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An approach to automatically detect impact craters on planetary surfaces is presented in this letter. It is built up from a boosting algorithm proposed by Viola and Jones (2004) whose simplicity combined with an original learning strategy leads to a fast and robust process with consistent results. The approach is validated with image data sets from Mars surface captured by the Mars Orbiter Camera onboard Mars Global Surveyor probe.
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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 1
Crater Detection by a Boosting Approach
Ricardo Martins1, Pedro Pina1,2, Jorge S. Marques1,3, and Margarida Silveira1,3
1Instituto Superior T´
ecnico
2CERENA-Centro de Recursos Naturais e Ambiente
3ISR-Instituto de Sistemas e Rob´
otica
Av. Rovisco Pais, 1049–001 Lisboa
Portugal
ricardo.martins@ist.utl.pt, ppina@ist.utl.pt, {jsm, msilveira}@isr.ist.utl.pt
* corresponding author
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 2
Abstract
An approach to automatically detect impact craters on planetary surfaces is presented in this letter. It is build
up from a boosting algorithm proposed by Viola and Jones (2004) whose simplicity combined with a learning
strategy leads to a fast and robust process with consistent results. The approach is validated with image datasets
from Mars surface captured by the Mars Orbiter Camera onboard Mars Global Surveyor probe.
Index Terms
Impact craters, automatic detection, learning, boosting, Mars.
I. INTRODUCTION
IMPACT craters are an essential source of information about the geology of planets and their surface
characteristics. The density of craters is closely related to the age of the surfaces and its computation
has been used to establish a chronology of the evolution of the terrains [1]. After the primordial
manual countings, several attempts to create reliable methods for automated crater detection have been
developed. These include diverse approaches such as the ones based on template matching methods [2],
[3], [4], [5], Hough transform [6], [7], [8], neural networks [9], [10], genetic algortihms [11], [12],
mathematical morphology [13] and a combination of multiple techniques [14], [15]. Anyhow, although
relevant contributions have been presented over the years, the degree of generalization of those methods is
not yet totally satisfactory, since adjustements or modifications on some of their steps are always necessary
to respond to differences on planetary surfaces. In particular, the wide range of crater dimensions (from
a few meters to thousand of kilometres) with distinct conservation conditions (from very fresh and well
contrasted to very old with eroded rims and filled or covered by other geological materials), occurring
in quite diverse geomorphological settings has also made difficult the choice of adequate and unique
parameters on the different automated approaches. Most of those diversified characteristics can be found
within single images, like the region of about 115 x 115 km2of Mars in Fig. 1 clearly shows.
Thus, the nature and varied characteristics of occurrence of these structures on planetary surfaces
demands a learning strategy that is able to adapt itself to every distinct situation. These circumstances
led us to explore a boosting approach whose dependence on the characteristics of the craters and the
terrains where the impacts took place is reduced. This way, we decided to use a machine learning tool,
the boosting algorithm proposed by Viola and Jones [16] in the context of face recognition. This algorithm
is able to select a small number of useful features in face images namely, the eyes and the mouth. The
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 3
underlying idea follows the use of weak classifiers (simple thresholding operation applied to a single
image feature) which are combined in an iterative procedure to create a strong classifier. We expect that it
will be also able to extract meaningful characteristics of the craters rims, although the problem is probably
more difficult due to the great variety of textures.
This letter is organized as follows: section II describes in detail the several steps of the crater detection
algorithm; section III introduces the strategy to deal with craters of different dimensions; section IV
presents the experimental results on a set of Martian images while the conclusions of using this approach
are presented in section V.
II. CRATER DETECTION
The detection of impact craters on planetary surfaces can be formulatedas a classical pattern recognition
problem where the information extracted from different locations in the images is assigned to one of two
classes: crater or non-crater. A region or block around each image pixel is extracted to determine if it
contains a crater or not; we will follow the approach used in [16] which achieved excellent results in
the field of face recognition but which has not yet been applied in the context of crater detection. The
decision (crater or non-crater) is given by a binary classifier using a set of image features; the classifier
must deal with craters of different dimensions and with artefacts that may be confounded with the impact
structures and which are produced by terrains of different constitutions and origins. Consequently, the
issues to be taken into account in the design of a detection approach should rely on the selection and
extraction of adequate features, on its classification and on a strategy to achieve robustness with respect
to scale changes (the first two issues are addressed in the following while the third one is addressed
separetely in section III).
A. Pre-Processing
Planetary images have various lighting directions according to the relative position of the sun at the time
of the capture of the image. Since the azimuth of the sun is known for each image, a rotation according
to the registered value is executed, in order to make sure that all images are aligned in the same lighting
direction.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 4
B. Feature Extraction
The features used in this work are obtained by probing each image block Bwith the set of ternary
masks (Haar-like features [17]) shown in Fig. 2. In these images, the grey tone stands for level 0 (region
out of the mask), while the black and white regions stand for -1 and +1, respectively. Since we are looking
for structures that may appear anywhere within the image block, we will consider the ternary masks at
different positions. Let φ(x)denote one of these masks. The corresponding feature is given by:
f(B)=[0,1]2
B(x)φ(x)dx (1)
where we assumed that the block Band the masks are continuous images defined in the interval [0,1]2. The
computation of these features is extremely fast if an auxiliary image (integral image) is pre-computed (see
details on how to do it in [16]). Using the integral image, each feature can be obtained by a reduced number
of additions (from 4 to 8). The number of generated features can attain a high value (typically thousands),
but with distinct importances, from really relevant to absolutely irrelevant. Therefore, a selection of the
most adequate features for this crater detection purpose must be performed.
C. Boosting classifier [16]
The classification algorithm used in this work is based on the variant of AdaBoost proposed by Viola
and Jones [16]. This algorithm is used to select the features and to classify each block extracted from the
image into one of two classes: ”crater” or ”non-crater”. First, a set of weak classifiers {h}(one classifier
per feature f) is defined, based on a thresholding operation:
h(B)=
1if p·f(B)p·θ
0otherwise (2)
where θis a threshold and p∈{1,1}is a polarity variable that determines if the feature fshould be
greater or smaller than the threshold in crater images. The output of each classifier depends only on a
single feature. Therefore, the boosting algorithm selects a weak classifier (feature) in each round. The
parameters of the weak classifiers are obtained by minimizing the criterium:
E(f)=
N
i=1
wi|h(Bi,p)yi|(3)
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 5
where Biis the ith training pattern, wiis the corresponding weight (see definition below) and yi∈{0,1}
is the correct decision (yi=1for the crater training patterns and yi=0for the non-crater patterns). This
algorithm selects one feature per iteration. The main steps are briefly described in the following (see [16]
for the details):
1) Extract all features ffrom each training block using eq.(1).
2) Initialize the weight w1,i for each training block i:
w1,i =
1
2·tc if iis crater
1
2·nc if iis non-crater (4)
where tc-number of true craters, nc-number of non-craters in the training set.
3) For t=1,··· ,T (Tis the number of features to be selected):
Normalize the weights wt,i.
For each feature ftrain the corresponding weak classifier minimizing eq.(3).
Feature selection: choose the weak classifier htwith the lowest error εt=min
fE(f).
Update the weights wt,i:
wt+1,i =wt,i ·β1ei
t(5)
using βt=εt
1εt;ei=0if the training block iis correctly classified and ei=1 otherwise.
4) Combine the outputs of all the weak classifiers to obtain a discriminant function H(B):
H(B)=
T
t=1
αt·ht(B)(6)
where αt=log(1
βt). The final decision C(B)is obtained by computing the local maxima of H(B)
using a non-maximum suppression algorithm. Accept or reject the local maxima by comparing
H(B)with a threshold as follows:
C(B)=
1if H(B)µ·T
t=1 αt
0otherwise (7)
where µ[0,1] is a constant defined by the user, which defines the trade-off between true and
false detections.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 6
III. MULTISCALE CLASSIFICATION
In order to detect craters of different sizes, the classifier should be scale independent. This problem
has been addressed before by several authors (e.g., [16], [18]). The image is analyzed using blocks of
different sizes [0,K]2, with K=15×1.25s1pixels, where sis the scale number. Each block is shifted
by 1 pixel at a time with respect to the previous block. The number of features considering all scales is
3216 per block. In order to allow for the simultaneous use of the same classifier at different scales, the
features are normalized to turn them scale independent:
f(B)= 1
K2[0,K]2
B(x)φx
Kdx (8)
To perform the detection of craters in an image, the outputs of the boosting classifiers at different scales
must be compared. This way, we search for the local maxima of H(B)in space ×scale volume, i.e.,we
look for the locations and scale in which H(B)achieves the highest values in a given neighborhood.
This means that the same classifier is used for all the scales considered in the classification procedure
being trained with patterns (crater and non-crater blocks) of different scales. This situation is possible to
attain since we are dealing with scale independent features.
IV. EXPERIMENTAL RESULTS
There is no standard procedure to evaluate crater detection algorithms, although very recent proposals
are being presented to change that situation [19]. Many algorithms are evaluated in a specific way by
the authors using their own metrics and datasets. In this paper we use well established metrics (True
Detection Rate and False Detection Rate) together with a set of images which was already used in
another study [5]. This set comprises 101 images obtained by the Mars Orbiter Camera (MOC) from 4
zones of Mars surface, covering about 1,500,000 km2and belonging to the Hesperian geological period.
All the images were manually classified in order to produce the ground-truth information. The bounding
boxes of all the craters were accurately specified by an expert. Therefore, we know the exact location
(contour, center and diameter) of 1272 craters in the images.
A. Training Data
The algorithm was tested using 4-fold cross-validation, i.e., the whole set of images was divided into
4 subsets with the same size; while three of them were used for training, the remaining one was used for
testing. This procedure was repeated 4 times, so that each subset could be used once for testing.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 7
The boosting classifier is trained using positive (crater) and negative (non-crater) examples extracted
from the training database. The positive examples are obtained using all the craters in the training images.
Each example is a square block centered on the crater with a size equal to 1.30 times its diameter. Some
criteria to select the negative examples are needed, since there are too many possibilities for defining
the non-crater blocks. We initially extracted negative examples occurring in the borders or rims of the
craters, because they correspond to highly textured regions confounded with craters and which are hard to
classify. Therefore, a small number of non-crater blocks is taken around each crater. This set of negative
patterns is called the Initial Training Set (InTS) which is used to train the initial classifier. Afterwards, we
found in practice that this approach was insufficient since it did not provide a representative collection of
negative patterns.
Thus, in order to enlarge and enhance this set of non-crater examples we enhanced the training set
with additional blocks corresponding to the false detections with higher discriminant value and repeat
the previous procedure. At each iteration, a new classifier is obtained trained with a larger dataset. This
enlarged set is called an Iterative Training Set (ItTS). This procedure is repeated a few times until the
improvement is negligeable.
B. Boosting Classifier
Each training block is characterized by 3216 features. The boosting algorithm extracts a small subset of
Tfeatures which are considered to be sufficient for the decision. In Fig. 3 the ten best masks selected by
the boosting algorithm for a given training set are shown, together with a crater image. These masks show
the kind of transitions which are considered the most relevant by the classifier. We considered several
values of Tranging from 10 to 50 features in the experimental tests.
C. Evaluation
The performance of the boosting algorithm is evaluated through the computation of True Detection
Rate (TDR) and False Detection Rate (FDR), given by following expressions:
TDR(%) = TD
GT ×100 (9)
FDR(%) = FD
TD +FD ×100 (10)
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 8
where GT is the total number of craters in the ground-truth image, TD is the number of true detections
and FD is the number of false detections. Only the craters with a diameter equal to or greater than 7 pixels
are taken into account to calculate the TDR values. The detections are automatically evaluated as true
or false by comparison with the ground truth images. Fig. 4 shows representative examples of detections
obtained with the proposed approach in three images with distinct characteristics.
For all retrieved classifiers in the 4-fold cross validation, the trade-off between the true detections and
false alarms is given by a receiver operating characteristic curve (ROC), which was built as a function of
the classifier threshold µon eq. 7.
Fig. 5 shows the global ROC curves obtained from the mean of the four curves for the initial training
set (InTS) and for three iterations of ItTS (ItTS1, ItTS2 and ItTS3). In particular, some of those values
are presented in Table I for three different threshold values µ.
The results obtained are comparable with the best performances achieved so far by other methods since,
for instance, we obtained with three iterations of ItTS a detection rate of 88.5% for 23.2% of false alarms.
The higher the true detections are, the higher the false detections become.
Nevertheless, the inclusion of non-craters patterns into the training sets obviously leads to major
improvements in the performance of false detections of about 2 to 4 times: for instance, for µ=0.60,
the FDR value is reduced to about one-third when InTS is enlarged to ItTS1 (from 24.29% to 8.88%) or
to about one fourth using ItTS3 (FDR=5.53%).
The influence of the number of features used in the classification was also evaluated. It can be noticed
that the performance of the classifiers increases with the number of features (iterations) used, i.e., the
performance increases with the use of more features, like shown by the ROC curves of Fig. 6 for five
different features sizes (from 10 to 50).
V. CONCLUSIONS
This letter describes a boosting algorithm for impact crater detection which accounts for changes in
illumination, visual appearance and size. The algorithm was evaluated in an objective way using images
from Mars related to the Hesperian period. The results obtained outperforms most published approaches.
Furthermore, this algorithm is computationally fast and also diminishes the minimum detection limit of
crater dimensions, i.e., it detects craters with a diameter equal to or greater than 7 pixels, a real and
valuable improvement when compared to the limit of at least 10 pixels of other approaches.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 9
The boosting algorithm is able to automatically select a small set of features characterizing the
presence/absence of craters in an image. Thus, the major improvements introduced by this approach are
its adaptive characteristics together with an original learning strategy, reflected on the robust performances
achieved by cross-validation.
We believe that this approach can be applied to other types of terrains, since the boosting algorithm
is able to automatically select meaninful features for each classification problem. Therefore, in the future
we plan to evaluate the performance of this algorithm on other terrains of Mars (namely the older or
Noachian ones) and also on other planetary surfaces.
ACKNOWLEDGMENT
This paper was partially supported by FCT-Fundac¸˜ao para a Ciˆencia e a Tecnologia (Portugal) under
the project PDCTE/CTA/49724/03 and by ISR/IST under pluriannual funding POSC, FEDER.
REFERENCES
[1] W.K. Hartmann and G. Neukum, ”Cratering chronology and the evolution of Mars”, Space Science Reviews, 2001, vol. 96, pp. 165-194.
[2] A. Flores-M´endez, ”Crater marking and classification using computer vision”, Lecture Notes in Computer Science, 2003, vol. 2905,
pp. 79-86.
[3] G. Michael, ”Coordinate registration by automated crater recognition”, Planetary and Space Science, 2003, vol. 51, pp. 563-568.
[4] T. Barata, E.I. Alves, J. Saraiva and P. Pina, ”Automatic recognition of impact craters on the surface of Mars”, Lecture Notes in
Computer Science, 2004, vol. 3212, pp. 489-496.
[5] L. Bandeira, J. Saraiva and P. Pina, ”Impact crater recognition on Mars based on a probability volume created by template matching”,
IEEE Transactions on Geoscience and Remote Sensing, 2007, vol. 45, no. 12, pp. 4008-4015.
[6] T. Vinogradova, M. Burl, and E. Mjolness, ”Training of a crater detection algorithm for Mars crater imagery”, in Proc. IEEE Aerosp.
Conf., Big Sky, MT, 2002, vol. 7, pp. 3201-3211.
[7] J.R. Kim, J.-P. Muller, S. van Gasselt, J.G. Morley and G. Neukum, ”Automated crater detection, A new tool for Mars cartography
and chronology”, Photogrammetric Engineering and Remote Sensing, 2005, vol. 71, pp. 1205-1217.
[8] B.D. Bue and T.F. Stepinski, ”Machine detection of martian impact craters from digital topography data”, IEEE Transactions on
Geoscience and Remote Sensing, 2007, vol. 45, no. 1, pp. 265-274.
[9] A. A. Smirnov, ”Exploratory study of automated crater detection algorithm,” Boulder, CO, 2002. Tech. Rep.
[10] P.G. Wetzler, B. Enke, W.J. Merline, C.R. Chapman and M.C. Burl, ”Learning to detect small impact craters”, in Proc. of
WACV/MOTIONS ’05, Seventh IEEE Workshops on Application of Computer Vision, vol. 1, pp. 178-184, 2005.
[11] S. Brumby, C. Plesko, and E. Asphaug, ”Evolving automated feature extraction algorithms for planetary science,” in Proc. ISPRS WG
IV/9: Extraterrestrial Mapping Workshop Advances-Planetary Mapping, Houston, TX, 2003.
[12] C. Plesko, S. Werner, S. Brumby, E. Asphaug, and G. Neukum, ”A statistical analysis of automated crater counts in MOC and HRSC
data,” in Proc. Lunar Planetary Sci. XXXVII, Houston, TX, 2006. Abs. no. 2012.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 10
[13] E.R. Urbach, ”Classification of objects consisting of multiple segments with application to crater detection,” in Proc. ISMM 2007, 8th
International Symposium on Mathematical Morphology, Rio de Janeiro, Brazil, 2007. vol.2, pp. 81-82.
[14] B. Leroy, G.G. Medioni, E. Johnson and L. Matthies, ”Crater detection for autonomous landing on asteroids”, Image and Vision
Computing, 2001, vol. 19, pp. 787-792.
[15] Y. Sawabe, T. Matsunaga and S. Rokugawa, ”Automated detection and classification of lunar craters using multiple approaches”,
Advances in Space Research, 2006, vol. 37, no. 1, pp. 21-27.
[16] P. Viola and M. Jones, ”Robust real-time face detection”, International Journal of Computer Vision, 2004, vol. 57, no. 2, pp. 137-154.
[17] C. Papageorgiou, M. Oren, and T. Poggio, ”A general framework for object detection”, in Proc. ICCV’98-Sixth International Conference
on Computer Vision, pp. 555-562, 1998.
[18] Y. Deng and G. Su, ”Face detection based on fuzzy cascade classifier with scale-invariant features”, International Journal Information
Technology, 2006, vol. 12, no. 5.
[19] G. Salamuni´ccar and S. Lonˇcari´c, ”Open framework for objective evaluation of crater detection algorithms with first test-field subsystem
based on MOLA data”, Advances in Space Research, 2008, vol. 42, no. 1, pp. 6-19.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 11
LIST OF TABLES
I Classification performances for different threshold values. . . . . . .............. 12
LIST OF FIGURES
1 Examples of impact craters and textural variation on the surface of Mars in a MOC image
(M23-00337) with a spatial resolution of aproximattely 240m/pixel (the side of the image is
about 115 km) [image credits: NASA/JPL/MSSS]. . . ..................... 12
2 The five types of masks used for feature extraction. . ..................... 12
3 The first ten features selected with boosting over a crater. . . . . . .............. 12
4 Classification of MOC images E05-00815, E19-00650 and M00-03044: (a), (c) and (e) ground
truth; (b), (d) and (f) classifier output (Solid - correct detections; Dashed - false detections)
[Image credits: NASA/JPL/MSSS]. ................................ 13
5 Receiver operating characteristic curve for different values of the threshold µand different
number of iterations of the training set. . . . . ......................... 14
6 Receiver operating characteristic curve for different values of the threshold µand different
number of features (T)....................................... 14
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 12
TABLE I
CLASSIFICATION PERFORMANCES FOR DIFFERENT THRESHOLD VALUES.
µInTS ItTS1 ItTS2 ItTS3
TDR(%) FDR(%) TDR(%) FDR(%) TDR(%) FDR(%) TDR(%) FDR(%)
0.55 94.48 60.47 91.09 33.71 88.82 24.83 88.55 23.20
0.60 90.79 24.29 82.82 8.88 80.70 7.01 79.24 5.53
0.65 81.07 8.93 71.25 2.51 67.24 1.98 67.03 1.91
Fig. 1. Examples of impact craters and textural variation on the surface of Mars in a MOC image (M23-00337) with a spatial resolution
of aproximattely 240m/pixel (the side of the image is about 115 km) [image credits: NASA/JPL/MSSS].
Fig. 2. The five types of masks used for feature extraction.
Fig. 3. The first ten features selected with boosting over a crater.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 13
(a) (b)
(c) (d)
(e) (f)
Fig. 4. Classification of MOC images E05-00815, E19-00650 and M00-03044: (a), (c) and (e) ground truth; (b), (d) and (f) classifier output
(Solid - correct detections; Dashed - false detections) [Image credits: NASA/JPL/MSSS].
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 6(1): 127-131 (PRE-PRINT) 14
Fig. 5. Receiver operating characteristic curve for different values of the threshold µand different number of iterations of the training set.
Fig. 6. Receiver operating characteristic curve for different values of the threshold µand different number of features (T).
... Under oblique illumination, such topography generates a distinct pattern of light and dark areas on an image. These characteristics of the images of craters have been used to design CDAs based on image analysis (Barata et al. 2004;Kim et al. 2005;Sawabe, Matsunaga, and Rokugawa 2006;Lon cari c 2008, 2010;Martins et al. 2009;Urbach and Stepinski 2009;Ding et al. 2010;Luo et al. 2011;W. Li, Hsu, and Hu 2021). ...
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