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then the other classifier determines the output. If one classifier is undecided between
two classes, the output of the other one can strengthen one of the classes and weaken
the other class.
The performance of the combined classifier on the training set is almost perfect.
Only one of the 4,351 examples is not recognized. It has a very rare meter value of
4.80 that is substituted for the most frequent value 4.60 .
The test set performance is also good. If no examples are rejected, only 10
(0.91%) of the 1,099 examples are substituted. Most substitutions can be rejected
easily by using as block confidence the minimum of the left and right digit confi-
dences. The substitution rate can be lowered to 0.45% if only 0.64% of the examples
are rejected. Rejecting 3.55% of the examples reduces the substitution rate to 0.18%.
Figure 7.19 summarizes the test set performance of the combined classifier and
compares it to the performance of the block classifier alone. Adding the digit clas-
sification stage to verify the examples rejected by the block classifier improved the
recognition performance significantly.
Figure 7.20 illustrates the combined recognition for some problematic examples.
Part (b) of the figure shows the five substitutions from the test set that are most
difficult to reject. One reason for these substitutions is that the meter value is not
present in the training set or is very rare, as in the examples in the first and the last
row. Other substitutions arise from failures to center the two digits of interest during
preprocessing. These failures may be caused by some additional strokes, as in the
third row, or by a missing digit, as in the fourth row of the figure. Finally, low image
contrast may also be a reason for substitutions, as in the example in the second row.
On the other hand, Part (a) of the figure contains some examples for which
the person labeling the meter values did not assign a valid label. Although these
examples are fairly hard to read, they were successfully recognized by the combined
classifier.
2
block classifier
combined classifier
ρ
recognized
substituted
rejected
0
1089 (99.1%)
10 (0.91%)
0
1.5
0.14
1087 (98.9%)
5 (0.45%)
7 (0.64%)
1
0.48
1059 (96.4%)
3 (0.27%)
37 (3.37%)
0.52
1058 (96.3%)
2 (0.18%)
39 (3.55%)
0.5
0.93
955 (86.9%)
1 (0.09%)
143 (13.0%)
0.97
864 (78.6%)
0
235 (21.4%)
0
0
5
10
15
20
25
(a)
(b)
Fig. 7.19. Performance of the combined meter value classifier on the test set: (a) substitutions
vs. rejects; (b) recognition as a function of the reject parameter ρ .
rejects %
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