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perform satisfactorily for any and all queries. Individual color descriptors
characterize one certain aspect of visual information. Visual content ought
to be characterized by multiple features to better match the perceived simi-
larity. The MPEG-7 standards specify individual visual features and do not
provide solutions to this problem, which is open for further research and
innovations.
11.3.1 relevance and Visual Similarity
Let
Q
be the query image set;
C
Q
the relevant subset of
Q
in the image collec-
tion
C
. An image retrieval system
R
is a mapping from
Q
to
R
Q
, as
ℜ→⊂
:
QC C
Q
.
(11.16)
Therefore, in set theoretic term, an image retrieval system
R
is realized as
an operation to determine the retrieved images in the collection, that is
C
Q
, as
CI
=∈
{
CP I
:
()
is true
},
(11.17)
Qi
Qi
where
P
Q
is a predicate that is true for the image
I
i
satisfying the predicate
given the query
Q
. An image is relevant to the query if the image meets the
information needs of the user as represented by the query. The ultimate goal
of the content-based image retrieval (CBIR) research is to define retrieval
strategies that the predicate
P
Q
is true when the image is relevant to the query
Q
and false when the image is irrelevant to the query
Q
. This is not a trivial
problem. Unfortunately, so far no such perfect retrieval strategies to realize
the predicate have been discovered for any practical systems that are able
to guarantee that the retrieved image set
C
Q
contains all and only relevant
images for a query. What the CBIR research strives to achieve is to formulate
the retrieval strategies so that
C
Q
contains as many relevant images and few
irrelevant ones as possible. Therefore, it is necessary to evaluate the perfor-
mance of CBIR systems. The most commonly used measure is the precision
and recall. If
T
⊂
C
is the subset of relevant images in
C
and the |
T
| the num-
ber of images in
T
, where |·| is the counting measure, then
|
TC
C
|
||
∩
Q
precision =
(11.18)
Q
and
|
TC
T
|
||
∩
Q
recall =
,
(11.19)
