Geoscience Reference
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in the gradient direction reflecting the change of slope angle, has been proved to
show good performance as crater rim indicator.
@x
2
@h
2
@y
2
@h
2
@
2
h
C
2
@
2
h
@x@y
@
2
h
@h
@x
@h
@y
C
@x
@y
cur.x;y/
D
m
p
n
3
(6.10)
where
m
D
(@
h
/@
x
)
2
C
(@
h
/@
y
)
2
and
n
D
m
C
1, the @
h
/@
x
and @
h
/@
y
are separately
the first derivative of the elevation in the
x
and
y
direction, and @
2
h
/@
x
2
is the second
derivative. Then, we use the value of curvature to produce a binary image of the site
according to the following transformation:
1.
black
/;
for
k.x;y/
k
th
0.
white
/;
for
k.x;y/>k
th
I
k
.x;y/
D
(6.11)
Here,
k
th
is a threshold value for concave areas. The chosen value of
k
th
represents
a tradeoff between selectivity and the presence of noise. Choosing
k
th
close to
Min[
k
(
x
,
y
)] selects only areas with the highest concavity, eliminating noise but
also misses the rims of smaller or degraded craters. In this test, we have chosen to
use relatively large value of
k
th
D
0.001 in order to increase detection chances for
small craters (Fig.
6.3
).
Site Segmentation
Craters are enclosed topographic basins, which mean that the “flooding” algorithm
can be used to determine crater areas in an idealized situation. This is because a real
Martian landscape includes enclosed basins that are not craters, some craters are not
basins due to degradation of their rims, and there are superimposed craters that form
only a single fragment. All these realities prevent flooding algorithm from becoming
Fig. 6.3
The DEM and curvature map of the test site
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