Digital Signal Processing Reference
In-Depth Information
1
2
d
(, )
A B
=
min
a
−
b
(5)
chamfer
N
bB
∈
aA
∈
To effectively calculate their chamfer distance, we use the two pass algorithm [18] to
get distance map from edge map, Fig. 3(d) displays the resulted distance map. After
getting the distance image, we caculate the chamfer distance from contour to edge by
summing up the distance of each pixel which contour is corresponded to. The defined
similarity measurement function
p
is:
edge
(6)
p
=−
exp(
d
(
edge contour
,
))
edge
chamfer
Finally we combine hand constraints probability functions with similarity probability
functions to build a total observation likelihood model:
p
=
p
p
p
p
(7)
observation
static
dynamic
color
edge
From this observation likelihood model we can judge the hand state is whether or not a
gesture, and it also gives its similarity probability according current observation, so the
optimal hand state can be estimated through this model.
4
Observation Model in Hand Tracking
We apply the established observation likelihood model to calculate particle's weight,
it includes three steps: particle revise, particle negative and particle weight caculation.
The details of the tracking algorithm are as follows:
(1)
Initialization: At time
t
=
0
, using the initial method proposed in [19] to get
initial hand states
x
, and then sample according priori probability
px
to get the
()
initial particles set
{(
i
x Ni N
,1 /
),
=
1,...
}
,
N
represents the number of particles and
i
x
0
0
represents the
ith
particle.
(2)
Prediction: Transfer the particles got from last time according the state transi-
tion equation
px x
−
(|
)
, then sample in the new position to get new samples
t
t
1
set {
t
xi N
i
,
=
1,...
}
. The state transition equation [20] can be expressed as
x
−
is the optimal state of last time,
A
is a constant
controlling the moving speed, and
Bw
is the random noise.
(3)
Weight calculation: Using the established observation likelihood mod-
el
observatio
p
to caculate the weight of each particle according current observation.
Firstly according
stati
p
to judge whether or not the joint angles of samples beyong
their maximal or minimal value, if so revise joint angle to the defined maximal or
minimal value. Secondly, according
dynami
p
to deny the dissatisfied particles and then
revise the dissatisfied particles to the optimal value of last time. Thirdly, give the
particles after revising and denying a similarity probability according
xxAxx w
−
i
=+
(
i
− +,
)
t
t
1
t
−
1
t
−
1
t
1
pp
,the
color
edge
