Graphics Reference
In-Depth Information
2.21
Suppose for a given pixel in belief-propagation-basedmatting, we gathered
the foreground samples and background samples given by
95
120
100
105
80
70
F
1
=
F
2
=
(2.92)
105
160
100
95
180
170
B
1
=
B
2
=
(2.93)
]
and had estimated that
Suppose we observed
I
i
=[
100, 140, 110
α
i
=
0.5.
F
i
,
B
i
)
Estimate the optimal samples
according to Equation (
2.59
). How
would the answer change if we instead used the distance ratio criterion in
Equation (
2.70
) from robust matting?
(
2.22
Show that minimizing
the
random walk objective
function in
Equation (
2.64
) leads to the linear system in Equation (
2.65
).
2.23
Show that Equation (
2.71
) and Equation (
2.73
) have the same minimum
with respect to
(that is, the objective functions differ by a constant term).
2.24 A typical sigmoid function for border matting resembles Figure
2.21
c and
can be parameterized using the profile
α
1
p
(
w
)
=
(2.94)
1
+
e
−
a
(
w
−
b
)
where
w
ranges from 0 to 1. If we observe the samples
{
(
w
i
,
p
i
)
,
i
=
1,
...
,
s
}
,
what would be good initial estimates for the values of
a
and
b
?
