Graphics Reference
In-Depth Information
7.5.1
Motion Interpolation
The most common motion editing problem is
interpolation
; that is, we want to
smoothly blend between two givenmotions
{
θ
(
,
T
}
.
For example, as illustrated in Figure
7.13
, we may want to blend the end of a walking
motion with the beginning of a runningmotion so that themotion seems to naturally
speed up over the transition.
The goal is to stitch the motion capture sequences together without altering them
too much. We must consider two important problems. First, we must make sure the
motions are spatially aligned, so that the second motion picks up at the location
and orientation that the first motion leaves off. Second, and more important, we
must make sure that the motions are temporally synchronized so that no artifacts
are introduced across the blending interval. For example, the feet in the interpolated
motion must appear to make natural contact with the ground.
The synchronization problem is commonly solved using
dynamic time warping
,
an application of dynamic programming similar to what we discussed for estimating
correspondence along conjugate epipolar lines in Section
17
. Figure
7.14
illustrates
the problem. We seek a correspondence between the
T
frames of the first sequence
and the
T
frames of the second sequence that minimizes the cost of a path from one
corner of the graph to the other.
Formally,
{
θ
(
t
)
,
t
=
1,
...
,
T
}
and
t
)
,
t
=
1,
...
the path
P
is defined by a set of
frame-to-frame matches
t
1
,
t
1
)
t
L
,
t
L
)
}
t
1
=
T
,
t
L
=
t
i
,
t
i
−
1
≤
t
i
,
i
T
and
t
i
−
1
{
(
L
.
That is, the path goes from one corner of the graph to the other and monotonically
increases in both directions. The cost of the path is the sumof the costs for associating
pairs of frames:
,
...
,
(
such that
t
1
=
1,
t
L
=
≤
=
2,
...
L
θ
(
t
i
))
(
)
=
(
θ
(
t
i
)
C
P
c
,
(7.31)
i
=
1
θ
(
t
))
where
c
is a distance function between poses. This cost can be minimized
using dynamic programming (see Appendix
A.1
). A simple choice for
c
(
θ
(
t
)
,
θ
(
t
))
is
the sum-of-squared distances between corresponding joint angles (not including the
root position and orientation). We might give more weight to poses in which a foot
(
θ
(
t
)
,
walk
run
walk
jog
run
Figure 7.13.
Motion interpolation for stitching sequences together. Dots indicate foot contact
with the ground. In this example, a walking motion is blended into a running motion to produce
a jog over the transition.
