Digital Signal Processing Reference
In-Depth Information
{
∞
-
,
x
is NOT adjacent to
y
frame t
-
→
→
,
y
is contained by
S
(0,
t
)
∞
→
-
exp(
log(0
.
75)
(
x,
→→
y
)=
c
(
n,t
)
∞
,
y
is further
d
(
S
initial
) than from the
S
(0,
t
)
-
→
vobject
) ,
otherwise
L
(
n,t
)
(4.26)
where
S
(0,
t
)
is a timeslice at time t of the initial surface,
L
(
n,t
)
is the
expected length of the contour
S
(
n,t
)
,
S
initial
is the initial surface esti-
mate, and
d
is a distance measure based on the initial surface estimate.
The Voronoi Order Space component will be added as the ordering of
problems in Eq. 4.30. To construct
R
(
n,t
)
-
→
→
(
x,y
), we combine our edge
vobject
detection and change detection
in step
#1:
(
I
,
x
) =
{
R
canny
(
I
(
x, y, t
)|
t=t'
,
x
),
2
R
(0,
t'
)
(
I
(
x
,
y
,
t
)|
t=t
'
,
x
),
→
→
x
X
change
(
I
)
canny
(4.27)
R
(0,
t'
)
→
(
0,t'
)
otherwise
→
where
I
(
x, y, t
)|
t=t'
is the isolated frame at time
t'
,
R
canny
is the intensity
map of Canny edge results for frame
t'
,and
X
change
are the set of pixels
that are marked as changing by our change detection analysis.
We add
our Viterbi Ring analysis in step #2:
R
(0,
t
)
(
I
,
x
)=
{
3
R
(0,
t
)
(
x
),
x
→→
X
bmc / vrings
(
I
)
1
→
(4.28)
R
(0,
t
)
1
(
x
),
→
otherwise
2
where
X
bmc/vrings
are the subset of points in the Viterbi Rings that pass
the
test
of boundary
motion
coherence.
In our final step,
we add our
spatial
and
time
smoothness
components:
{
R
(0,
t
)
X
smooth
(
S
(
n
-1,
*
)
)
→
(
x
)
R
2
→
+
δ
(
n
)
x
R
(
n,t
)
(
S
(
n
-1,
*)
,
x
)
→
=
2
sur face
(0,
t
)
→
(
x
)
otherwise
(4.29)
where
X
smooth
is the set of points from a smoothed version of
S
(
n
-1,
*
),
and
(
n
) is a smoothness measure that increases with the number of
iterations to converge the surface optimization.
The framework for the Iterative Viterbi Algorithm is shown in Fig-
ure 4.17. The decomposition of the problem into iterative framework
divides the problem into two major stages, similar to Expectation and
Maximization (EM) algorithm: an Optimization step and Re-estimation
step. Applying the algorithm of Figure 4.13 within an iterative frame-
work, we can calculate the surface through these steps:
δ
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