Graphics Reference
In-Depth Information
this is not the case with facial surfaces; 3D face recognition approaches based on EGI often
assume that the 3D face has (to an extent) a convex shape. Other disadvantages of EGIs include
the possible information loss during mapping (the actual positions of the 3D points) and its
susceptibility to noise due to the reliance on normals and curvatures.
Curvature-like method:
The method proposed by Al-osaimi et al. (2008) extracts 11 scalar
quantities pertaining to local attributes of the facial surface at each point, each called a scalar
filed, and 3 other fields pertaining to the global structure of the face. Some of these local fields
are (conceptually) similar, to an extent, to surface curvatures but are in contrast less affected
by noise. Discriminative and transformation invariant features are extracted by constructing a
2D histogram from each combination of a local and a global field. The histograms are indexed
in one direction by the local field and in the other direction by the global field. The bins of each
histogram store the area of the surface with the local and the global field values corresponding
to its indices. The histograms are vectorized and concatenated. PCA is then used to compress
these concatenated features.
The local fields are extracted at each vertex from a 3D facial mesh from the triangles
t
i
within a small and a large neighborhood, denoted by
N
2
, respectively. Six local
fields are defined as the thee eigenvalues of the covariance matrix in Equation 2.56 for each
neighborhood, where
r
i
is the vector from the point to the centroid on the
i
th triangle,
a
i
is its
area, and
A
is the total area of the neighborhood.
N
1
and
a
i
r
i
r
i
A
r
i
.
(2.56)
a
i
∈
N
Three other local fields are defined as the singular values of the matrix in Equation 2.57, where
n
and
n
are the normal of the
i
th triangle and the mean normal, respectively. The fields that
involve the normals were only extracted from the larger neighborhood to reduce the effect of
noise because they are more sensitive to the noise than to the
r
vectors.
n
)
r
i
a
i
(
n
i
−
.
(2.57)
A
r
i
a
i
∈
N
2
Two other local fields are defined as (one from each neighborhood)
r
i
a
i
n
i
·
.
(2.58)
A
r
i
a
i
∈
N
2
The global fields are the dot products between the vectors from the global centroid
C
of the
cropped facial surface to each vertex
c
i
and each of the three principal directions of the face.
The principal directions of the face are the eigenvalues the matrix in Equation 2.59.
a
i
(
c
i
−
C
)
.
C
)(
c
i
−
(2.59)
