Geoscience Reference
In-Depth Information
Fig. 6.2
The distribution of the sum weight of the candidates
Therefore, we should find these two thresholds in the next step, as the following:
1. According to the distribution range of the numeric value of the features, we will
divide the ranges into some intervals to calculate the sum weight of craters
g
(
x
)
and noncraters
ng
(
x
).
2. For every interval
x
i
, we can subtract
ng
(
x
) from
g
(
x
) and get
h
(
x
)
D
g
(
x
)
ng
(
x
).
3. After obtaining the value of max (
h
(
x
)), the
x
max
corresponding to
h
(
x
)
max
can
be found. On the left and right side of
x
max
,
x
1
and
x
2
can be got to satisfy the
equation:
h
(
x
)
D
0. In fact, the function
h
(
x
) is not continuous, so the requirement
cannot be satisfied strictly. Therefore, the value of x will be selected when
h
(
x
)
vary from negative to positive or positive to negative. The classification errors
can be minimized when we use
x
1
and
x
2
as two thresholds.
Postprocessing
In this methodology, it is possible that we allow for multiple candidates, classified
as “craters,” to correspond to a single crater, and it cannot be distinguished
automatically by the machine. Thus, in order to eliminate the repeat count from the
approach, we need to do further work and analysis in this step. Based on the research
by Bandeira et al. (
2010
), the craters labeled candidates fulfilling the following
criteria are taken to correspond to a single crater and grouped together:
LJ
LJ
d
i
d
j
LJ
LJ
max
d
i
;d
j
Ǜ and
dis
c
i
;c
j
max
d
i
;d
j
(6.9)
Here
d
i
and
d
j
are the diameters of craters
i
,
j
,where
c
i
and
c
j
are their
centers. The values of Ǜ, are determined experimentally with a best choice for
free parameters Ǜ
D
D
0.5. The criteria for the selection is that the candidate
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