Graphics Reference
In-Depth Information
If the position and orientation of each camera are known with respect to the global coordinate sys-
tem, along with the position of the image plane relative to the camera, then the images of the point to be
reconstructed (
I
1
,
I
2
) can be used to locate the point,
P
, in three-space (
Figure 6.4
). Using the location of
a camera, the relative location of the image plane, and a given pixel location on the image plane, the
user can compute the position of that pixel in world coordinates. Once that is known, a vector from the
C
1
þ k
1
ðI
1
C
1
Þ¼P
(6.1)
C
2
þ k
2
ðI
2
C
2
Þ¼P
(6.2)
¼C
2
þk
2
(
I
2
C
2
). In three-space, this
represents three equations with two unknowns,
k
1
and
k
2
, which can be easily solved—in an ideal
world. Noise tends to complicate the ideal world. In practice, these two equations will not exactly inter-
sect, although if the noise in the system is not excessive, they will come close. So, in practice, the points
of closest encounter must be found on each line. This requires that a
P
1
and a
P
2
be found such that
P
1
is
on the line fromCamera 1,
P
2
is on the line fromCamera 2, and
P
2
P
1
is perpendicular to each of the two
By setting these equations equal to each other, C
1
þk
1
(
I
1
C
1
)
ðP
2
P
1
ÞðI
1
C
1
Þ¼
0
(6.3)
ðP
2
P
1
ÞðI
2
C
2
Þ¼
0
(6.4)
See
Appendix B.2.6
on solving for
P
1
and
P
2
. Once the points
P
1
and
P
2
have been calculated, the
midpoint of the chord between the two points can be used as the location of the reconstructed point. In
the case of multiple markers in which marker identification and tracking have not been fully established
for all of the markers in all of the images, the distance between
P
1
and
P
2
can be used as a test for
correlation between
I
1
and
I
2
. If the distance between
P
1
and
P
2
is too great, then this indicates that
I
1
and
I
2
are probably not images of the same marker and a different pairing needs to be tried. Smooth-
ing can also be performed on the reconstructed three-dimensional paths of the markers to further reduce
the effects of noise on the system.
6.4.1
Multiple markers
The number and positioning of markers on a human figure depend on the intended use of the captured
motion. A simple configuration of markers for digitizing gross human figure motion might require only
14 markers (3 per limb and 2 for positioning the head). For more accurate recordings of human motion,
markers need to be added to the elbows, knees, chest, hands, toes, ankles, and spine (see
Figure 6.5
).
Menache [
6
]
suggests an addition of three per foot for some applications. Also refer back to
Figure 6.1
,
which shows a sample marker set on mocap talent.
6.4.2
Multiple cameras
As the number of markers increases and the complexity of the motion becomes more involved, there is
greater chance for marker occlusion. To reconstruct the three-dimensional position of a marker, the
system must detect and identify the marker in at least two images. As a result, a typical system
may have eight cameras simultaneously taking images. These sequences need to be synchronized either
Search WWH ::
Custom Search