The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
One possible way to discriminate between secondary and 
primary craters is through depth-diameter information on each 
individual crater. Crater cataloguing with 3D data, has never 
been attempted before due to the lack of such high quality 
information but the authors consider this to be most worthwhile 
for such purposes as well as other research areas such as the 
physical mechanisms underlying impact crater formation. The 
release of HRSC stereo imagery makes this idea feasible. 
However, it is not easily achievable considering the relatively 
poor vertical accuracy of stereo DTMs, the limited resolution of 
raw stereo images and the contamination of HRSC image by 
compression errors. We address these problems by 
implementing a 3D stereo matching system incorporating re 
constructed 2D crater boundaries derived from HRSC images. 
2. ALGORITHMS 
2.1 Algorithms for 2D crater data base extraction 
There are a relatively small number of fundamental techniques 
underlying all of the automated crater detection systems which 
hav been developed to date. These can be classified into two 
broad groups, namely supervised and unsupervised. Supervised 
methods rely on machine learning from human input whereas 
unsupervised perform the detection process autonomously. 
The unsupervised methods usually comprise three main 
algorithmic steps: 1) focusing, 2) feature extraction, 3) 
classification. 
The focusing stage is aimed at reducing the computational cost 
required by differentiating between areas to be eliminated and 
areas to be processed further. Techniques for achieving this 
include edge detection, edge direction analysis and texture 
analysis. During feature extraction, all possible features are 
identified and selected from the results of the focusing stage. 
Most algorithms employ some form of Hough Transform to 
achieve this, although genetic algorithms are another possibility 
used by Cheng (2003),whilst Kim et al (2005) used conic 
section fitting. The final stage is to classify the output from the 
selection of candidate features. This involves a trade-off 
between over and under detection, the goal being to maximize 
detections while minimising false positives. 
Supervised systems begin with a learning or training phase 
where examples of features being sought are fed to the 
algorithm. The algorithm is then applied to an unlabelled data 
set. 
This research contains the following material re-organised and 
summarised from Kim et al (2005a) and Kim (2005) which both 
describe the algorithm in greater detail. 
The 3 stages in the overall algorithm is as follows: 
• a focusing stage to define target edge segments in 
regions of interest (ROIs) 
• an organization stage to find optimal ellipses 
• a refinement and verification stage to remove false 
detections 
The focusing stage reduces the search space by extracting edge 
magnitude and direction using a Canny operator and then 
extracts regions of interest (ROIs) using a Grey Level Co 
occurrence Matrix (GLCM) texture classification. 
The organisation stage takes the preliminary crater rims created 
in the focusing stage and organises them into optimal ellipses 
using graph-based conic section fitting methods. First, the 
Direct Least Squares (DLS) fitting method (Fitzgibbon et al, 
1996) is applied, as being the most computationally efficient. In 
the final fitting stage the osculating ellipse (OE) detection 
algorithm (Kanatani and Ohta, 2004) is used to find the best 
conic section from candidate craters. 
Verification and refinement, the final stage, first refines the 
feature selections by employing a template matching scheme 
where the maximum correlation for each crater against pre 
specified templates are chosen, provided they exceed a given 
threshold. The final operation is to remove false detections 
using eigencrater construction (Turk and Pentland, 1991) and 
neural network template recognition involving training vectors 
representing a set of craters and a set of non craters. 
However, application of such a set of impact crater detection 
algorithms over a single image strip do not provide 2D crater 
GIS over extensive areas. For this, multiple image strips are 
required together with a merging process to compile the 
detection results together from individual images. 
Adjacent images invariably have areas of overlap which means 
that most, if not all, craters detected in the overlap region will 
appear duplicated in the set of results for each image. These 
duplicates must be identified and resolved to a single crater. 
This could be done manually but the ultimate aim is total 
automation of the entire process, so a simple version of 
automated duplicate detection was needed. It is likely that the 
actual crater descriptions for duplicate craters will not be 
absolutely identical, due to variations between the images, 
algorithmic artefacts or co-registration issues. This means that 
two definitions of the same crater may differ in terms of the 
centre locations, the radii or both. 
To incorporate craters from different catalogues, Salamuniccar 
and Loncaric (2007) proposed a simple function, very similar to 
that used in Vinogradova et al (2002), which relates diameter 
and radius such that variations in the most significant of either 
of these can be compared against a critical value and used to 
determine whether the definitions in each catalogue are likely to 
refer to the same crater. Their method consists of two stages: 
firstly, obtain a quantifiable measure of the differences between 
crater radii and centre point location and then compare this 
against some critical value. If the measure is less than some 
critical value then it is likely that a duplicate has been identified. 
This is formalised in the two equations below (Salamuniccar 
and Loncaric, 2007), both conditions of which must be satisfied. 
'2 ^ ) (1) 
< ./; 
Where fin is the difference measurement factor, rl and r2 are 
the radii, chosen such that rl > r2; d is the distance between the 
crater centres and fc is the critical factor value. 
The selection of a suitable critical factor is important. If the 
value is too high, too few duplicates or spurious duplicates will 
be found, and true duplicates will be missed. They suggest that 
the critical value should be less than the smallest value for the 
distance measurement factor fin found in either dataset. The 
distance or overlap between duplicates, although small, often 
exceeded that found internally within the data sets and so would 
result in duplicates not being correctly identified. A factor of 2.0 
was found to be suitable. After a set of potential duplicates is 
identified, all possible combinations are tested and the two with 
the smallest distance/radius difference measure are resolved into 
a single crater using the mean centre and radius. 
2.2 3D crater DTM extraction 
For this purpose, we use the 2D crater boundary as a priori 
knowledge for stereo matching. The usual area-based stereo 
image matchers are not robust over the distorted surface. One 
possible solution is finding the estimated disparity surface using 
the approximate 3D shape of the impact crater. Then the image 
matching will be performed along the surface of the pre- 
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