Information Technology Reference
In-Depth Information
4.3
Similarity Measures
In this section, we define 5 different image similarity measures approaches and 4 dif-
ferent versions of each of them for a total of 20 measures.
1
.
1-NN Similarity Average -
s
The simplest similarity measure only consider the
closest neighbor for each
p
x
∈
d
x
and its distance from the query point
p
x
. The similar-
ity between two documents
d
x
and
d
y
can be defined as the average similarity between
the local features in
d
x
and their closest neighbors in
d
y
. Thus, we define the
1-NN Sim-
ilarity Average
as (for simplicity, we indicate the number of local features in an image
d
x
as
|d
x
|
):
1
s
1
(
d
x
,d
y
)=
max
p
y
∈
(
s
(
p
x
,p
y
))
|
d
x
|
d
y
p
x
∈d
x
s
m
.
A reasonable measure of similarity between two image
d
x
and
d
y
is the percentage of local features in
d
x
that have a match in
d
y
.Using
the distance ratio criterion described in 4.2 for individuating matches, we define the
Percentage of Matches
similarity function
s
m
as follows:
Percentage of Matches -
1
s
m
(
d
x
,d
y
)=
m
(
p
x
,d
y
)
|
d
x
|
p
x
∈d
x
where
m
(
p
x
,d
y
)
is 1 if
p
x
has a match in
d
y
and 0 otherwise (see Sec. 4.2).
s
σ
.
The matching function
m
(
p
x
,d
y
)
used in the
Percent-
age of Matches
similarity function is based on the ratio between closest to second-
closest neighbors for filtering candidate matches as proposed in [14] and reported in
Section 4.2. However, this distance ratio value can be used directly to define a
Distance
Ratio Average
function between two images
d
x
and
d
y
as follows:
Distance Ratio Average -
1
s
σ
(
d
x
,d
y
)=
σ
(
p
x
,d
y
)
|
d
x
|
p
x
∈
d
x
Please note that function does not require a distance ratio
c
threshold.
Hough Transform Matches Percentage -
s
h
.
As mentioned in Section 4.2, an Hough
transform is often used to search for keys that agree upon a particular model pose. The
Hough transform can be used to define a
Hough Transform Matches Percentage
:
s
h
(
d
x
,d
y
)=
|
M
h
(
d
x
,d
y
)
|
|
d
x
|
where
M
h
(
d
x
,d
y
)
is the subset of matches voting for the most voted pose. For the
experiments, we used the same parameters proposed in [14], i.e. bin size of 30 degrees
for orientation, a factor of 2 for scale, and 0.25 times the maximum model dimension
for location.
