Face Localization - Hierarchical Neural Networks for Image Interpretation - page 210

0.5 2

TST
TRN

TST
TRN

0.45

0.4

1.5

0.35

0.3

0.25 1

0.2

0.15

0.5

0.1

0.05

0 0

0 2 4 6 8 10 12 0 2 4 6 8 10 12

(a) (b)

iteration iteration

Fig. 10.15. Performance over time: (a) average distance d eye ; (b) sum of squared changes in
the network's output.

in the second example is almost outside the image, the preprocessing has destroyed
the upper part of the head, including the eyes. This leads to localization failure. The
third example is difficult as well since the face appears relatively small and in an
unusual posture. In the rightmost example, the network is probably distracted by the
reflections on the glasses and produces a blob only for one of the eyes. The failure
of the network to localize these faces correctly is not problematic since they can be
rejected easily.
Figure 10.15 illustrates the network's performance over time. The average rel-
ative distance d eye drops rapidly within the first five iterations and stays low af-
terwards. The average changes in the network's output are large during the first
iterations and decrease to almost zero even when updated longer than the ten steps
it has been trained for. Thus, the network shows the desired behavior of iterative
refinement and produces stable outputs.
To investigate if the network is able to track a moving input, the test example
from Figure 10.3 was translated with a speed of one pixel per iteration 40 pixels to
the left, then 80 pixels to the right, and finally 40 pixels to the left. The left and right

0.2

dx = 40 dx = 40

0.15

0.1

0.05

dx = -40 dx = -40

0

0 20 40 60 80 100 120 140 160

iteration

Fig. 10.16. Face localization recall with moving input. The test image from Fig 10.3 is moved
40 pixels to the left, 80 pixels to the right, and 40 pixels to the left. The relative distance d eye
of the network's output to the given moving eye positions is shown.