Information Technology Reference
In-Depth Information
To give an intuition of the kNN entropy estimator, let us mention that it can be
considered as the combination of the kNN PDF estimator
p
with the Ahmad-Lin
entropy approximation
H
AL
[40]
⎧
⎨
⎩
k
(
W
,
x
)
δ
|
ρ
k
(
W
,
x
)
1
w
∈
W
p
(
x
)=
x
−
w
|
<
|
W
|
v
d
ρ
(23)
1
|
w
∈
W
log
p
(
w
)
H
AL
(
W
)=
−
|
W
d
,
W
is a set of
d
-dimensional realizations whose un-
where
x
is an element of
R
derlying PDF is
p
,
|
W
|
is the cardinality of
W
,
v
d
is the volume of the unit ball in
d
,
R
ρ
k
(
W
,
x
) is the distance between
x
and its
k
-th nearest neighbor among the ele-
ments of
W
,and
(
B
) is equal to 1 if
B
is true and zero otherwise. Replacing
p
in
H
AL
with
p
leads to a (biased) kNN-based entropy estimator close to the unbiased
version proposed in [35, 36, 37].
Subtracting the kNN entropy estimation from the kNN cross-entropy estimation
leads to the following kNN Kullback-Leibler estimation:
δ
|
V
|
d
d
|
u
∈
U
logρ
k
(
V
,
u
)
−
|
u
∈
U
logρ
k
(
U
,
u
)
.
D
KL
(
U
||
V
)=log
1
+
(24)
|
U
|−
|
U
|
U
3.3
Scalable Content-Based Queries with Patches Descriptors
In this section we assess the quality of the proposed GOP dissimilarity measure for
the retrieval problem. The experiments were performed on video sequences from
the ICOS-HD project database. After a brief description of the database, we analyze
retrieval results based on spatial frame descriptors alone, temporal/motion descrip-
tors alone, and both sets of descriptors combined together.
3.3.1
ICOS-HD Video Database
The ICOS-HD project provides a large database of both original full HD videos and
edited versions. Each original sequence contains 72 Full HD frames (1920
1080
pixels) and has been manually split up into clips, such that the boundary between
the clips roughly corresponds to a relevant motion transition. In addition, common
geometric and radiometric deformations were applied to the original HD video se-
quences, thus obtaining different versions of each video clip.
For these experiments, we used ten video sequences (see some thumbnails in
Figure 13). The deformations we considered are scaling and quality degradation by
high JPEG2000 compression, for a totla of four different versions of each video clip:
×
•
original Full HD (1920
×
1080 pixels), referenced as
1920
in the figures;
•
two rescaled versions (960
×
540 pixels), referenced as
960
;
•
two JPEG2000 coded versions (low and very low quality) referenced as
jpeg-q1
and
jpeg-q10
.
