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

[ (
∂Φ
∂t =∇Φ µ 1 div(g ∇Φ
)
|∇Φ| ) − µ 2r − αg
− ∑ |I − c i | 2 + ∑ ]
|I − c j | 2 , (5.16)
i
j
g 0
g =(1 −
max(g 0 ) )2 , g 0 = log(1 + |∇I| 2 ) 2 (5.17)
{
1/dt dt ≠ 0
r =
(5.18)
MAXDIST dt = 0
where µ 1 is a constant, µ 2 and α are constants in the interval between 0 and 1, I
is the image color component, c i and c j are the average color components of facial
component i over region Ω + i
and component j over Ω − j , respectively, r is the component
repulsion, dt is the absolute Euclidean distance map of the face graph, and
MAXDIST is the maximum distance in the image. We further preserve facial topology
using topological numbers and the narrow band implementation of level-set functions
[183]. The preliminary results are shown in Fig. 5.13 with evolution details and in
Fig. 5.14 without the evolution details.
The facial distinctiveness of individuals can be seen from the changes among the
generic, the fine fitted, and fine deformed face templates, shown in Figs. 5.13(a),
5.13(d), and 5.13(e).
Comparing the two approaches for deforming interacting
snakes, we believe that the first approach, parametric active contours, is better suited
to the deformation of semantic face graphs.
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