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

where D σ (x) is the derivative of the Gaussian with zero mean and variance σ 2 , and
⊛ is the convolution operator. Unlike the Canny edge detector, our edge detection
requires only a single standard deviation σ (a spread factor) for the Gaussian that is
estimated from the size of the eye-mouth triangle.
( ) −ws
2 1/2
σ =
; ws = Max(dist io , dist em ), (3.14)
8 ln(wh)
where ws is the window size for a Gaussian, which is the maximum value of the
interocular distance (dist io ) and the distance between the interocular midpoint and
the mouth (dist em ); wh = 0.1 is the desired value of the Gaussian distribution at the
border of the window. In Fig. 3.12, the magnitudes and orientations of all gradients
have been squared and scaled between 0 and 255. Fig. 3.12 shows that the gradient
orientation provides more information to detect face boundaries than the gradient
magnitude. So, an edge detection algorithm is applied to the gradient orientation
and the resulting edge map is thresholded to obtain a mask for computing the face
boundary. The gradient magnitude and the magnitude of the gradient orientation
are masked, added, and scaled into the interval [0, 1] to construct the face boundary
map. The center of a face, indicated as a white rectangle in the face boundary map
in Fig. 3.12, is estimated from the first-order moment of the face boundary map.
The Hough transform is used to fit an elliptical shape to the face boundary map.
An ellipse in a plane has five parameters: an orientation angle, two coordinates of the
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