3D Morphable Models for Face Surface Analysis and Recognition - 3D Face Modeling, Analysis and Recognition - page 123

Figure 4.2 Face morphing along eigenvectors starting from the mean face (center column). Different
weights for the principal eigenvectors (e.g., i = 1 , 2) changes the global face shape. For latter eigenvectors
the shape changes locally (e.g., i = 50)

is modified and evaluated. Only in the first and last iteration are all vertices evaluated. Notice
that this also reduces the number of vertices to fit and therefore the computation costs.
The fitting process starts with the mean face and morphs in place toward the scan data, which
means that the scan data should be well aligned to the mean face. To do so, the segmented
and pose normalized face is placed with its center of mass on the center of mass of the mean
face, and finely aligned using the iterative closest point (ICP) algorithm (Besl and McKay,
1992). The ICP algorithm iteratively minimizes the RMS distance between vertices. To further
improve the effectiveness of the fitting process, our approach is applied in a coarse-fitting and
a fine-fitting step, see the next subsections.

4.3.3 Coarse Fitting
The more the face scan differs from the mean face S , the less reliable the initial alignment of
the scan data to the mean face is. Therefore, the mean face is coarsely fitted to the scan data
by adjusting the weights of the first 10 principal eigenvectors ( m max = 10) in a single iteration

( k max = [-1.35,-1.05,...,1.05,1.35], see Algorithmmodel

fitting( S , scan). Fitting the model by optimizing the first 10 eigenvectors results in the face
instance S coarse , with global face properties similar to those of the scan data. After that, the
alignment of the scan to S coarse is further improved with the ICP algorithm.

1) with 10 different values for w new =

4.3.4 Fine Fitting
Starting with the improved alignment, we again fit the model to the scan data. This time the
model-fitting algorithm is applied using all eigenvectors ( m max = m ) and multiple iterations

9). In the first iteration of Algorithm model fitting ( S , scan), 10 new weight values
w new are tried for each eigenvector, to cover a large range of facial variety. The best w new
for every sequential eigenvector is used to morph the instance closer to the face scan. In the
following k max -1 iterations only four new weight values w new are tried around w i with a range
w range equal to w incr of the previous iteration. By iteratively searching for a better w i in a

( k max =