Binarization of Matrix Codes - Hierarchical Neural Networks for Image Interpretation - page 166

2000 2000

degraded TRN
original TRN

degraded TST
original TST

1500 1500

1000 1000

500 500

0 0

0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1

(a) (b)

confidence confidence

TRN TST

degraded original degraded original

confidence .9646 .9812 .9649 .9811

output error 757.4 238.5 756.6 238.6

(c)

Fig. 8.16. Recall of iterative Data Matrix binarization. Shown are confidence versus squared
output error for the original and the degraded images: (a) training set; (b) test set; (c) average
confidences and squared errors.

performance of Data Matrix codes. If one wanted to produce a longer decrease of
the average difference to the desired output, one could always train the network for
more iterations. This was not done here since ten iterations seem to be sufficient to
solve the binarization task.
Both parts of Figure 8.15 display data for the training set as well as for the
test set. Since both curves are almost indistinguishable, it can be claimed that the
network generalized the binarization task well.
The output of the network approaches an attractor that is characterized by black
and white cells, represented by activities of one and zero, respectively. Intermediate
activities indicate uncertainty. Of course, the network's uncertainty is maximal at
the start of the computation and decreases as the network makes decisions about
the output. As described above, the network has not reached a stable attractor for
all examples at iteration 10. In addition, even at an attractor, the output can remain
undecided if the input is ambiguous. To measure the networks certainty, for each
output activity a , a confidence c is computed from the minimal squared distance to
one of the extreme values:

(0 − a ) 2 = a 2 , =

d 0

(1 − a ) 2 , =

d 1

1 − 4 · min( d 0 ,d 1 ) .

c =

(8.4)

Since a is in the interval [0 , 1] , c is in [0 , 1] as well. The confidence of an entire
image is the average confidence of all output feature cells.