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where p ki is percentage and a k,l is the similarity coefficient between two colors
c k and c l ,
1
dd
/
dT
dT
>
kl
,
ax
kl
,
d
a
=
,
(11.3)
al
,
0
kl
,
d
where d k,l is the Euclidean distance between two colors
d
=−
c
c
.
(11.4)
kl
,
k
l
T a is the maximum distance for two colors to be considered similar and
d max = α T d .
If color variances are present, the following similarity measure is used.
N
N
N
N
N
N
1
2
1
2
1
2
DFF
(, )
12
=
p pf
+
pp f
2
pp f
,
(11.5)
v
1111
i
j
i
j
222
i
j
i
2
j
1212
i
j
ij
i
=
1
j
=
1
i
=
1
j
=
1
i
=
1
j
=
1
where
c
v
c
v
c
v
1
xiyjl
xiyju
xiyjv
f
=
exp
+
+
,
(11.6)
xiyj
vv v
xiyjlxiyju
xiyjv
xiyjl
xiyju
xiyjv
and
c
=−
(
c
c
) 2
(11.7)
xiyjl
xil
yjl
v
=−
(
v
v
) 2
(11.8)
xiyjl
xil
yjl
This matching method is a good example of applying different similarity
measures when different data are available in the descriptor.
11.2.1.2 Scalable Color Descriptor (SCD)
This descriptor is a color histogram in hue, saturation and vale (HSV) color
space that is encoded by a Haar transform. The histogram in HSV color space
i is u n i f or m ly q u a nt i z e d i nt o 2 56 bi n is a nd t h e h i is t o g ra m va lue is a r e t h e n no n l i n -
early quantized. The 4-bit values then are transformed by a Haar transform.
The SCD captures the color distribution in images.
The similarity matching for the SCD can be performed in both the Haar
transform and histogram domains. The L 1 norm is recommended for match-
ing in both domains.
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