Digital Signal Processing Reference
In-Depth Information
, the MAP problem is
reduced to a maximum likelihood (ML) problem to maximize the joint likelihood
function
P
By assuming the uniform distribution of prior
P
(
f
p
)
, which is evaluated using the color cue modeled by the GMM,
combined with the depth and motion cues modeled using the histogram:
(
x
p
|
f
p
)
P
(
x
p
|
f
p
)=
P
color
(
c
p
|
f
p
)+
P
depth
(
d
p
|
f
p
)+
P
motion
(
m
p
|
f
p
)
=
log
g
(
c
p
|
f
p
)+
log
h
(
d
p
|
f
p
)+
log
h
(
m
p
|
f
p
)
,
(5.9)
where
c
p
is RGB color channels of
p
,
d
p
,and
m
p
denote the depth and motion
features of
p
respectively.
Uncovered New Regions
If the pixel in the previous frame is labeled as foreground object (
f
t
−
1
p
∈
F
fore
), it
will only transit to the intersected same layer or the back layer.
Similarly, finding the corresponding layer is an ML problem:
f
t
p
=
arg
max
P
(
x
p
|
f
p
)
,
(5.10)
f
t
p
≥
f
t
−
1
p
f
t
p
=
f
t
−
1
p
f
p
∈
F
feasible
=
{
(
∪
0
)
∩
Ins
(
)
}
where
f
t
−
1
f
t
−
1
−
(
)
is defined
as the set of layer that
f
t
−
p
intersects with, and
F
feasible
is the feasible label set
for a foreground object, which is located in the same or back layer in
ins
is the label of
p
in the previous frame at time
t
1.
Ins
p
p
f
t
−
1
)
.
The transition between the same layer corresponds to the new uncovered part of the
object. The transition from the front layer to the back layer indicates the exposure
of occluded part.
(
p
Feature selection
: For the uncovered regions appearing on the scene, the new ex-
posed parts may not be consistent with its associated object, eventhough they are
very similar to the other object. Under such condition, the color component in the
joint likelihood function in (
5.9
) will mislead the label decision, which makes the
color evidence invalid. To avoid this from happening, we select the appropriate fea-
tures in the evaluation of joint likelihood function based on the statement of new
uncovered regions described in (
5.10
). Since the label that will be transited to should
exist in
F
feasible
, we traverse all the possible labels to measure the color likelihood,
and find the label that corresponds to the maximum color likelihood which is not in
the feasible set
F
feasible
:
f
t
p
=
f
t
p
arg
max
P
color
(
c
p
|
f
p
)
,
∈
F
feasible
.
(5.11)
f
p
∈
F
foreground
∪
0
This bias indicates that new uncovered parts have nonhomogenous appearance
with the associated object. Thus, we remove the color term and retain the depth
and motion terms in (
5.9
). Otherwise, we combine color and depth cues to calculate
P
(
x
p
|
f
p
)
, which is distinctive enough to make a good decision.
