Graphics Reference
In-Depth Information
clean plate (background) B
image with foreground I
Figure 2.27.
A clean plate and an image containing a foreground element.
2.4 Consider
as a function of
I
b
and
I
g
in Vlahos's equation (
2.4
), where both
color channels are in
α
1
2
and
a
2
=
1. What
happens as
a
1
is increased for fixed
a
2
? What happens as
a
2
is increased for
fixed
a
1
? Interpret your results.
2.5 The color
I
i
=[
[
0, 1
]
. Plot this surface for
a
1
=
]
was observed in front of a pure blue background.
Compute two possibilities for (
40, 50, 150
α
i
,
F
i
), keeping inmind both valuesmust stay
in a valid range.
2.6 Derive the triangulation formula for
α
; that is, prove that the solution of
Equation (
2.5
) is given by Equation (
2.6
).
2.7 A pixel is observed to have intensity
]
[
150, 100, 200
in front of a pure
]
blue background, and intensity
[
140, 180, 40
in front of a pure green
using triangulation.
2.8 Prove that Equation (
2.16
) and Equation (
2.17
) minimize the Bayesian
matting objective function.
background. Compute
α
2.9
Suppose that the foreground and background pdfs in amatting problemare
modeled as Gaussian distributions with
150
150
150
20 5 5
5 08
585
µ
=
=
(2.88)
F
F
50
50
200
500
050
0015
µ
=
=
(2.89)
B
B
]
, compute
F
,
B
, and
If the observed pixel color is
[
120, 125, 170
α
by alter-
nating Equation (
2.16
) and Equation (
2.17
), assuming
σ
d
=
2. Repeat the
10 and interpret the difference.
2.10 Continuing Problem
2.9
, suppose the foreground is modeled with a mix-
ture of two Gaussian distributions: the one from Equation (
2.88
) and one
experiment with
σ
d
=
