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

where Map(x, y) is either the eye or the mouth map; the parameter α is equal to
0.5 for the initial threshold value, and is equal to 0.8 for the stopping threshold.
The use of upper bounds on the number of eye and mouth candidates can prevent
the algorithm from spending too much time in searching for facial features. In our
implementation, the maximum number of eye candidates, N eye , is 8 and the maximum
number of mouth candidates, N mth , is 5.
3.3.4 Face Boundary Map
Based on the locations of eyes/mouth candidates, our algorithm first verifies whether
the average orientation of luma gradients around each eye matches the interocular
direction, and then constructs a face boundary map from the luma. Finally, it utilizes
the Hough transform to extract the best-fitting ellipse. The fitted ellipse is used for
computing the eye-mouth triangle weight. Figure 3.12 shows the boundary map that
is constructed from both the magnitude and the orientation components of the luma
gradient within the regions that have positive orientations of the gradient orientations
(i.e., have counterclock-wise gradient orientations). We have modified Canny edge
detection [170] algorithm to compute the gradient of the luma as follows. The gradient
of a luma subimage, S(x, y), which is slightly larger than the face candidate in size
is estimated by
∇S(x, y) = (G x , G y ) = (D σ (x) ⊛ S(x, y), D σ (y) ⊛ S(x, y)), (3.13)
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