Geoscience Reference
In-Depth Information
Circle Fitting and Crater Checking
The circle fitting method used in this CDA is least square circle fitting. Based on the
coordinates of the detected rim pixels, we can get the best fit circles representative
of craters with the criteria by finding the minimal value of errors, E ( a , b , r ).
E.a;b;r/ D X h .x a/ 2
r 2 i 2
C .y b/ 2
(6.12)
where a and b are the coordinates and r is the radius of a fitted circle and x , y are the
coordinates of rim pixel. In order to remove some false candidates in the detection,
three criteria, including a restriction on rim completeness, the slope filter, and the
depression filter, are used. It is normally checked by comparing the sum of discrete
pixels (SDPs) on the rim and the perimeter of the corresponding circle. There is
some kind of linear relationship between the SDP and the ratio of the radius R of
the circle and the resolution g of the DEM. The coefficients of the relationship are
presented as follows:
SDP D 5:658 R=g C 11:95
(6.13)
The threshold can then be set according to the applied DEM data. Secondly, the
slope filter will be aimed at checking the average slope near the rims of craters.
Finally, the depression filter will be used to check the ratio of the area of depression
to that of non-depression inside a crater. After all these steps have been done, the
final detection results can be obtained.
6.3
Validation of Methods
It is a fact that different geologists or even the same geologist at different times
would assign slightly different coordinates and radius for the same crater. It has
great possibility that two different craters have similar coordinates or radius in the
catalogue. Also, it has to be expected that different CDAs would not assign identical
coordinates and radius to the same crater, which may have already been labeled
in a ground truth (GT) catalogue. A ground truth catalogue, which contains the
locations and sizes of known craters, is an important element in the evaluation of
CDAs developed for a wide range of applications.
The importance of crater registration lies in the fact that, in general, every
identification (manual or machine) of a given crater results in a different set of
assigned parameters. Manual crater mappers assign coordinates of crater center and
its diameter based on their criteria. Since this is done by human beings, the resulting
catalogues are considered to be ground truth. However, manual assignment of the
crater center and diameter may vary even between successive determinations by the
same human operator, so in fact we really have a fuzzy GT. Different automated
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