Graphics Reference
In-Depth Information
specific discriminative information and to appear under neutral expression. Before fitting,
the AFM is registered to the 3D facial scan using ICP. Then, external forces are iteratively
applied on the AFM to displace its vertices towards the 3D facial surface. The external forces
are countered by forces proportional to the displacement (elastic force), the acceleration of
displacement (inertial force) and the speed of displacement (damping force). The fitting of
AFM intuitively converges when the elastic forces are in balance with the applied external
forces. It is the elastic fitting that provides the fitted AFM with the discriminative information
but also include some of the expression deformations. Since the AFM looks like a neutral face
and the expression deformations can vary more the discriminative information, the fitting is
likely to mitigate the effects of expression variations.
Exercises
1.
For
a
cropped
3D
facial
surface
under
a
near
fontal
pose,
the
princi-
25219]
,
p
1
=
44172]
,
pal
directions
are
p
1
=
[
−
0
.
30
.
92 0
.
[0
.
88159 0
.
16639 0
.
86098]
[0
35).
A.
Find the rigid transformation that pose-corrects the facial surface so its principal direc-
tions become
p
1
=
.
36442 0
.
35484
−
0
.
and the tip of the nose is located at (10
,
−
15
,
−
[0 1 0]
,
p
2
=
[1 0 0]
and
p
3
=
1]
and the tip of the
[0 0
−
0).
B.
Explain how quaternions can be used to achieve the same transformation in part A.
nose be at the origin of the reference frame, (0
,
0
,
2.
For a facial range image and using the method of the kernels of Gaussian derivatives to find
surface derivatives:
A.
Write a MatLab function that computes the first and second fundamental forms at each
range pixel and on the basis of the fundamental forms computes the Gaussian and the
mean curvatures.
B.
For different
values of the Gaussian function and different sizes of the filtering
kernel, compare estimates of the Gaussian and the mean curvatures of the same image
and suggest appropriate
σ
σ
value and kernel size.
3.
From a publicly available data set of 3D facial scans, randomly pick a set of neutral facial
scans and a set of non-neutral scans for use as probes. As a gallery set, pick one neutral
scan for every individual in either of the two probe sets. Then, compute and compare the
identification rates of the following:
A.
When using PCA for the identification of the scans in the neutral probe set.
B.
When using PCA for the identification of the scans in the non-neutral facial scans.
C.
Crop off the lower part of the facial scans, just below the nose, in both the gallery and
probe sets. Then, use PCA for the identification of the scans in the neutral probe set.
D.
When using PCA for the identification of the cropped non-neutral probe set.
E.
When using ICP for the identification of the scans in the neutral probe set.
F.
When using ICP for the identification of the scans in the non-neutral facial scans.
G.
When using ICP for the identification of the cropped neutral probe set.
H.
When using ICP for the identification of the cropped non-neutral probe set.
4.
Select 10 facial scans of the same subject and under different facial expressions from a
publicly available data set and estimate the repeatability rate of key-point detection of the
principal direction approach.
