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

(shown in Fig. 4.2(c)) are followed by displacement (of model vertices) propagation,
in order to blend features in the face model.
Displacement propagation inside a triangular mesh mimics the transmission of
message packets in computer networks. Let N i be the number of vertices that are
connected to a vertex V i , J i be the set of all the indices of vertices that are connected
to the vertex V i , w i be the sum of weights (each of which is the Euclidean distance
between two vertices) on all the vertices that are connected to the vertex V i , and d ij
be the Euclidean distance between the vertex V i and a vertex V j . Let ∆V j be the
displacement of vertex V j , and α be the decay factor, which can be determined by
the face size and the size of the active facial feature in each coordinate. Eq. (4.1)
computes the contribution of vertex V j to the displacement of vertex V i .
∆V ij =
{
w ∆Vj ·
i −d ij
w i·(N i −1) · e−αd ij , N i > 1, w i = ∑ j∈J i
d ij
∆V j · e −αd ij , N i = 1, j ∈ J i .
(4.1)
In other words, ∆V ij is computed as the product of the displacement, the weight, and
V j 2
’
Vj 2
Vj 2
Vi j 1
d i j 2
Vi j 2
d i j1
Vj 1
Vj 1 Vj’
1
: Vertex
: New Location
: Triangle Edge
Vi
Figure 4.7.
Displacement propagation.
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