Graphics Reference
In-Depth Information
4.5 Face Matching
Our model-fitting algorithm determines a set of model coefficients that morphs the mean face
to a clean model instance that resembles the 3D face scan. On the basis of this model instance,
we use three different methods to perform face matching. Two methods use the newly created
3D geometry as input, namely the landmarks-based and contour-based methods. The third
method uses the model coefficients as a feature vector to describe the generated face instance.
4.5.1 Comparison
Landmarks.
All vertices of two different instances of the morphable model are assumed to
have a one-to-one correspondence. Assuming that facial landmarks such as the tip of the nose
and corners of the eyes are morphed toward the correct position in the scan data, we can use
them to match two 3D faces. So, we assigned 15 anthropometric landmarks to the mean face
and obtain their new locations by fitting the model to the scan data. To match two faces
A
and
B
we use the sets of
c
=
15 corresponding landmark locations:
c
d
corr
(
A
,
B
)
=
d
p
(
a
i
,
b
i
)
,
(4.4)
i
=
1
where distance
d
p
between two correspondences
a
i
and
b
i
is the squared difference in Euclidean
distance
e
to the nose tip landmark
p
nt
p
nt
))
2
d
p
(
a
i
,
b
i
)
=
(
e
(
a
i
,
p
nt
)
−
e
(
b
i
,
.
(4.5)
Contour curves.
Another approach is to fit the model to scans
A
and
B
and use the new
clean geometry as input for a more complex 3D face recognition method. To perform 3D
face recognition, we extract from each fitted face instance three 3D facial contour curves, and
match only these curves to find similar faces, see ter Haar and Veltkamp (2009).
Model coefficients.
The iterative model-fitting process determines an optimal weight
w
i
for
each of the
m
eigenvectors. These weights, or model coefficients, multiplied by
describe a
path along the linearly independent eigenvectors through the
m
dimensional face space. For
two similar scans one can assume these paths are alike, which means that the set of
m
model
coefficients can be used as a feature vector for face matching.
In the case of multiple components, each component has its own set of
m
model coefficients.
Blanz et al. (2007) simply concatenated sets of model coefficients into a single coefficient
vector. Here, we also concatenate the coefficient vectors of multiple components. To determine
the similarity of faces with these coefficient vectors, we use four distance measures, namely
the
L
1
and
L
2
distance before and after normalizing the vector's length. Amberg et al. (2008)
assume that caricatures of an identity lie on a vector from the origin to any identity and use
the angle between two coefficient vectors as a distance measure. Normalizing the length of
the coefficient vectors and computing the
L
2
distance has this same effect and results in the
same ranking of retrieved faces.
σ
