Digital Signal Processing Reference
In-Depth Information
and Cb that are formed by subtracting luminance from RGB red and blue compo-
nents. Then we use Gaussian mixture model(GMM) to model skin color and back-
ground. GMM is a robust model that can accommodate large variation in color space,
highlights and shadows [16]. GMM is defined as:
1
1
k
k
T
−
1
Px
( )
=
wp x
(
)
=
w
exp[
−
(
x
−
μ
)
Σ
(
x
−
μ
)]
(1)
i
i
i
i
i
i
i
i
i
1/ 2
(2
π
Σ
)
2
i
=
1
i
=
1
i
x
is a color vector representing Y, Cr, Cb;
k
is the number of mixture components
and
are the mean vector and
covariance matrix respectively , and they can be estimated from training data through
the following formula:
w
is the contribution of the
i
th component;
μ
and
Σ
i
i
1
1
n
n
T
μ
=
x
;
Σ =
(
x
−
μ
) (
x
−
μ
)
(2)
i
j
i
j
i
j
i
n
n
−
1
j
=
1
j
=
1
Where
n
is the total number of training samples.
Firstly the parameter of GMM of the background can be estimated from a set of
background images captured in real-time. Secondly, we estimate the parameters of
GMM of skin color from a set of skin images. According the initialization method
proposed in [17], the hand keeps in a relative fixed position and we only sample on
the palm area because it is bigger and not easy to contain non-skin pixels, so the skin
image is also captured in real-time, as displayed in Fig. 1 left. After getting the para-
meters of GMM of background and skin color, the pixel in the image has a probability
belongs to background or skin color, and the hand region can be separated from back-
ground according a threshold which is set to the ratio of skin color probability and
background probability, the separation result is display as Fig. 1 right.
Fig. 1.
The left is the origin image and the pixels inside green rectangle are the skin color train-
ing data. The right is the separation result, red pixel represents the skin color.
On the other hand we can get hand model silhouette from model projection, th
e knuckle of each finger and palm are treated as rigid so that they can be approx
imately expressed as quadrilateral, the got hand model silhouette is disp-layed as
Fig. 2 left. Now we define a similarity measurement function accordi-ng the non-
overlap area between the separated skin region and hand model sil-houette:
n
m
=
∏∏
p
p
background
p
skin
(3)
color
i
j
i
=
1
j
=
1
