Face Detection and Modeling for Recognition - Biometrics Research ...

f(u j , v j ) =
θ(u j , v j ) =
S∑
|∇G σs (u j , v j ) ⊛ Y (u j , v j )| (5.5)
s=0
S∑
arg (∇G σs (u j , v j ) ⊛ Y (u j , v j )) , (5.6)
s=0
where Y is the luma of the color image I, and G σs
is the Gaussian function with zero
mean and standard deviation σ s . The largest standard deviation σ S is limited by the
distance between eyes and eyebrows where S = 4, and ∇ and ⊛ are the gradient and
convolution operators. The gradient magnitude, gradient orientation, eye map [175]
and coarse alignment results for the subject in Fig. 5.4(a) are shown in Fig. 5.5.
The eye map is an average of a symmetry map [177] and an eye energy map (will be
explained in Section 5.3.1). Furthermore, we construct a shadow map of a face image
in order to locate eyebrow, nostril, and mouth lines, based on the average value of
luminance intensity on a facial skin region (i.e., rectangles shown in Figs. 5.6(a) and
5.6(c)). These feature lines, shown as dark lines in Figs. 5.7(c), are used to adjust
corresponding facial components of a semantic graph. Fig. 5.7 shows five examples
of coarse alignment.
5.3 Fine Alignment of Semantic Face Graph via
Interacting Snakes
Fine alignment employs active contours to locally refine facial components of a semantic
face graph that is drawn from a 3D generic face model. The 2D projection of
118