-1
1
rows(shape)
←
⋅
yc
(shape )
i1
i=0
for s
∈
0..rows(shape)-1
cmom
←
cmom+[(shape
s
)
0
-xc]
p
·[(shape
s
)
1
-yc]
q
·(shape
s
)
2
cmom
µ
(p,q,im)
η
(p,q,im):=
p+q
2
+1
µ
(0,0,im)
M1(im):=
η
(2,0,im)+
η
(0,2,im)
M2(im):=(
η
(2,0,im)-
η
(0,2,im))
2
+4·
η
(1,1,im)
2
M3(im):=(
η
(3,0,im)-3·
η
(1,2,im))
2
+(3·
η
(2,1,im)-
η
(0,3,im))
2
Code 7.5
Computing
M1
,
M2
and
M3
(a) F-14 fighter
(b) F-14 fighter rotated and scaled
(c) B1 bomber
M1 = 0.2199
M2 = 0.0035
M3 = 0.0070
M1 = 0.2202
M2 = 0.0037
M3 = 0.0070
M1 = 0.2264
M2 = 0.0176
M3 = 0.0083
(d) Invariant moments for (a)
(e) Invariant moments for (b)
(f) Invariant moments for (c)
Figure 7.23
Describing a shape by invariant moments
parameterisation for centralised moments. The
complex
Zernike moment,
Z
pq
, is
2
p
+ 1
Z
=
V
(, )* (, )
r
θθθ
f r
rdrd
(7.89)
pq
pq
0
0
where
p
is now the radial magnitude and
q
is the radial direction and where * denotes the
complex conjugate of a
Zernike polynomial
,
V
pq
, given by
V
pq
(
r
,
) =
R
pq
(
r
)
e
jq
θ
where
p
-
q
is
even
and 0
θ
≤
q
≤
p
(7.90)
where
R
pq
is a real-valued polynomial given by
