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

(a) (b) (c)
Figure 5.1. Semantic face graph is shown in a frontal view, whose nodes are (a)
indicated by text; (b) depicted by polynomial curves; (c) filled with different shades.
The edges of the semantic graph are implicitly stored in a 3D generic face model and
are hidden here.
regions. The vertices at the top level are labelled with facial components such as the
face outline, eyebrows, eyes, nose, and mouth (see Fig. 5.2). Let T 0 denote the set of
all semantic facial components, which are nodes of the generic semantic graph, G 0 .
That is T 0 = {{left eyebrow}, {right eyebrows}, {left eye},..., {hair boundary}}. Let
T be a subset of T 0 , that is T ⊂ 2 T 0
. Let M be the number of facial components
in T . For example, T can be specified as {{left eye}, {right eye}}, {mouth}}, where
M is 3. Let the semantic graph projected on a 2D image, represented by the set
T, be G. The coordinates of component boundary of G can be represented by a
pair of sequences x i (n) and y i (n), where n = 0, 1, . . . , N i − 1 and i = 1, . . . , M, for
component i with N i vertices. The 1D Fourier transform, a i (k), of the complex signal
u i (n) = x i (n) + jy i (n) (where j = √ −1) is computed by
a i (k) = F{u i (n)} =
N∑
i −1
n=0
113
u i (n) · e −j2πkn/N i
, (5.1)