Information Technology Reference
In-Depth Information
Managing the Asymmetry.
All the proposed similarity functions are not symmetric,
i.e.,
s
(
d
x
,d
y
)=
s
(
d
y
,d
x
)
does not hold. Consider the case in which the set of local fea-
tures belonging to
d
x
is a subset of the ones belonging to
d
y
. In this case the similarity
s
(
d
x
,d
y
)
is 1 while the same does not hold for
s
(
d
y
,d
x
)
.
In searching for images similar to
d
x
, it is not clear in advance whether
s
(
d
x
,d
y
)
or
s
(
d
y
,d
x
)
would be a better similarity measure for the recognition task. Thus, we tested
various combinations.
Given an image
d
Te
belonging to
Te
(i.e., an image that we want to automatically
classify), and an image
d
Tr
belonging to
Tr
(i.e., an image for which the class label is
known in advance) we define various versions of the similarities defined before:
-
s
Te
(
d
Te
,d
Tr
)=
s
(
d
Te
,d
Tr
)
- is the canonical approach which tries to find points
in the test image that are similar to the ones in the training one.
-
s
Tr
(
d
Te
,d
Tr
)=
s
(
d
Tr
,d
Te
)
- is the inverse approach which uses the points in
training documents as queries.
-
s
or
(
d
Te
,d
Tr
)=max(
s
(
d
Te
,d
Tr
)
,s
(
d
Tr
,d
Te
))
- is the fuzzy
or
of
s
Te
and
s
Tr
.
This considers equivalent two images if any of the two is a crop of the other.
-
s
and
(
d
Te
,d
Tr
)=min(
s
(
d
Te
,d
Tr
)
,s
(
d
Tr
,d
Te
))
- is the fuzzy
and
of
s
Te
and
s
Tr
. This never considers equivalent two images if any of the two is a crop of the
other.
-
s
avg
(
d
Te
,d
Tr
)=(
s
(
d
Te
,d
Tr
)+
s
(
d
Tr
,d
Te
))
/
2
- is the mean of
s
Te
and
s
Tr
.
Thus, we have defined 5 versions of our 4 similarity measures for a total of 20 similarity
measures that will be denoted as
s
m,Te
,s
m,Tr
,s
m,or
, ..., s
h,Te
,etc.
5
Local Feature Based Image Classifier
In the previous section, we considered the classification of an image
d
x
as a process
of retrieving the most similar ones in the
training set
Tr
and then applying a kNN
classification technique in order to predict the class of
d
x
.
In this section, we propose a new approach that first assigns a label to each local
feature of an image. The label of the image is then assigned by analyzing the labels
and confidences of its local features. This approach has the advantage that any access
method for similarity search in metric spaces [18] can be used to speed-up classification.
The proposed
Local Feature Based Image Classifiers
classify an image
d
x
in two steps:
1. first each local feature
p
x
belonging to
d
x
is classified considering the local features
of the images in
Tr
;
2. second the whole image is classified considering the class assigned to each local
feature and the confidence of the classification.
Note that classifying individually the local features, before assigning the label to an
image, we might loose the implicit dependency between interest points of an image.
However, surprisingly, we will see that this method offers better effectiveness than the
baseline approach. In other words we are able to improve at the same time both effi-
ciency and effectiveness.
