ENHANCING IMPACT CRATER CONTOURS

TO INCREASE RECOGNITION RATES

Lourenço P.C. Bandeira, José Saraiva, Pedro Pina

CVRM/Centro de Geo-Sistemas, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Keywords: Impact craters, Mars, automatic recognition.

Abstract: This paper introduces an enhancement to the edge detection procedures that are part of a general

methodology which aims at increasing the robustness of the automatic recognition of impact craters on

planetary surfaces. It is demonstrated that the proposed improvement is a major contribution to increase the

recognition rates and to simultaneously diminish the rates of false positives. Its performance is evaluated

through a comparison with other classic edge detectors, which are applied to a set of images of the surface

of Mars acquired by the MOC instrument aboard Mars Global Surveyor, a probe currently orbiting the

planet.

1 INTRODUCTION

The identification and counting of impact craters is

an approach that has been widely used when

establishing the chronology of planetary surfaces

(Hartmann and Neukum, 2001). The early manual

crater counts on optical images can now be aided by

several semi-automatic approaches from the image

processing and pattern recognition fields - Homma

et al. (1997), Honda and Azuma (2000), Leroy et al.

(2001), Costantini et al. (2002), Vinogradova et al.

(2002), Michael (2003), Flores-Méndez (2003), Kim

and Muller (2003), Brumby et al. (2003), Magee et

al. (2003), Plesko et al. (2004), Barata et al. (2004),

Kim et al, (2004), Earl et al. (2005) and Matsumoto

et al. (2005) – but the generalization of procedures

still meets with evident difficulties. Even in a recent

study (Neukum et al., 2004) in which a refinement

of chronology was proposed for a number of small

areas of the surface of Mars, automatic recognitions

were not fully trusted, and ended up being edited

and manually corrected by human experts. The

difficulties faced are many, and are due to several

reasons: the different types of terrain, which produce

different scattering behaviours; the conditions of

illumination of the scene; the state of the atmosphere

(when it exists); the location of the sensor; possible

confusion with structures which show similar

morphologies (volcanic craters, small valleys or

basins, collapse structures); the existence of crater-

saturated areas where overlapping structures are

very frequent; and the degradation of structures by

weathering agents (wind, dust, ice, water) and

endogenous geological activity (faulting, eruptions).

The majority of the approaches published so far

have a quite similar structure: in a first step, the

image is screened for edges that correspond to the

borders or rims of craters, and these are selected as

candidate regions to be used as input for a second

step, a matching procedure. So far, the efforts have

been more focused on developing the matching

phase than on the edge detection one. Thus, as we

feel that any improvement that can be achieved in

this complicated realm of application can have an

important outcome in the final recognition result, we

decided to pay more attention to the edge detection

phase. Our aim is to supply better candidate regions

to the subsequent matching phase, with the goal of

increasing the recognition rate and at the same time

substantially diminishing the recognition of false

positives, i.e., structures that are not craters and that

are frequently and wrongly recognized as such.

The variety of textural characteristics which

occurs between the images (when they are form

widely distant regions) but also within the same

image (covering a smaller region) makes it hard to

choose a general and single operator. The majority

of available edge detectors applied to the images of

the surface of Mars normally result in an excess of

bad candidates that are difficult to filter out, thus

producing unsatisfactory results. Hence, an edge

detector based on local information is envisaged, in

order to be adaptable to the common variations in

the surface features. We compare its results to other

classic approaches, in a non-exhaustive mode.

407

P. C. Bandeira L., Saraiva J. and Pina P. (2006).

ENHANCING IMPACT CRATER CONTOURS TO INCREASE RECOGNITION RATES.

In Proceedings of the First International Conference on Computer Vision Theory and Applications, pages 407-412

DOI: 10.5220/0001375104070412

 SciTePress

2 GENERAL METHODOLOGY

We are establishing and developing a general

methodology to automatically recognise impact

craters on planetary surfaces. Currently, it is being

tested with images from the surface of Mars

acquired mainly by the instruments MOC and

HRSC, the cameras aboard the Mars Global

Surveyor (NASA) and Mars Express (ESA) probes,

respectively.

The approach being followed is based on the

following main phases:

1. Pre-processing and evaluation of the

parameters of image acquisition.

2. Selection of candidate regions belonging to

crater rims (edge detection).

3. Crater recognition based on template

matching (several approaches are being

tested and the results compared, namely, the

FFT, the Hough transform and other recent

template matching algorithms).

This paper addresses the problems related to the

second of these phases. The difficulties presented by

traditional edge detectors lead us to propose another

but simple approach with important improvements

in the robustness of the automatic recognition.

3 EDGE ENHANCEMENT

Impact craters are characterized by a generally

circular shape, with a wide variation of contrast to

the surrounding terrains, a reason why edge

detection techniques can play a fundamental step in

crater recognition (Fig. 1). The search for edges in a

numeric image is one of the most studied problems

in image processing due to the very intuitive nature

of edges and their clear visual impression.

Figure 1: Image R0100925 acquired with the sensor

MOC/WA. The spatial resolution is 245 meters/pixel

(NASA/JPL/MSSS)

This section presents the different phases that

constitute the proposed edge detection algorithm.

This method is based on a local threshold approach

and detects an edge whenever a local variation of

grey-level is significant. The first requirement is to

determine a threshold that incorporates information

about the local variations in grey-levels in the

original image. For this purpose, the following steps

are taken:

1. A 3x3 mask M is centred over each pixel

of the original image, in order to compute the local

maxima

A , according to the equation:

[

]

mMMmA

−

)max(),min(max (1)

where

m is the mean of the 9 pixels in the mask

2. The threshold

t is then obtained, taking into

account the global range of the matrix A, a

procedure which can be translated by the following

rule:

[

]

)min()min()max( AAAt +

−

(2)

where λ is a constant, defined by the percentage

of the range that is considered. All of the results

presented in this paper have λ = 0.2. This value

resulted from an experimental process of fine-tuning

driven by a search for the best result.

Next, this threshold

t is applied to each pixel A

of matrix A, in order to compute the value (0 or 1)

that will be assigned to each new pixel

of the

resulting binary image B.

This method produces binary images where only

highly contrasted local edges are selected.

Simultaneously this operation globally reduces the

noise.

In comparison to traditional edge detection

techniques (such as the first order derivative

operators developed by Sobel (1970), Roberts

(1965), Prewitt et al. (1966) and Canny (1986) and

the second order derivative method introduced by

Marr and Hildreth (1980) and designated as the

Laplacian of Gaussian (LoG)), this new algorithm

shows, in most situations, a better enhancement of

the rims, thus allowing a sharper definition of the

crater shapes and anticipating a more correct

recognition. This is illustrated by the image in Fig. 1

and the images with the edges detected by all the

methods mentioned in Fig. 2.

Fig. 1 illustrates the fact that, sometimes,

features that can be easily identified as craters by the

human eye can be extremely hard to recognize by

computational methods. For instance, the rim of the

larger crater that can be seen on this image does not

VISAPP 2006 - IMAGE ANALYSIS

408

(a) (b) (c)

(d) (e) (f)

Figure 2: Edge detection results using: (a) the proposed method; (b) Sobel; (c) Roberts; (d) Prewitt; (e) Canny and (f)

LoG.

present enough contrast to be clearly detected by any

of the methods employed (Fig. 2).

From the six images presented one can gather

that the different operators naturally produce

differing results. It is perceivable at once that the

results given by the Canny and LoG operators (Fig.

2e and Fig. 2f, respectively) are not at all suitable for

crater recognition. The typical retention of major

details by these two approaches becomes a drawback

since they are very sensitive to low-frequency

perturbations, which are a major feature of the

images from the surface of Mars. It can also be

noticed that, as expected, the Sobel, Roberts and

Prewitt operators produce very similar results (Fig.

2b, Fig. 2d and Fig. 2e, respectively), with the

Roberts operator detecting a smaller number of

minor edges than the other two. Finally, our

approach produces an image (Fig. 1a) where the

contours with higher contrast become reinforced: the

resulting edges are thicker and a merging of adjacent

regions occurs, producing a smaller number of

connected components (and avoiding the problem of

double edges, a consequence of the long shadows

produced by the topography of crater rims and the

angle of the sun). Moreover, the smaller edges with

low local contrast are not retained, which means that

we end up with a less noisy image.

4 CRATER RECOGNITION

The results (binary images) obtained by the

application of the edge detection techniques

mentioned were used as input for a method for crater

recognition that is still in development (phase 3 of

our general methodology). Currently the best results

are obtained by a procedure based on a template

matching approach, through the application of the

Fast Fourier Transform (FFT). The general sequence

of this crater recognition method is the following:

1. Template matching with a simple circular

crater model (a crown) using the FFT approach;

2. Analysis of the correlation matrix in order to

find the local maxima;

3. Selection of the maxima in the correlation

matrix according to a circularity index.

These steps are performed for each crater radius

value within a certain predefined range (normally

from 5 to 100 pixels).

This sequence was performed with our approach

and with two other edge detectors (Sobel and

Roberts). Since the Prewitt operator images were

very similar to the ones given by the Sobel operator

it was decided to work only with the latter. For

illustrating purposes, the craters recognized in the

image of Fig. 1 with these three operators are

presented in Fig. 3. From the 14 craters that can be

visually detected in Fig. 1 (craters with very small

ENHANCING IMPACT CRATER CONTOURS TO INCREASE RECOGNITION RATES

409

radius were not considered), our approach was able

(a) (b) (c)

Figure 3: Crater recognition results for image of Fig. 1 using: (a) the proposed method; (b) Sobel; (c)

Roberts.

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

Figure 4: Crater recognition results for images (a) E1900566; (b) E1900716 and (c) R0200837 using: (d, e, f) the

proposed method; (g, h, i) Sobel operator and (j, k, l) Roberts operator. [NASA/JPL/MSSS].

VISAPP 2006 - IMAGE ANALYSIS

410

to detect 9 true craters (64% of success) and only

one false one (Fig. 3a). The Roberts operator

detected a total of 8 objects, from which 7 (50%)

were true craters and 1 was false (Fig. 3b). On other

hand, the Sobel operator (Fig. 3c) did not put in any

false crater, but instead was only able to recognize 3

true craters (21%).

Other examples applied to quite different images

are presented in Fig. 4.

Although globally our approach is the best one,

with higher recognition rates among the three and

lower number of false crater recognitions, there are

some points that deserve to be mentioned.

For the image E1900566 (Fig. 4a), our approach

and the Sobel operator are not able to detect the

crater located at right centre, which the Roberts

operator is able to recognize. This is sometimes the

price to be paid when the detection of false craters is

to be kept low: our approach and the Sobel operator

add both one single false crater (Fig. 4d and Fig. 4g,

respectively) while the Roberts operator includes 3

additional fake structures (Fig. 4j). The linear edges

that are visible in this image do not disturb the

recognition (but this is due to the matching approach

followed).

The results obtained on image E1900716 (Fig.

4b) by our approach (Fig.4e) demonstrate that the

craters can be recognized without being completely

included in the image (see the recognition of the

crater at top left corner) and also that overlap-ping

structures can be recognized without any problem.

A compromise between the detection of all the

craters and the inclusion of false craters is evident in

image R0200837 (Fig. 4c): our approach (Fig. 4f)

introduces one false crater but detects correctly 15

out of the 18 craters available; the Roberts operator

(Fig. 4l) does not add up any false crater but is only

able to detect 10 out 18 craters. Moreover, the

detection of the larger crater would be possible but it

would introduce an undesirable number of false

craters.

5 RESULTS, DISCUSSION AND

FUTURE WORK

We have applied three different edge detectors (our

approach, Sobel and Roberts) to a set of 26 images

obtained by the Mars Orbiter Camera aboard the

Mars Global Surveyor probe during the mapping

phase. These images, with a spatial resolution of

about 245 metres/pixel, cover a total area of

approximately 350000 km

, and were selected from

different regions of the planet so that the

methodology could be tried on the whole range of

cratered terrains present on its surface. The global

results can be seen in Table 1.

Table 1: Comparison of results between the proposed

approach and other edge operators.

Craters Our

approch

Sobel Roberts

# 157 98 147

Recognised

% 62.30 38.89 58.33

# 32 27 34

False

% 16.93 21.60 18.78

On average, 62.30% of the 252 craters with a

diameter larger than about 1.2 km (5 pixels) that are

visually recognizable on the 26 images were

correctly detected, a result that can be regarded as

very satisfactory, considering the differing

characteristics of the areas under study. This value is

on the same level of crater recognition which is

announced in other recent publications (Plesko et al.

(2004), Barata et al. (2004), Kim at al. (2004) and

Earl et al. (2005)). Our edge detector approach

obtains better results than the other two methods, not

only in what concerns crater recognition, but also as

regards the number of false positives. This is a

problem that plagues all the approaches to the issue

under consideration, and the results currently

presented can be considered as major improvements.

For the future we intend to fully automate the

proposed method of edge detection, by making the

choice of parameter λ independent from human

intervention. We believe that this goal can be

achieved through the use of some quality criteria,

namely the ones proposed by Levine and Nazif

(1985).

In what concerns the template matching phase,

which is out of the scope of this paper, the

corresponding methodology for crater recognition is

under development, and improvements are to be

expected. These should lead to higher precision in

crater recognition, as well as even smaller numbers

of false crater detections.

ACKNOWLEDGEMENTS

The results presented in this paper have been

developed in the frame of research project

PDCTE/CTA/49724/03.

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411

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