Information Technology Reference
In-Depth Information
image areas. During testing, stage
i
is passed successfully if the weighted sum exceeds
a stage threshold
t
i
:
M
i
β
i
=
α
ij
h
ij
(
x
)
≥
t
i
(1)
j
=1
All components including weak classifiers, weights and thresholds are learned during
the training stage.
A detection occurs when an image area passes all
N
stages. For our method, we also
consider
incomplete detections
, that is, when the image area only passes
s
stages and
gets rejected by stage
s
. We calculate a
score
o
i
+1
(
x, y
)
for an image area of scale
i
,
centered at pixel
as follows. A completely successful detection has passed all
N
stages, and hence is assigned the score
o
(
x, y
)
=
s/N
=
N/N
=1
. A partially successful
N
.
Without
k
, the score is proportional to the number of passed stages. To smooth this
step function,
k
is set to the degree of success within a stage, in the range from zero to
exclusive one,
k
o
=(
s
+
k
detection has passed
s
stages,
s
∈{
0
,
1
, .., N
−
1
}
, and is assigned the score
.
Considering only one stage,
k
is ideally set proportional to the sum of weights below
the threshold
t
i
:
∈
[0; 1)
β
i
−
β
min
k
=
β
min
,
where
β
min
=mi
A
α
j
h
j
(
x
)
(2)
t
i
−
j∈A
for any subset
A
of weights. Note that the weights
α
j
can be positive or negative and
that the minimum achievable sum
β
min
need not be zero. We avoid computing all com-
binations of weights to find
β
min
and, instead, set it to a fixed value and ensure
k
.
This has worked well in practice without negative impact on the generated probability
image.
≥
0
3.2
Formal Justification of Prior
For this score to reflect the probability of a hand, care has to be taken during training to
provide the AdaBoost algorithm with a representative set of negative
training
images
per stage. If this set is too uniform, then the resulting stage will not proportionally
dismiss a more diverse set of negative
test
areas. In other words, if the first few stages do
not typically discard test areas at the same rate as later stages, then the score obtained
from the first few stages will be artificially inflated. We trained a Viola-Jones-based
detector on hands in arbitrary postures and varied the negative training set to avoid such
artifacts, allowing us to obtain this appearance-based posture-independent score that an
area's appearance could be attributed to a hand.
To aid in placing tracked LK-features, it is desirable to know a probability instead
of a score, to know this per pixel instead of per scanned area, and to be considerate of
areas scanned at the same center but at multiple scales. The next subsection details how
the scores obtained from incomplete detections are integrated over scale and space to
yield the prior probability.
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