Identi�cation of Martian Polygonal Patterns

Using the Dynamics of Watershed Contours

Pedro Pina�� Jos�e Saraiva�� Louren�co Bandeira� and Teresa Barata�

� Centro de Geo�Sistemas� Instituto Superior T�ecnicoAv� Rovisco Pais� �������� Lisboa� Portugal

ppina�alfa�ist�utl�pt� Centro de Geof�isica� Universidade de CoimbraAv� Dias da Silva� ������ Coimbra� Portugal

Abstract� This paper presents a methodology to automatically identifypolygonal patterns on the surface of Mars� These structures� which aretypical of periglacial regions� result from climate oscillations and presenta wide variation in size� shape and topology and occur in dierent typesof terrains with rather dierent constituents and spectral re�ectances�The proposed approach is mainly based on the analysis of the dynamicsof watershed contours and is successfully applied to a set of dierenttypes of patterned terrains of Mars shown by MGS�MOC images�

� Introduction

Polygonal patterns occurring in periglacial regions of the surface of the Earth arethe signature of climatic oscillations� Similar structures appear on the surface ofMars and their characterization could provide a better understanding of the pastmartian climate ����� The occurrence on Mars of similar polygons to those foundin periglacial regions of the Earth has been a matter of discussion for the lastthree decades� Large polygonal patterns were �rst identi�ed in the Viking images�middle ���s � possibly originated by periglacial processes� but with a moreprobable origin on tectonic stresses� Later� in the late ���s� the higher spatialresolution images of the Mars Orbiter Camera �MOC of the Mars Global Sur�veyor probe �MGS have shown small�scale polygons much more similar in sizeto terrestrial patterned ground �� ���� If these polygons are caused by periglacialprocesses� their study can yield information about recent modi�cations of ice dis�tributions and climate on Mars� The formation of patterned terrains on Earthoccurs in periglacial or alpine regions that are subject to permanent or tem�porary freezing temperatures� The climatic e�ects that control their formationare the freeze�thaw �formation of sorted polygons and the thermal contractioncycles �formation of crack networks due to the decrease in ground ice duringsummer � It must be pointed out that in both of these processes the presenceof ice in the ground plays a fundamental role ����� For illustrating purposes wepresent in �gure � a small set of images of these martian patterns acquired byMOC�MGS on several locations of the southern hemisphere� The di�erences onthe size� shape and topology are quite evident� on a great diversity of terrains�

a� M������� b� R������� c� R�������

d� S������� e� R������� f� M����

g� E������� h� E������ i� E������

Fig� �� Examples of some martian polygonal patterns extracted from MOC�MGS im�ages NASA�JPL�MSSS��

Moreover� the cracks or contours of the polygons appear sometimes darker andother times brighter than the terrain itself�

In what concerns related works� there exist several studies presenting de�tailed characterizations of these polygons on the surface of Mars� Most of thempresent qualitative descriptions ���� �� ��� �� and the ones presenting quantita�tive approaches ��� ��� use manual processes to extract the relevant features� Formartian terrains none of these approaches uses an automated method to extractand characterize those patterns� The only published study proposing an auto�mated approach focus on Venus and in the detection of polygonal fractures onSAR images obtained by the Magellan probe ����� Although the complexity ofvenusian radar images is high� the textural variations from location to locationare not very marked and allowed a good recognition�

Consequently� we developed an automated approach to identify polygonalpatterns on the surface of Mars� It is constituted by two main phases and it isintended to be applied to a polygonal ground independently of the type of terrainwhere these patterns occur� The �rst phase consists of a pre�processing stage�where noise is �ltered out and contours are enhanced� This goal is achieved byapplying opening and closing by reconstruction �lters� In the second phase� thecontours of the images are identi�ed through the watershed transform� This isfollowed by their analysis according to their relevance relatively to the minima ofthe adjacent basins which permits to construct an image containing informationabout their dynamics� The adequate thresholding of this image leads to obtainingthe most relevant contours that correspond in our images to the cracks separatingthe polygons�

� Filtering

The patterns themselves divide the terrain into a set of polygonal structures� i�e��the soil or ice is divided by cracks constructing normally a connected network�In other situations� the cracks are branches with terminations� i�e�� branches notconnected in one of its extremities� These cracks always exhibit a certain contrastwith the background� sometimes darker than the terrain itself �normally whenthe terrain is constituted by ice � sometimes brighter than the terrain �whenthe terrain is mainly soil � In order to segment these images we applied thewatershed transform directly to the images� However� a pre�processing stage isneeded before segmentation in order to �lter out some local noise and to enhancethe borders of the polygons�

Normally� some of the edges of the polygons in the initial images acquired bythe MOC instrument are not well de�ned in some locations due to insu�cientspatial resolution or due to some un�nished physical process� We admit thatsome of these �faulty� edges� whose distance is inferior to a certain distance ��can be recovered� In addition� the presence of some local intensity variations onthe images should also be �ltered out�

A good approach to enhance the edges and to �lter some noise is to apply amorphological �lter by reconstruction which has the property of simplifying the

images while preserving contours ����� The most common of these �lters are theopening and closing by reconstruction� The opening by reconstruction removespixels of the foreground from an image by any given criteria and reconstructsall connected components of the image that had not been totally removed� Theopening � by reconstruction R of size � of an image f ���R is de�ned as thereconstruction by dilation � of f from the erosion � of size � of f �

��R�f � R�f ��

��f �� ��

The closing � by reconstruction R ���R is the dual transform of the openingby reconstruction and is de�ned as�

��R�f � R�f ��

��f �� ��

The application of these �lters is illustrated with an image selected for thepurpose� which is the one presented on �gure �c� Firstly� we apply a closing ofsize � � � ��gure �a � which has the e�ect of reinforcing the brighter struc�tures �including the contours of the polygons � and to �ll or group some localminima� Secondly� we apply a closing by reconstruction of the same dimension��gure �b � where the edges are maintained and reinforced� Since not all theminima are �ltered� we have applied� after the closing by reconstruction� anopening by reconstruction to �lter out those structures ��gure �c � The evalu�ation of the results of this �ltering phase will be done in the next section withthe corresponding watershed results�

a� b� c�

Fig� �� Morphological �ltering with dimension � � �� a� Closing� b� Closing byreconstruction� c� Closing and opening by reconstruction�

� Segmentation and dynamics

The segmentation of the polygons is performed through the watershed transform�this is followed by the analysis of the dynamics of its contours in order to retainonly the relevant edges� Currently we force the polygon cracks in the images

to be lighter than the patterns by computing� when necessary� the negativeimage in order to apply correctly the watershed transform� In the future we willautomatically verify this situation and proceed with the required adjustments�

��� Segmentation by watershed

Using a �ooding analogy from the minima of a topographic surface� the catch�ment basins CB of an image f associated with a minimum MIN are obtainedthrough the application of the watershed transform WS ���� These basins canbe considered as the in�uence zones of the minima MIN of the image� beingthe watershed lines given by the skeleton by in�uence zones SKIZ of theseminima ���� Thus� the watershed WS of an initial input image f is then givenby�

WS�f � SKIZf �MIN�f �� ��

Complete overviews of the watershed transform can be found in ��� ��� One ofthe most common and fastest approaches to compute the watershed transformis based on immersion simulations ����

We then compute the watershed lines of the images resulting from the �lteringphase ��gure � � The minima of the image �ltered by closing are almost as abun�dant as in initial one� and lead naturally to an overssegmented image ��gure �a �In the image �ltered with a closing by reconstruction� some of the minima arenot reconstructed and the corresponding watershed is a less segmented imagewith a higher approximation to the real polygonal structures ��gure �b � Any�how� most of these contours are locally very irregular� a fact which re�ects theirregularity of the minima� The application of an opening by reconstruction af�terwards� permits to smooth these contours and to �ll some of their small holes�Consequently� the watershed lines are locally more regular ��gure �c �

Although the number of basins was considerably reduced with the �lteringphase� we still have a large number of contours that do not correspond to crackson the terrain �false positives � In general� the contours corresponding to thecracks are lighter than the other contours� but due to a large variation on someparts of the contours� this cannot be adopted as a �xed rule� A pattern canindeed be found in the local contrast between each contour and the two minimaof its adjacent basins� The exploitation of this di�erence is the objective of thenext section�

��� Dynamics of watershed contours

The contours detected by the watershed transform should be analysed in orderto decide which ones are relevant and those that are not� We follow the ap�proach presented by Najman and Schmitt ���� that established a dynamics ofthe contours through a contrast criterion that measures the grey�level di�erencebetween a peak and its surrounding minima�

a� b� c�

Fig� �� Segmentation with minima �rst row� and watershed lines second row� for theimages of �gure �� a� Closing� b� Closing by reconstruction� c� Closing and openingby reconstruction�

Let the set of catchment basins be designated by fBig and an arc of thewatershed by C� Among the set of x points that constitute each arc� we designatethe one with the lowest level by s� being its value given by I�s � minx�C �I�x ��The point s is called a saddle point�

Let Bas�C be the set of points of the catchment basins that can be reachedfrom s by following a path with all values lower than I�s and mi its minimum�mi � minx�Bi�C �I�x �� The dynamics of the contour dyn�C can in this way bede�ned as in ���� through the expression�

dyn�C � min�I�S �mi�� ��

The dyn�C has a range of values between � and ��� To measure the dy�namics of each contour it is necessary to individualize each contour or edge�The removal of the vertices or multiple points of the watershed lines permits toobtain all the edges� Each contour has two neighbouring basins each one witha local minimum� The computation of the dynamics of each contour is easy toperform ��gure �b � We can visually compare this result with an image of thevalues of the watershed transform on the initial image ��gure �a � and concludethat this step is a major improvement enhancing the di�erent importance of thecontours�

The thresholding of this dynamics image at adequate levels permits to obtainthe image of the relevant contours� i�e�� the contours that correspond to the

real cracks ��gure �a � The corresponding ground�truth image is presented in�gure �b�

a� b�

Fig� �� Values of the watershed contours on the� a� initial image� b� dynamics image�

a� b�

Fig� �� a� Thresholding of contour dynamics image� b� Ground�truth contours�

� Results

We have applied the same sequence ��ltering by closing and opening by recon�struction of size � � � followed by the analysis of watershed contour dynamics �to a subset of the images previously presented ��gure � � The evaluation of ourapproach was performed by measuring the length of all contours and comparingthem with the ground�truth images� whose contours were manually identi�ed�The results obtained are presented in table ��

The results obtained are highly satisfactory� The recognition rate is in allcases above ��� and� in one particular image �R������ � the success was al�most complete� We are aware� that this image shows a particular type of terrain

were the cracks are almost always very well de�ned against a spectrally uniformbackground terrain�

Another important conclusion to retain is the low level of detection of falsepositive contours� The observation of these �fake� contours leads to the conclu�sion that they normally have small lengths and result from strong local minimathat were not suppressed during the �ltering phase�

Table �� Recognition rates of polygon contours�

Image Ground�truth Automatic Automatic False Positives pixels� pixels� �� pixels�

M������� ���� ��� ����� ��R������� ���� ���� ����� ���R������� ��� ���� ����� ���M���� ����� ��� ���� ���E������� ���� ����� ���� ��

� Conclusions

The main objective of the development of this methodology was achieved sinceit can be considered capable of general application to the identi�cation of polyg�onal patterns in a wide variety of Martian terrains with very few algorithmicparameters to tune�

Although the results obtained demonstrate the robustness of the proposedapproach� we believe that there is still room for improvement� In order to increasethe recognition rates� we think that further enhancement of the crack contoursduring the �ltering phase is still possible� The introduction of some directionaloperators to reinforce these structures is a possible solution� In addition� theautomated selection of the thresholding levels on the contour dynamics image isa feature that we intend to incorporate in the future�

Finally� we intend to apply our methodology to images of larger dimensionand to link this identi�cation phase to a characterization phase where geometricand topological features will be computed�

� Acknowledgements

This paper results from the research developed in the frame of the researchproject PDCTE�CTA��������

References

�� Beucher S�� Lantu�ejoul Ch�� Use of watersheds in contour detection� In Proceedings ofInternational Workshop on Image Processing� Real Time Edge � Motion Detection�

Estimation� Rennes� France ����� �� pages��� Beucher S�� Meyer F�� The morphological approach to segmentation� The watershedtransformation� In Mathematical Morphology in Image Processing� E�R� Dougherty�Ed�� pp� ������ Marcel Dekker� New York� ����

� Bleau A�� Leon L�J�� Watershed�based segmentation and region merging� ComputerVision and Image Understanding� �� ����� ������

�� Buczkowski D�L�� McGill G�E�� Topography within circular grabens� Impli�cations for polygon origin� Geophysical Research Letters� ���� ����� �����doi�������������GL�������

�� Hiesinger H�� Head III J�W�� Characteristics and origin of polygonal terrain in south�ern Utopia Planitia� Mars� Results from Mars Orbiter Laser Altimeter and Mars Or�biter Camera data� Journal of Geophysical Research� ���E� ����� ������������

�� Kargel J�S�� Mars � A warmer� wetter planet� Springer� Berlin� ������� Kossacki K�J�� Markiewicz W�J� Martian seasonal CO� ice in polygonal troughs insouthern polar region� Role of the distribution of subsurface H�O ice� Icarus� �� ����� �����

�� Langsdorf E�L�� Britt D�T�� Classi�cation and distribution of patterned ground inthe southern hemisphere of Mars� Lunar and Planetary Science XXXVI� ��� ������

�� Malin M�C�� Edgett K�S�� Evidence for recent groundwater seepage and surface run�o on Mars� Science� ��� ����� ������

��� Malin M�C�� Edgett K�S�� Mars Global Surveyor Mars Orbiter Camera� Interplan�etary cruise through primary mission� Journal of Geophysical Research� ���E� ����� ����������

��� Mangold N�� Maurice S�� Feldman W�C�� Costard F�� Forget F�� Spatial re�lationships between patterned ground and ground ice detected by the NeutronSpectrometer on Mars� Journal of Geophysical Research� �� E�� �����doi�������������JE������

��� Moreels P�� Smrekar S�E�� Watershed identi�cation of polygonal patterns in noisySAR images� IEEE Transactions on Image Processing� ���� ���� ��������

�� Najman L�� Schmitt M�� Geodesic saliency of watershed contours and hierarchi�cal segmentation� IEEE Transactions on Pattern Analysis and Machine Intelligence�

����� ����� ����������� Salembier P�� Serra J�� Flat zones �ltering� connected operators� and �lters byreconstruction� IEEE Transactions on Image Processing� ��� ����� ���������

��� Seibert N�M�� Kargel J�S�� Small�scale martian polygonal terrian� Implications forliquid surface water� Geophysical Research Letters� ���� ����� ��������

��� Smrekar S�E�� Moreels P�� Franklin B�J�� Characterization and formation of polyg�onal fractures on Venus� Journal of Geophysical Research� ���E�� ����� �����doi�������������JE�������

��� Soille P�� Morphological image analysis� Principles and applications� Springer�Berlin �����

��� van Gasselt S�� Reiss D�� Thorpe A�K�� Neukum G�� Seasonal variations of polyg�onal thermal contraction crack patterns in a south polar trough� Mars� Journal ofGeophysical Research� �� E�� ����� doi�������������JE������

��� Vincent L�� Soille P�� Watersheds in digital spaces� an e�cient algorithm based onimmersion simulations� IEEE Transactions on Pattern Analysis and Machine Intel�

ligence� ���� ����� �������