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We propose two measures useful for analysis of DEM values for different datasets
and different visual descriptors: stability and ranking. Stability describes dispersion
of DEM values for the given descriptor. It exists in two variants: internal and external.
Individual internal stability
SII
is defined for the given feature
D
,set
u
i
and descriptor
evaluation measure
M
with the following equation:
N
i
j
=
1
M
ij
(
i
2
MD
D
)
−
μ
MD
i
=
σ
CV
MD
i
SII
i
(
D
,
M
)
=
·
√
N
i
=
,
(12.25)
MD
i
MD
i
μ
μ
N
i
1
N
MD
i
μ
=
M
ij
(
D
),
j
=
1
MD
i
where
M
ij
(
D
)
is a value of DEM
M
of the descriptor
D
in the subset
u
ij
,
μ
MD
i
σ
denotes the mean value of DEM
M
of the descriptor
D
in the set
u
i
,
is the
standard deviation of the same data and
CV
coefficient of variation.
Stability is given as an average dispersion of DEM values related to their mean
value, therefore the smaller its value is, the greater stability of the DEM is and the
better the visual descriptor is suited for object re-identification.
Internal stability
SI
aggregates partial stabilities of all DEMs of all sets:
N
M
N
U
(
)
=
SII
i
(
,
),
SI
D
D
M
(12.26)
M
=
1
i
=
1
where
N
M
denotes number of DEMs used.
External stability
SE
measures normalized dispersion of DEMs of a particular
feature
D
across different datasets in
U
. It is given with the equation:
2
N
M
N
U
MD
i
MD
μ
−
μ
SE
(
D
)
=
,
(12.27)
MD
μ
M
=
1
i
=
1
N
U
1
N
MD
MD
i
μ
=
1
μ
,
i
=
MD
denotes the average of mean values of DEM
M
of the descriptor
D
in
all datasets
U
. The smaller the value of
SE
, the greater the independence of DEMs
of the descriptor
D
from dataset selection and the better the descriptor is suited for
visual object identification.
Ranking is the second measure developed for analysis of DEM values for different
datasets and various visual descriptors. It also exists in two variants: value-based and
position-based. Individual value-based ranking
RVI
is defined for the given feature
where
μ
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