Neurocomputing in Space - High Dimensional Neurocomputing: Growth, Appraisal and Applications - page 123

In early methods for 3D face recognition curvatures and surface features, kept in a
cylindrical coordinate system, were used. Moreno et al. found that curvature and line
features perform better than area features [ 15 ]. Point cloud is the most primitive 3D
representation for faces and Housdroff distance has been used for matching the point
clouds in [ 16 ]. The base mesh is also used for alignment in [ 17 ], where features are
extracted from around landmark points and nearest neighbor, and after that PCA is
used for recognition. In [ 8 ] the analysis-by-synthesis approach that uses morphable
model is detailed. The idea is to synthesize a pose and illumination corrected image
pair for recognition. Depth maps have been used in 3D imaging applications [ 18 ].
The depth map construction consists of selecting a view point and smoothing the
sampled depth values. Most of the work that uses 3D face data use a combination
of representations. The enriched variety of features, when combined with classifiers
with different statistical properties, produce more accurate and robust performance.
As a result of fast development in 3D imaging technology, there is strong need to
address them using high-dimensional neural networks.

6.4.1 Normalization

3D linear transformation has been considered for normalization of 3D faces. Its
purpose is to align each face on a same scale and at same orientation. In order to
make the standard alignment for facial features, the origin is translated to the nose
tip. It is assumed that the scanned 3D face data are of front part of face and almost
straight (variation 40 ⓦ -50 ⓦ allowed) and accordingly it is translated. Logically, nose
tip is the peak of a face, and hence can have maximumZ-coordinate value. Therefore,
the Z coordinate ( Z max ) on 3D face data is searched, and their corresponding X

, Y

coordinates, say Z max · X and Z max · Y are determined. Now, origin is translated to

nose tip as follows:

X Y Z

= X − Z max · X = Y − Z max · Y = Z − Z max

Thus, we obtain a face data with the origin on the nose tip. Now face is rotated
about Y and X axis. For Y axis rotation, replacement in coordinates can be done as
follows:

⊧
⊨

⊫
⊬

cos 0

0100
sin

ʸ 0 sin ʸ

z =

z × cos ʸ − x × sin ʸ

x =

z × sin ʸ + x × cos ʸ R y (ʸ) =

0
0001

ʸ 0 cos ʸ

⊩ ⊭

y =

y

tan 1 x / z )

where, is an angle to which vector is rotated about Y axis. Similarly,

the face is rotated about the X axis. Once the nose tip is identified, one can search
in the y direction to determine the nose dip. Both nose tip and nose dip must lie on
the same line. The scaling of all the faces has been done by taking distance between

ʸ = (