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t = 0
t = 0.25
t = 0.5
t = 0.75
t = 1
Figure 5.21.
Simply cross-dissolving between two original images (far left and right) produces
an unrealistic transition between them (intermediate images).
^
I
t
I
1
M
t
I
t
^
I
2
Figure 5.22.
The process of image morphing using dense correspondence fields. Intermediate
images
I
1
and
I
2
are created by applying forward and backward optical flow fields to the original
images
I
1
and
I
2
, respectively. The morph image
M
t
is created as a weighted average between
the colors of
I
1
and
I
2
. In this sketch,
t
1
3
, so the morph image
M
t
is closer to
I
1
both in structure
≈
and color.
intermediate images don't look like they contain a single object of the same type
as either of the two original images.
The key to an effective morph is to
warp
each image toward the other before
performing the cross-dissolve; in this way, the image structures are aligned in each
image of themorphing sequence. The process is illustrated inFigure
5.22
. Specifically,
we apply the following basic algorithm to create each image
M
t
.
1. Compute intermediate images
I
1
and
I
2
by warping
I
1
and
I
2
a fraction of the
way along their estimated flow fields:
I
1
(
tu
fwd
tv
fwd
x
,
y
)
=
I
1
(
x
+
(
x
,
y
)
,
y
+
(
x
,
y
)
(5.61)
I
2
(
u
bwd
v
bwd
)
=
(
+
(
−
)
(
)
+
(
−
)
(
)
x
,
y
I
2
x
1
t
x
,
y
,
y
1
t
x
,
y
2. Cross-dissolve between the intermediate images to create the morph
sequence image
M
(
t
)
:
)
I
1
(
t I
2
(
M
t
(
)
=
(
−
)
+
)
x
,
y
1
t
x
,
y
x
,
y
(5.62)
Figure
5.23
illustrates an example with real images. We can see that each inter-
mediate image
I
1
is the result of warping the pixels of
I
1
the fraction
t
of the way to
their corresponding locations in
I
2
. Thus,
I
1
(the rightmost image in the first row of
Figure
5.23
) contains the pixel intensities of
I
1
at the locations in
I
2
. A similar argu-
ment holds for the intermediate images
I
2
in the second row of Figure
5.23
. We can
