Game Development Reference
In-Depth Information
of both cameras. The person produces various kinds of expressions, such
as opening of the mouth or squinting of the eyes. Two stereo sequences are
then recorded.
3)
Marker detection and tracking
: Each sequence is processed by some
marker detection algorithm (ref. Figure 2) and the markers (currently 19
per frame) are tracked throughout the sequence. Thus, two sequences of
19 moving points are generated.
4)
3-D reconstruction
: At this stage, a pair of stereo sequences of 19 moving
points are available. As all parameters of the two utilized cameras are
known, a sequence of 3-D coordinates of the 19 points can be reconstructed
that reflect the motion of the 19 points in 3-D space.
5)
3-D face model analysis
: From the reconstructed 3-D sequence, FAPs
can be calculated to analyze their correspondence relation with the human
facial expression.
3-D reconstruction
With the reconstruction-distortion model, the 2-D coordinates of all tracked
points can be easily converted to the undistorted coordinates by equation 12
immediately after step 3. On the other hand, if the imaging-distortion model is
employed in the calibration software, a distortion correction (Lei & Hendriks,
2002) by simple backward mapping can be applied to all obtained images
immediately after step 2. So 2-D distortion-free coordinates of all facial control
points are available at step 4. Between them and their corresponding 3-D
coordinates exists a linear relation that can be expressed by equation 17.
In terms of matrix notation, equations 19 and 20 can be rewritten as:
x
w
1
4
3
4
im
1
1
3
1
im
1
2
3
2
im
1
3
3
3
im
p
−
p
x
−
p
+
p
x
−
p
+
p
x
−
p
+
p
x
=
y
w
.
(50)
2
4
3
4
im
2
1
3
1
im
2
2
3
2
im
2
3
3
3
im
p
−
p
y
−
p
+
p
y
−
p
+
p
y
−
p
+
p
y
z
w
It is easy to see from equation 50 that no unique solution for
x
w
can be determined
with one known
x
im
and the calculated
i
p
(
i
= 1...3;
j
= 1...4). That is why two
x
im
that correspond to the same
x
w
are needed to recover it uniquely. Suppose
these two
x
im
are denoted as
im
r
im
l
x
x
and
respectively, then:
Search WWH ::
Custom Search