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possible, because we enhanced the model with the facial variety of 16 faces at once. We expect
that the residual errors of
S
single
can be lowered further, by iterating the process of (1) fitting
the enhanced model using multiple components, (2) replacing the 16 face instances
S
mult
, and
(3) building a new PCA model. In fact, we tried it for the face scan in Figure 4.9 and lowered
its RMS distance for
S
mult
(0.68 mm) and
S
single
(0.69 mm) to 0.64 mm for
S
mult
. So, iteratively
replacing the 16 instances of the enhanced model with their improved instances
S
mult
, will
probably help to some extend. Note that the residual errors are lowest for our local set, which
contains the highest resolution scans, and the highest errors for the low resolution CAESAR
faces. This is as a result of the RMS distance that measures point-to-point distances. Because
we are interested in the difference between residual errors, this works fine, otherwise, one
could use a surface mesh comparison tool instead. In previous experiments, we used
metro
Cignoni et al. (1998) for that.
In Figure 4.10, we show some of the resulting model fits and their distance maps acquired
with our bootstrapping algorithm. In this figure, we show the two faces per data set that achieved
the smallest and largest difference in residual errors in the same order as in Table 4.3. Visual
inspections of the fitted models shows an improved single component fit of the enhanced model
to the scan data (
S
single
), compared with the single component fit using the initial morphable
model (
S
single
). This can be seen in the residual error maps as well. That the bootstrapping
algorithm successfully incorporated the 16 face scans in the morphable face model, can be seen
by face instances
S
mult
and
S
single
, which are very similar. The initial morphable face model
consisted of neutral expression scans only. Nevertheless, the use of multiple components
allows for correspondence estimation among some expression data as well.
Redundancy Estimation
To distinguish between new and redundant face data, we computed the residual errors for face
instances
S
single
and
S
mult
using the RMS distance measure. In Table 4.3, we reported the RMS
errors for our set of 16 faces. These differences in RMS error for
S
single
−
S
mult
vary between
0.05 and 0.45. The maximum difference of 0.45 was achieved for the sad looking person on
row four in Figure 4.10. With the use of a threshold
t
for the difference in RMS error, we
decide whether a face is redundant or new. On the basis of the visual inspection of the faces in
Figure 4.10, we decided to select
t
=
.
17 for our experiments. In case the RMS difference is
higher than
t
, we consider a face to be new and otherwise as redundant. With this threshold,
we classify only the faces in row two, four, and five as being new.
We applied our bootstrapping algorithm to the 277 UND scans, and let our algorithm
automatically select potential faces to add to the model, without actually adding them. This
way we can see which face scans (persons) are new to the model. For these persons, we
may assume a difficulty in identifying them, because a coefficient-based recognition system
may confuse that person with a different person that has those coefficients. Out of the 277
UND scans, 35 scans were found as being new to the system, that is, having a decrease in
RMS error of
S
single
−
0
S
mult
higher than threshold
t
. Some of these produced fits are shown in
Figure 4.11. Most of the selected faces have indeed new face features and should be added to
the morphable face model. However, some of the faces that are covered by facial hair produce
less reliable fits. To improve on these fits, one could apply a skin detection algorithm and
remove the hair beforehand.
