Graphics Reference
In-Depth Information
3.9
HOMEWORK PROBLEMS
3.1
Sketch the hard composite implied by the images
S
,
T
, and
M
in Figure
3.39
.
S
T
M
Figure 3.39.
Source, target, and mask images for a compositing problem.
3.2 Consider the corresponding rows of a source and target image given by
Figure
3.40
. We want to use a weighted transition region between columns
50 and 70 so that pixels to the left of column 50 come entirely from the
source, pixels to the right of column 70 come entirely from the target, and
pixels in the transition region are a linearly weighted blend between the two
images. Sketch the row of the composite, indicating important values on
the
x
and
y
axes.
250
250
200
50
50 60 70
100
50 60 70
100
Source row
Target row
Figure 3.40.
Two corresponding rows of a source and target image.
3.3
Show that the pyramid image
G
i
can also be obtained as
G
i
=
(
K
i
∗
I
)
↓
2
i
(3.45)
where
I
is the original image, and
K
i
is a low-pass filter whose spatial extent
increases with
i
.
3.4 Prove that Equation (
3.5
) is true — that is, that the original image can be
obtained as the sum of the upsampled images of the Laplacian pyramid.
Use induction; that is, show that
G
i
=
(
G
i
+
1
)
↑
2
+
L
i
(3.46)
=
...
−
is true for
i
0,
,
N
1.
