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2
M
1
2
(8)
d
2
( , )
e p
=
h m h m
[ ]
[ ]
Eculidean
e
p
m
=
0
min( [ ,] [ ])
h m h m
e
p
d
( , ) 1
e p
= −
(9)
H
int sec
er tion
M
1
M
1
min(
h m
[ ],
h m
[ ])
e
p
m
=
0
m
=
0
2
T
(10)
d
( , ) (
e p
=
h h A h h
) (
)
)TQuadratic
e
p
e
p
Where A is a matrix of similarity weights, [ ]
ij
, 0
< ,
i a = and
A a
=
a
1
1
ij
1 /
0 ,
d d
d
T
=
i j
,
max
i j
,
d
a
(11)
i j
,
di j T
>
d
d ij is the Euclidean distance between colors i and j, and d max is the greater distance between colors on
the normalized HSV/I space. That is, coefficients a ij for two colors are defined by: 0 ( , , )
and
m
=
h s v
e e e
.
m
=
( , , )
p
h s v
1
p
p
new Similarity Measure in r ough Sets
In this section, we adopt a new similarity measure in rough sets. Let
be the features sets,
U x x x
=
{ , ,... }
n
1
2
the similarity between two values is defined as follow:
1, if ([x] ) contains and
x
x
n
R
i
j
SM x x
( , )
=
Similar x x
( , )
=
i
j
i
j
0, otherwise
A category in equivalence relationship R containing an object xε U
eXPeri Ment al r esul ts and discussion
In our experiment, we used two image databases. The first one consists of 521 images of size adjusted
to 512x512 acquired from the ground level using the Sony Digital Mavica camera. The second one
consists of 630 images of size adjusted to 1024x1024 - 24 bit color images (http://www.visualdelights.
net). We convert the images from RGB to HVC space. The transformation from RGB to HVC has been
obtained through the CIE L*a*b* model. The weight vector is set to be 1/3.
Once the feature values associated with the images have been computed and stored, queries may be
done. Various models have been proposed for similarity analysis in image retrieval systems (Swets &
Weng, 1999; Wu & Huang, 2000). In this work, we use the vector space model, which is widely used
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