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(a)
(b)
(c)
Figure 2.6.
Difference matting. The difference between the image with foreground (a) and clean
plate (b) can be thresholded to get a hard segmentation (c). Even prior to further estimation of
fractional
α
values, the rough matte has many tiny errors in places where the foreground and
background have similar colors.
(a)
(b)
(c)
(d)
Figure 2.7.
(a),(b) Static objects are photographed in front of two backgrounds that differ in
color at every pixel (here, two solid-color backgrounds). (c) Triangulation produces a high-quality
matte. (d) Detail of matte.
since there are still three equations in four unknowns, the matte and foreground
image can't be determined unambiguously. In particular, since the clean plate may
contain colors similar to the foreground, mattes created in this way are likely to
contain more errors than mattes created using blue or green screens.
Smith and Blinn observed that if the foreground
F
was photographed in front of
two different backgrounds
B
1
and
B
2
, producing images
I
1
and
I
2
, we would have six
equations in four unknowns:
I
1
=
α
F
+
(
1
−
α)
B
1
(2.5)
I
2
=
α
F
+
(
1
−
α)
B
2
As long as
B
1
=
B
2
, we can solve Equation (
2.5
) for
α
as
(
I
1
−
I
2
)
·
(
B
1
−
B
2
)
α
=
1
−
(2.6)
(
B
1
−
B
2
)
·
(
B
1
−
B
2
)
Then
F
can be recovered from the matting equation or by solving the overdeter-
mined system in Equation (
2.5
). Smith and Blinn called this approach
triangulation
,
and it can be used for generating high-quality ground-truth mattes, as illustrated
in Figure
2.7
. However, triangulation is difficult to use in practice since four sepa-
rate, precisely aligned images must be obtained (i.e.,
B
1
,
I
1
,
B
2
, and
I
2
). It can be
