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It is essential to fit the 3D range data of the mean face so that it models a
face found in a 2D image. Assume we have a 2D image with the coordinates of
the eyes, the nose and the mouth perfectly pinpointed, as in
Figure . Denote the 2D positions of the eyes, nose and mouth
as
.
The parameters of the 3D
model
must be
tuned to align its 3D anchor points
so that their 2D projections
coincide with the set of 2D anchor points
.
Note that the alignment to the
destination points
involves
minimizing 8 distances since each of these points is a 2D position. We observe
that Equation , which only has 7 degrees of freedom, is
overspecified. Thus, there is usually no exact solution to the fitting
problem, only approximations.
Figure 4.9:
Image of U.S. President Ford with eyes, nose and mouth located

Tony Jebara
20000623