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(a) (b)
Fig. 10.9. Relative error measure for face localization, as suggested in [111]: (a) manually
labeled eye positions (C l ,C r ) , estimated eye positions (
e
e
C r ) , and eye distances (d l ,d r ) ;
(b) relative error d eye from the right eye (shown left), a circle with radius d eye = 0.25 is
drawn around the eye.
C l ,
After transforming these eye positions into the original coordinate system, a
scale-independent relative error measure was computed, as suggested in [111]:
e
= k
C l C l k ,
d l
e
= k
C r C r k ,
d r
=
max( d l ,d r ) / k C l C r k .
(10.2)
d eye
e
e
The distances of the estimated eye positions
C r to the given coordinates
C l and C r are denoted by d l and d r , respectively. A small relative distance of
d eye < 0 . 25 is considered a successful localization since d eye = 0 . 25 corresponds
approximately to the half-width of an eye, as illustrated in Figure 10.9.
The estimated eye coordinates, the given coordinates and the relative eye dis-
tances are shown in Figure 10.10 for the two test examples from Fig. 10.8. One can
verify that for these examples the estimated eye positions are at least as exact as the
given ones.
To test how the network is able to localize the other examples from the dataset,
the relative distance d eye was computed for all images. Figure 10.11 shows the
network's localization performance for the training set (TRN) and the test set (TST)
C l and
(a) (b)
d eye = 0.0211 d eye = 0.0107
Fig. 10.10. Face localization output for the test examples from Fig. 10.8: + mark the given
eye coordinates; × are drawn at the estimated eye coordinates.
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