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

(f ⊕ g σ )(x, y) = Max{f(x − c, y − r) + g(c, r)};
(f ⊖ g σ )(x, y) = Min{f(x − c, y − r) + g(c, r)};
(x − c, y − r) ∈ F, (c, r) ∈ G ,
(3.3)
(x − c, y − r) ∈ F, (c, r) ∈ G ,
(3.4)
g σ (x, y) =
{
( ∣∣1
|σ| · ∣ )
− (R(x, y)/σ)
2 1/2 − 1 ; R ≤ |σ|,
−∞;
R > |σ|,
(3.5)
R(x, y) = √ x 2 + y 2 , (3.6)
where σ is a scale parameter, which will be described later in Eq. (3.11). An example
of a hemispheric structuring element is shown in Fig. 3.10. The construction of the
Figure 3.10. An example of a hemispheric structuring element for grayscale morphological
dilation and erosion with σ = 1.
eye map from the luma is illustrated in Fig. 3.9(b). Note that before performing the
grayscale dilation and erosion operations, we fill the background of the face mask
with the mean value of the luma in the face mask (skin regions) in order to smooth
the noisy boundary of detected skin areas.
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