3D Morphable Models for Face Surface Analysis and Recognition - 3D Face Modeling, Analysis and Recognition - page 135

Figure 4.9 Redundancy estimation. From left to right, the face scan, S single , the residual errors of S single ,
S mult , the residual errors of S mult , and the color map for the point-to-point distances (in mm). Copyright
C

2009, IEEE

Therefore, we estimate the redundancy of encountered example data. First, the morphable
face model is fitted as a single face component to the 3D scan data, which we refer to as S single .
Second, we fit the morphable face model using multiple face components with the improved
correspondence estimation described earlier, S mult . After the model-fitting process, a residual
error between the vertices of the model fit and the scan data remains. The difference of the
two residual errors of S single and S mult , can be used to estimate the redundancy of the new face
scan. In case the residual error of S single is significantly larger than that of S mult , then the face
scan is most likely not contained in the current morphable face model, and we should add S mult
to the model.
To compute the residual error of these model fits we use the RMS distance of closest point
pairs,

n

1
n

d rms ( S , scan) = e min ( p i , scan) 2 (4.3)

i = 1

using all n vertices of S single and S mult . Closest point pairs ( p , p ) for which p belongs to the
boundary (including holes) of the face scan, are not used in the distance measure. Figure 4.9
shows for one face scan, the two model fits and their residual error maps. For this example the
RMS error for S single is 0.89 mm and for S mult 0.68 mm.

4.4.2 Results
We fit the morphable face model to 3D scan data from the UND (Chang et al., 2005), GAVAB
(Moreno and Sanchez, 2004), BU-3DFE (Yin et al., 2006), Dutch CAESAR-survey (2008),
and our local data set. From all except the UND set, we randomly select four scans, giving
a first test set of 16 scans. These scans vary in pose, facial expression, resolution, accuracy,
and coverage. This set of 16 face scans is used to test our bootstrapping algorithm. To test
the automatic redundancy check, we use a subset of 277 face scans from the UND data set,
namely the first scan of each new subject. To acquire the 3D face data from the scans, we
apply the face pose normalization and face segmentation methods described in Section 4.2).