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

In the Baysian framework, given an image I, minimizing the energy of interacting
snakes is equivalent to maximizing a posteriori probability p(V |I) of interacting snakes
V (s) with a 0/1 loss function:
p(V |I) =
p(I|V ) · p(V )
, (5.8)
p(I)
where p(I|V ) ∼ e −E obersvation , p(V ) ∼ e
−E prior
, p(V ) is the prior probability of snakes’
structure and p(I|V ) is the conditional probability of the image potential of interacting
snakes. From calculus of variations, we know that interacting snakes which
minimize the energy function in Eq. (5.7) must satisfy the following Euler-Lagrange
equation:
⎡
⎤
N∑
⎣αv i ′′ (s) − βv (4)
i (s) −∇E
} {{ } repulsion (v i (s)) −∇E
} {{ } attraction (v i (s)) ⎦ = 0,
} {{ }
i=1
Internal Force Repulsion Force Attraction Force
(5.9)
where α and β are coefficients for adjusting the second- and the fourth- order derivatives
of a contour, respectively.
Repulsion force field is constructed based on the
gradients of distance map among the interacting snakes as follows:
⎛⎡
⎤ ⎞
⎜
N⋃
−∇E repulsion (v i (s)) = ∇ ⎝⎣EDT ( v j (s)) ⎦2
⎟ ⎠ , (5.10)
j=1,j≠i
where EDT is a signed Euclidean Distance Transform [178]. Figure 5.9 show the
repulsion force fields for the hair outline and the face outline. The use of the repulsion
force can prevent different active contours from converging to the same locations of
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