Digital Signal Processing Reference
In-Depth Information
(θ
T
1
/
2
)
(cf. Sect.
11.3.2.1
) is replaced by a Gaussian function
G
:
exp
2
−
(θ
−
μ)
G
(θ)
=
,
(11.24)
2
2
σ
2
2
T
of the ballroom
and the parameters
μ
and
σ
are set to the values of
μ
T
and
σ
dance style.
Next, the candidate
θ
T
1
/
2
that maximises the function
G
(θ
T
1
/
2
)
is selected as
θ
T
∗
. With this new tatum, a new flattened metre vector
m
∗
is
calculated, and used for determination of the quarter-note tempo. The elements
m
i
are multiplied by a Gaussian weighting factor
G
the final tatum tempo
2
in
(θ
i
)
, and the parameters
μ
and
σ
2
q
according to the ballroom dance style.
θ
i
indicates the tempo the metre vector element
m
i
Equation (
11.24
) are chosen as
μ
q
and
σ
belongs to (cf. Sect.
11.3.2.2
)
[
6
]. Then, the index
i
max
that maximises
m
i
is determined, and the tempo
θ
i
max
according to this index
i
max
is chosen as the detected quarter-note (beat level)
tempo
·
G
(θ
i
)
θ
q
.
11.3.3 Performance
Table
11.5
depicts benchmark WA for the detection with and without prior ballroom
dance style recognition. These were computed in a ten-fold SCV as were further
results in this section based on data. Thereby, at no time throughout processing test
instances' labels are used except for the final comparison if the decision was correct.
Tempo tolerance in the evaluation is 3.5 % relative BPM deviation as in [
24
]. For the
case without ballroom dance style recognition a single predefined Gaussian is used
for the overall tempo distribution instead of the nine dance style specific Gaussians.
As can be seen in the table, WA is increased by almost 20 % absolute with the
prior recognition of the ballroom dance style. With the 'perfect' ballroom dance style
as given by the manual annotation, the tempo octave is near always correct. Overall,
88 % of all instances were assigned the correct tempo octave.
With all steps as described in Sect.
11.3.2.4
, the performances in Table
11.6
are
obtained, which are the best on this data set to-date [
67
,
68
]. There, ballroom dance
style recognition is obtained without the quarter-note tempo as feature information.
Table 11.5
WA for tempo detection on the BRD set without (w/o BDS), with prior ballroom dance
style recognition (w/ BDS), and using manually annotated 'ground truth' ballroom classes as upper
idealistic benchmark (gt BDS)
WA [ %]
w/o BDS
w/ BDS
gt BDS
Tempo
88.8
92.4
93.1
Octave
70.0
88.5
93.0
