Game Development Reference
In-Depth Information
This technique is known as the pseudo-inverse solution to the linear least-
squares problem. Of course, it should be noted that this technique reduces the
precision of the estimated coefficients with a factor of two because of the
squared condition data. This flaw can be avoided by employing so-called Least
Squares with Orthogonal Polynomials or Weighted Least Squares .
In fact, the requirement that two pixels that correspond to the same 3-D point are
needed to reconstruct the 3-D coordinate of that point is consistent with our
intuitive observation on the imaging process discussed in the first section, as two
lines are needed to uniquely determine a 3-D point.
The above process is applied to each pair of corresponding points in every frame.
Thus, a sequence of 3-D coordinates can finally be obtained.
The projection and 3-D reconstruction process on the 3-D face model we used
is described intuitively in Figure 3.
3-D face model examples
Since all tracked points are important facial control points, the reconstructed
sequence of 3-D coordinates of those points reflects more or less facial actions.
Thus, this sequence can be used as a coarse 3-D face model. If more control
points are selected, a finer 3-D model can be obtained.
Based on the reconstructed model, FAPs can be calculated. To show the
accuracy of the face model qualitatively, a VRML file is generated automati-
cally. Figure 4 shows three example frames of such a VRML file.
Figure 4. Three example frames of the reconstructed 3-D face model. Blue
points are control points that were reconstructed.
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