Automatic Recognition of Impact Craters on the Martian Surface from DEM and Images - Planetary Exploration and Science: Recent Results and Advances - page 103

6. Update the weights, w tC1;i D w t;i LJ 1e i ,where e i D 0if C i is classified correctly
e i D 1if C i is classified incorrectly LJ t D " t /(1 " t )
7. End.
8. The final strong classifier is given by

8
<

Ǜ t h t .C/ T

X

T

X

crater if Ǜ t >

H.C/ D (6.6)

:

t D 1 t D 1

non - crater otherwise

where Ǜ t D log(1/LJ t )and is a threshold probability.

The Modified Weak Classifier

In the traditional algorithm, a sequence of weak classifiers was generated and
combined to assemble a strong classifier through a weighted boosting approach.
A set of weak classifiers h t ( C ) D h ( C , f t , p t , t ) is defined like this:

1 if p f.C/ p
0 else

h.C I f;p;/ D (6.7)

where C is an image block representing a crater candidate and f is the numeric
value of each feature. The discriminative power of the weak classifier is determined
by the threshold and a polarity variable p 2f 1, 1 g which means that the feature
value should be greater or smaller than the threshold. In fact, each single weak
classifier always identifies candidates into craters with low confidence because of
its low discriminative power. However, in each round of the training process, a best
weak classifier will be selected with the minimum weighted errors. If all these weak
classifier has an ability of correct classification with a detection rate higher than 0.5,
the final strong classifier can perform well by combining many weak classifiers.
Figure 6.2 shows the proportion of crater and noncrater candidates in all
candidates when the feature value increases. Considering the distribution of the
sum weight of all the candidates, we can conclude that the feature value of crater
candidates distributes in a relatively narrow interval when comparing to noncrater
candidates. It has been shown that only a single side threshold employed to
determine craters will result in some false results, like the noncrater candidates with
very high or low features considered to be craters. Therefore, the classifier with a
dual threshold is constructed for the detection. It can be easily proved that smaller
classification errors will be obtained when a weak classifier with a dual threshold is
employed, which is introduced on the following:

1 if 1 f.C/< 2
0 else

h.C I f; 1 ; 2 / D (6.8)