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1998) on standard face databases. Model based ap-
proaches for human faces obtained popularity in last
decade due to their compact and detailed representa-
tion (Blanz and Vetter, 2003)(Abate et al., 2007)(Park
et al., 2004)(Cootes et al., 1998). In the literature of
face modeling, some useful face models are point dis-
tribution models (PDM), 3D morphable models, pho-
torealistic models, deformable models and wireframe
models (Abate et al., 2007).
The remaining part of the paper is divided in three
main section. Section 2 discusses face modeling in
detail. In section 3, we thoroughly provide experi-
ments performed using our approach as compared to
conventional AAM. Finally section 4 gives conclu-
sions of our work with future extension of this ap-
proach.
2 HUMAN FACE MODELING
We study structural and textural parameterization of
the face model separately in this section.
2.1 Structural Modeling and Model
Fitting
Our proposed algorithm is initialized by applying a
face detector in the given image. We use Viola and
Jones face detector (Viola and Jones, 2004). If a face
is found then the system proceeds towards face model
fitting. Structural features are obtained after fitting
the model to the face image. For model fitting, lo-
cal objective functions are calculated using haar-like
features. An objective function is a cost function
which is given by the equation 1. A fitting algorithm
searches for the optimal parameters which minimizes
the value of the objective function. For a given image
I, if E(I, c
i
(p)) represents the magnitude of the edge
at point c
i
(p), where p represents set of parameters
describing the model, then objective function is given
by:
f (I, p) =
1
n
n
∑
i=1
f
i
(I, c
i
(p)) =
1
n
n
∑
i=1
(1 − E(I, c
i
(p)))
(1)
Where n = 1, . . . , 113 is the number of vertices c
i
describing the face model. This approach is less prone
to errors because of better quality of annotated images
which are provided to the system for training. Further,
this approach is less laborious because the objective
function design is replaced with automated learning.
For details we refer to (Wimmer et al., 2008).
The geometry of the model is controlled by a set
of action units and animation units. Any shape s can
be written as a sum of mean shape s and a set of action
units and shape units.
s(α, σ) = s + φ
a
α + φ
s
σ (2)
Where φ
a
is the matrix of action unit vectors and
φ
s
is the matrix of shape vectors. Whereas α denotes
action units parameters and σ denotes shape param-
eters (Li and Jain, 2005). Model deformation gov-
erns under facial action coding systems (FACS) prin-
ciples (Ekman and Friesen, 1978). The scaling, rota-
tion and translation of the model is described by
s(α, σ, π) = mRs(α, σ) +t (3)
Where R and t are rotation and translation matri-
ces respectively, m is the scaling factor and π contains
six pose parameters plus a scaling factor. By chang-
ing the model parameters, it is possible to generate
some global rotations and translations. We extract 85
parameters to control the structural deformation.
2.2 View Invariant Texture Extraction
The robustness of textural parameters depend upon
the quality of input texture image. We consider per-
spective transformation because affine warping of the
rendered triangle is not invariant to 3D rigid transfor-
mations. Affine warping works reasonably well if the
triangle is not tilted with respect to the camera coor-
dinate frame. However, most of the triangles on the
edges are tilted and hence texture is heavily distorted
in these triangles. In order to solve this problem we
first apply perspective transformation. Since, the 3D
position of each triangle vertex as well as the cam-
era parameters are known, we determine the homo-
geneous mapping between the image plane and the
texture coordinates by using homography H.
H = K.
r
1
r
2
−R.t
(4)
Where K, R and t denotes the camera matrix, rota-
tion matrix and translation vector respectively, r
1
and
r
2
are the components of rotation matrix. It maps a
2D point of the texture image to the corresponding
2D point of the rendered image of the triangle. A pro-
jection q of a general 3D point p in homogeneous co-
ordinates is,
q = K.
R −R.t
. p (5)
Each 3D homogeneous point lying on a plane with
z = 0, i.e. p = (x y 0 1) leads to above equation. If p
0
being the homogeneous 2D point in texture coordi-
nates then,
ON THE EFFECT OF PERSPECTIVE DISTORTIONS IN FACE RECOGNITION
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