Hough Transform for Region Extraction in Color Images

SarifKumarNaik C. A. MurthyMachineIntelligenceUnit MachineIntelligenceUnitIndianStatisticalInstitute IndianStatisticalInstitute

203B. T. Road,Kolkata-700108 203B. T. Road,Kolkata-700108sarif r@isical.ac.in murthy@isical.ac.in

Abstract

Thisarticle aimsto proposea methodto usethe ideaofHoughTransform(HT) implementedin grey scaleimagesto color imagesfor region extraction. A region in an imageis seenasa unionof pixelson several line segmentshavingthe homogeneityproperty. A line segmentin an image isseenasa collectionof pixelshavingthepropertyof straightline in Euclideanplaneand possessingthe sameproperty.Theproperty ’homogeneity’ in a color image is basedonthetraceof thevariancecovariancematrix of thecolors ofthepixelson thestraight line. Asa possibleapplicationofthemethod,it is usedto extract thehomogeneousregionsintheimagestakenfromtheIndianRemoteSensingSatellites.

1. Intr oduction

HoughTransform(HT)hasbeena widely usedmethodfor extracting arbitrary shapesfrom images. It was de-signedto extractstraightline segmentsfrom binaryimagesby Hough[3]. Usually HT is appliedon binary images[4].To extract line segmentsor any geometricstructureusingHT, from a gray scaleimage or color image one has totransformit to a binary imageusing thresholdingor anyothermethod.Usually, thesebinarizedimagesaretheedgemapsof the original grey level or color image. Thereareveryfew worksdealingwith applyingHT ongrey scaleim-agesdirectly[8, 10, 5] i.e. without thebinarization.To thebestknowledgeof the authors,no methodhasever beenproposedfor implementingHT directly to color or multi-spectralimages.

Hough transformis an extensively studiedmethodoffeature(line/curve)extractionfor binaryimages[7, 6, 1] be-causeof its robustnessto imagenoiseandthediscriminationability againstunwantedshapes[4]. A survey of theHT forbinaryimagesappearsin [2]. Thusonly abrief introductionto HT is presentedto introducethe notationandterminol-

ogyusedin thelaterpartof thearticleandashortsurvey ofit usesin grey level imagesis presentedhere.

Basically, HT is avotingprocesswhereeachpixel of theimagevotesfor all possiblepatternspassingthroughthatpoint. The votesareaccumulatedin an accumulatorarray���������

, where,�

is the anglemadeby the normal to thestraightline with the � � axisand

�is theperpendiculardis-

tanceof thestraightline from theorigin. Therepresentationof thestraightline in (

�����) form is

������� ����� ����� ������ (1)

This accumulatorarray���������

is called the HoughSpace. Number of votes for eachcell in

����������repre-

sentsthenumberof pixelsin thepatternpassingthroughthepoint (� �!� ). In this processeachpixel in theimagespaceismappedto a sinusoidalcurve in theHoughspace.SoHT isa transformationfrom a point to acurve.

Lo et al,[8] proposeda techniqueto implementHT di-rectly to grey scaleimagewithout thresholding,andwith-out finding the edgemapof the image. They useda fourdimensionalaccumulatorarray, where "�# , the grey valueof the pixel is the additionaldimensionalongwith

�and�

ascomparedto conventionalHT. Hereeachpixel (��# �!� # )in theimagespaceis associatedwith its grey value "�# andeachaccumulatorcell

���$�����%� " # in thegrey-scaleHoughparameterspace.It findsline segmentsin grey-scalebands.This methodis expensive in thesenseof spacecomplexity.Shapiro[11] proposeda methodthat replacesthe originalimageby its digital half toningequivalent.A decisionmak-ing procedurecalledDigital Half toningHoughTransform(DHHT), allowing theHT to work with arbitrarymultilevelimagesis proposedin this paper. DHHT is an amalgamof theconventionalHT andDigital Half toning. Kesidisetal[5] proposedaGrey-scaleInverseHoughTransformalgo-rithm whichis combinedwith amodifiedGrey-scaleHoughTransform.Thesaidmethodis implementedto detectlinesegmentsdirectly from a grey-scaleimage.

UmaShankaret al [10] proposeda techniqueto extractline segmentsdirectly from a grey scaleimagewithout us-

ing thresholdingor the edgemapof the image. A regionon a grayscaleimagehasbeendefinedasunionof severalconnectedline segmentsanda line segmentis definedasastraightline with thepropertyof uniformity amongthepix-els on the line. The propertyof uniformity is the valueofvarianceof grayvaluesof thepixelsontheline. Theformaldefinitionsof thesearediscussedin thelaterpartof thearti-cle. Thesaidtechniqueis usedto find uniformregionsfromremotelysensedimages.

The main ideabehindthis work is describedin section2. Definitionsrelatingto this andsomepropertiesarede-scribedin section3. Section5 dealswith implementationand results. Section6 providesan analysisof the resultsandthescopefor furtherresearch.

2. Moti vation

The idea of the methodproposedby Uma Shankaretal., for region extraction using HT in grey-scaleimages.The work in [10], canbe extendedto color images.Theirmethodhasbeenrevisitedhereparallellywith thedevelop-mentof our methodwith somechangesto the definitionsproposedby them. Uma Shankaret al [10], constructedabinaryimageconsistingof all homogeneousline segmentswith the help of HT. A line segmentis considered,its ho-mogeneityis checkedandall homogeneousline segmentsarefound in this process.A generalizationof the above isto

1. constructapropertyP,

2. checkwhetherthepixelsin theline segmentsatisfyP,

3. createafile of line segmentspossessingthepropertyP.

The propertyP has to be definedaccordingto the re-quirement.For region extractionthepossiblepropertycanbe the uniformity of grey valuesor color of the concernedsetof pixels.

3. Definitions

A line segmentin a grey level imageshould,in princi-ple,representahomogeneoussetof pixelslying onthelinesegment,homogeneity is to be measuredwith respecttogrey valuesof theconcernedpixels. Theword homogene-ity maybeviewedin differentways.Onewayis to makethevariationin thegrey valuesof thepixelsontheline segmentsmall.Anotherway is to definesimilarity betweentwo pix-elsdependingon thegrey valuedifference,andmakingallthepointson the line segmentsimilar to eachother. Thereareotherwaysof viewing homogeneity. In this article,werestrictourselvesto theabovetwo waysonly.

Theabove two conceptsyield differentexpressions.Forexample,if � & � �(' �� � � �� �*) denotethegrey valuesof thepix-els lying on a line segmentin a grey level image,in orderto implementthe first way we needto find the varianceof� & � � ' �� � � �� � ) andcheckwhetherit is lessthana thresh-old value. Secondway is to considera thresholdvalue +anddefinethattheconsideredline segmentis a valid oneif, � # �-�*. ,0/ +21�3 �!4 . Thesetwo waysof measuringhomo-geneityleadto differentmeasuresof evaluatingthevalidityof line segments.Uma Shankaret al[10] incorporatedthefirst way to find line segmentsandconsequentlyregionsinthe grey level images.We shall generalizethe above con-ceptsfor color images,asstatedbelow.

Unlike,grey level images,apixel in acolor imageis notrepresentedby a scalarbut by a vector( 5 � " ��6 ), denotingfor red, greenand blue componentsof color respectivelyandeachof themliesbetween0 to 255.

Homogeneityof color pixels on a line segmentmay beviewedin two ways.Onewayis to definethatasetof pixelspossesshomogeneityif for eachof the threecomponents,the pixels arehomogeneous.Anotherway of definingho-mogeneityof thepixelsis by combiningthevaluesof all thesetof pixelswithout looking at themindividually. Formaldefinitionsof all theseconceptsarestatedbelow.

Let 7 be a color imageandthe color of a pixel (3 �!4 ) isdenotedby ( 5 � 3 �!40!� " � 3 �!408��69� 3 �!40 ).Definition 1: Let : �<;� 3�& �84 & !�=� 38' �84 ' !�� � � ��>� 3?) �!4 ) 8@ bean ordered set of pixels. : is said to be connected if(3?A%BC& �84 ADBE& ) is in the 8-neighborhoodof (3?A �!4 A ) 1GF �H �?IJ�� � � LK

.Definition 2: A set of connected pixels : �;�� 3 & �!4 & 8�>� 3 ' �!4 ' 8�� � � >� 3 ) �!4 ) 8@ is said to be a possibleset for a line segment (PSLS) if M � and

�such that

3 A ���D� ���N4 A �?��� �O�2� 1NP�QRFSQ KT Fromtheabovediscussion,homogeneityof asetof pix-

elsfor a color imagecanbedefinedin any of thethreewaystatedbelow.Definition3: Let : �R;�� 3UA �84 A V F � P � H �� � � LKW@ bea setofpixelsandlet thetriplet ( 5 � 3?A �!4 A 8� " � 3?A �84 A !��69� 3?A �84 A ) bethecolor of the F�XZY pixelof theset. : is saidto behomoge-neousif it satisfiesanyoneof thefollowing threecriteria:

1.

[]\�^A� 5 � 3 A �!4 A ? � [ ���A

� 5 � 3 A �!4 A ? / +`_ �

[]\D^A� " � 3 A �!4 A ? � [ ���A

� " � 3 A �!4 A ? / +`a �[]\�^A

�869� 3UA �!4 A U � [ ���A�!6]� 3?A �84 A U / +�b �

where, + _ � + a and +`b are the thresholdvalues for5 � " � and

6componentsrespectively.

2. c '_ / + _ed KTf c 'a / + agd KTf c 'b / +�b , wherec '_ � c 'a d KTf c 'b are thevariancesand + _ � + ahd KTf +�b

are thethresholdvaluesfor 5 � " � d KTfi6 componentsrespectively.

3. j�& � j' � j�k / + , where, j�& � j�' d KTf jk are theeigenvaluesof the variancecovariancematrix l of the setof pixels. + is a thresholdvalueof thesumof theeigenvalues. Alternatively, Trace(l )

/ + is the equivalentconditionbecausetheTrace(l ) is sumof theeigenval-ues.

Note 1: Thoughhomogeneitycould be definedfor anycolor space, the definition is given for 5i" 6 color spacehere becausethe valuesfor each of the threecomponentsvary in thesameinterval of 0 to 255,which is necessarytocomputethevariancecovariancematrix.Note2: Thechoiceof takingthesumof theeigenvaluesisproper becauseof the propertyof the eigen valuethat the3UXZY largesteigen valueof the variancecovariancematrixgivesthevarianceof the 3?XZY principal component[9].

Definition 4: A possibleset of line segment(PSLS) issaidto bea valid line segment(VLS) if it is a setof pixelswith homogeneouscolor and the cardinality of the set ismon

.n

is the minimumnumberof pixelson a straight linesegment.

Mathematically, a line segmentcanbe definedin termsof two thresholdparameters

nand + , where

nis the mini-

mumnumberof pixels in thePSLSand + is themaximumallowedvaluefor thesumof theeigenvaluesof thevariancecovariancematrix. With theseparametersa mathematicalwayof defining pO:Wq usingdefinition3(3r3r3 ) is givenbelow.Definition5: A PSLS : � n � + s�e;�� 3 A �!4 A !� F � P � H �� � � rKW@is saidto bea VLS if

1. numberof pixelson theline segmentL(n � + ) mtn ,

2. Trace(l )/ + where, l variancecovariancematrix.

Definition 6: Two line segments: & � n � + and : ' � n � + aresaid to be connectedlines if : & � n � + vu : ' � n � + ]w�ex

or Manytwo pixels y{zh: & � n � + and |ezh: ' � n � + such that yis an 8-neighborof | .Definition7: Let } �e; :vA � n � + 8� F � P � H �� � � ~ ���@ is a setof�

line segments.} is saidto bea connectedsetof linesegmentsif :vA%BC& is connectedto :vA�1EF � H �UIJ�� � � ���� .Definition 8: Let � ��; :�A � n � + !� F � P � H �� � � �����@ is aconnectedsetof line segmentand

} ���A`�W& :�A

� :vA�z��

Then } is saidto bea region if : A � n � + z�� is a valid linesegment1EF Note3: In definition3, threewaysof defininghomogene-ity are given. Amongthem,the definition which providesa combinedaffectof thethreecomponents5 � " ��6 is the

definition3(3L3r3 ). Secondly, thenumberof thresholdvaluesto be chosenis lessfor definition 3(3r3r3 ) compared to def-initions 3(3 ) and (3L3 ). Thus,we shall confineourselvestodefinition3(3L3r3 ) in theremainingportionof thisarticle.

Figure 1. Original Kolkata Image taken from IRS-1A

Figure 2. Extracted regions in Kolkata Image(IRS-1A) with� = 16,n= 14, + = 1.2

4. Formulation and Implementation

HT canbeimplementedon theentireimagedirectly butit is notwiseto applyonthewholeimageatatime,because,it is notgoingto becomputationallyefficient. Additionally,it requiresmorememoryspace.If the sizeof an imageis�����

and�

and�

arevery largethenthresholdvaluenfor the lengthof the line hasto bechosenlarger, thereby

Figure 3. Extracted regions in Kolkata image(IRS-1A) by

K-meansalgorithm with��� H

eliminatingfinding smalleruniform regions. To avoid thisproblema smallwindow of size � � � needsto bemovedon theentireimageandvalid line segmentsareto befoundin eachof the � � � windows. It may alsobe notedthatsuitablediscretizationof

�and

�valuesneedsto bedonefor

computerimplementation.Thus,thestepsto befollowedtoextractvalid linesegmentsin awindow aredescribedbelow.

1. Considera � � � window.

2. ConstructtheHoughaccumulatorspaceby transform-ing theeachpixel of thewindow usingdifferentvaluesof�

andtheircorresponding�

values.Value�

for each�canbefoundusing(1). Thevaluesof

�variesfrom�(�

to P~� �(� � �~� XZ�8� with a steplength�~�XZ�8� . Note that� �

XZ�8� is to bechosenin sucha way that P�� � � is a mul-tiple of

� �XZ�8� . Theobtainedvalueof

�is approximated

to thenearestinteger.

3. After constructingtheHoughSpacefor awindow, scantheHoughSpaceandconsiderthosecellswherecountis greaterthan or equal to

nand re-mapthis cell of

Houghspaceto imagespace.This is a possiblelinesegment.Thecellswith count

/ naresimply ignored.

In this way spuriousline segmentswhoselengthsarelessthan

nareeliminated.

4. ComputeTrace(l ) of the color triplets of the pixelscorrespondingto eachof the cells with count

m�n. If

it is lessthan + thenconsiderit asa valid line segmentelsetheline is ignored.Thisstepeliminatesthoselineswhichdo not possesshomogeneouscolorpixels.

5. Restorethe color triplet from the original imagein a

new imagefor the valid line segmentsdetectedin theabovestep.

Without consideringthe original color triplet in the im-ageandfor a fixedwindow size � , thepossiblesetof linesegmentsaresamefor all the possiblewindows in the im-age. Thuscomputingthe steps(3L3 ) and(3r3L3 ) onceis suffi-cient. This reducesthe computationtime significantly. Inorderto find regionsin the image,line segmentsarefoundin all possible� � � windows. A file of theselines aremade.This file of linesform a region if thereis a homoge-neoussetof connectedpixelspresentin theimage.Thusintheprocessof finding theline segmentsregionsarelocatedin theimage.

5. Results

The parametersto be tunedin this algorithmare � � n �and + . � is theheight(numberof rows)andwidth (numberof columns)of thewindow. Thewindowstakenhereareallsquarewindows.

nis the minimum numberof pixels on a

possibleline segmentand + is themaximumallowedvalueof Trace(l ). Valuesof theseparametersare to be chosenproperly.

In this section,resultsprovided by the proposedalgo-rithm on IndianRemoteSensingSatellites(IRS) aregiven.Two imageframes,one from IRS-1A andone from IRS-1C, areconsideredfor this purpose.A pixel in an IRS-1Aimageoccupies,approximately,

I��J HD�%� � ID�J HD�%�area

on earthwhereas,in IRS-1C, it occupies,approximately,H I0 �%� � H I0 �%�. Boththeimageshavered,greenandblue

bands.In IRS-1A, thegrey valuesof eachbandvary from0 to 127whereasin IRS-1C,they vary from 0 to 255.Eachimageis a

� P H � � P H image.Sincetheoriginal imagespos-sesspoorintensityvalues,enhancedimagesof theoriginalsareshown in [Figs.1and4] herefor betterclarity andunder-standing.Fig.1showsenhancedimagesof theKolkatacitytakenby IRS-1A andFig.4shows theenhancedimageof asuburb namedBarrackporein thenorthernpartof Kolkata,takenby IRS-1C.

The valuesconsideredfor the lengthof the window(� )are P � and � . Minimum numberof pixelson a line segmentis consideredto be P�� when � � P � , andis consideredtobe � when � � � . The thresholdvalue + is taken to bea small value (i.e., + is

� � � P H or P � ) when the spatialresolutionis coarser(i.e., the imagetaken from IRS-1A),andthethresholdis takentobealargervalue(i.e., + is P �0� H �orI H

) whentheresolutionis finer.

6. Analysis and Conclusion

In this articlewe proposeda methodof extractionof re-gions from color imagesusing HT. Definitions of unifor-

mity of a region areprovided. A region is definedby theunionof several line segments.The methodhasbeenableto detectan arbitrary shapelike the Hooghly river in theKolkataimages.

Theresultsprovidedby theproposedalgorithmarecom-paredwith the resultsobtainedusingK-meansalgorithm.Outputof the K-meansalgorithmdependsuponthe initialpartition of the dataset, and thus the resultsmay be dif-ferent for different initial partitions. Here K-meansalgo-rithm is implementedtakingfive differentinitial partitions.The resultwhich is closestto the groundtruth is includedherefor eachof theimagesconsidered.K-meansalgorithmis chosenfor comparisonbecauseboth the proposedalgo-rithm and K-meanswith

��� H, result in classifyingof

pixels in two differentclusters.The proposedmethodhasbeenimplementedwith severalsetsof parametersasmen-tionedearlieron both the images.After the carefulobser-vation of the resultsobtainedwith theseparametervaluesFig.2andFig. 5 arefoundto beclosestto thegroundtruth.The parameterset usedto obtainedthesetwo resultsare(� � P �J� n � P~� � + � P H ) and(� � P �J� n � P~� � + � H � )respectively. The resultswith othersetsof parametersarenot includedheredueto lackof space.If weobservethere-gionsextractedin KolkataimagestheriverHooghlyis sep-aratedfrom therestclearlyby theproposedmethod.In Fig.3(resultfoundfrom K-meansalgorithm),riverHooghlyhasnot beenclearlyseparatedfrom theconcretestructureareapresentonbothsidesof theriver. This is especiallytrueforthesouthernpartof riverHooghly[Fig.3]. Thetwo bridges(Ravindra SetuandBally Bridge)on the river arealsonotclearly distinguishable[Fig. 3], whereasthe proposedal-gorithmprovidesthem[Fig.2 and5].

The definition of homogeneity(definition 3) of a setofpixels is givenwith threedifferentcriteriaandit is experi-mentallyseenthatall the threecriteriagive almostequiva-lentresultsvisually. Theresultsof usingthesehomogeneitycriteriaarenotshown herein theform of figuresdueto lackof space.Note that, with the criterion (3r3r3 ), the algorithmneedslesshumaninterventionbecauseit requireslessnum-ber of parametersto be supplied. Criteria (3 ) and(3r3 ) arestrict in the sensethat if the inequalityfails for any oneofthe components,the setof pixels is declaredasnot homo-geneous.In many situations,if the inequalityfails for oneor two componentsandif the over all variationis within alimit, thesetof pixelscanbesaidto behomogeneous.Thisis takencareof in criterion(3r3L3 ) andthusit makesthealgo-rithm robust. Thusthecriterion(3r3r3 ) in definition3 is usedto generatetheresultsprovidedhere.

Validity of a PSLS is controlledby tuning the parame-ter + . Eigenvaluesof thevariancecovariancematrix givesthevariationpresentin thecorrespondingprincipalaxesofthecolor vector. Thus,Trace(l ) is theoverall variationofcolor presentin thesetof pixels. This implies that the less

Figure 4. Original Barrac kpore Image taken from IRS-1C

thevalueof Trace(l ), lessis thevariationandmoreis theuniformity. In this way, by varying the valueof + , the va-lidity condition(i.e a PSLS is a valid line segment)canberelaxedor tightened.Thus,by increasingthevalueof + wearerelaxingthevalidity conditionfor a line segmentandin-creasingthechanceof a line to bevalid line segment.Thisjustificationis evidentif we observetheresultsof thesameoriginal imagewith same� and

nbut different + ’s. It is

observed that by increasingthe valueof + , the numberofregionsandthenumberof pixelsin eachregionareincreas-ing.

Connectednessand homogeneityof a set of pixels arethe two properties,which aretaken careof while decidinga setof pixels to be a region. Both of thesepropertiesdonot dependon the maximumandminimum grey valuesineachof the components.Homogeneitycondition is veri-fiedby checkingthevariationof coloramongtheconcernedsetof pixels. Homogeneityconditiononly dependson thethresholdvalue + . Thepresentwork doesnot give a proce-dureto choose+ . This needsfurther research.The valuesof + taken hereare1.2 for the IRS-1A images,and24 forIRS-1C image. Thesevaluesof + arechosenexperimen-tally. The valueof Trace(l ) of Kolkata andBarrackporeimagesare

H�  � � � � ��H and� P � � � � �D� I respectively. These

variancesarecomputedover the whole image. It may benotedherethat thevaluesof Trace(l ) in IRS-1A andIRS-1C imagesaresignificantlydifferent. This maybetherea-sonthat thevaluesof + for Kolkata(IRS-1A) imageis sig-nificantlysmallerthanthevaluesof + for Barrackpore(IRS-1C)image.Thevaluesof � aretakento be P � and� because�¢¡ P � maybetoobig whereas� / � maybetoosmallforextractingregions.Valueof

nis takento be7 when � � �

andnis takenas14 when� � P � . Thesamevalueof these

parametersarechosenalsoby UmaShankaret al[10]. Thevalueof � is takento beapowerof

Hthough,in practice,�

Figure 5. Extracted regions in Barrac kpore image(IRS-

1C) with � = 16,n= 14, + = 24

canbeany evennumber.The proposedmethodfails to find an object if the ob-

ject region containsmany small uniform regions. Nakedeye canfind structuresin an imagewhereasthe proposedalgorithmneednotfind them.Notethat,thehexagonalpor-tion of Kolkataimage[Fig. 1] is not classifiedasa regionby the proposedmethod. It is taken to belongto a singleclusterby K-meansalgorithm [Fig. 3]. An increasein +valueof theproposedmethodwould providethehexagonalstructure.But, it maybenotedthatan increasein + wouldentailseveralotherpixelsto becomepartof aregion,whichneednot beadvisablealways. Fine tuningof � � n and + isaproblemto beattemptedin nearfuture.

Thisarticledescribesanapproachto useHT to color im-ages.Resultsareencouraging.Hereline segmentsareob-tainedin color imagesusinga particulardefinition of theword “Homogeneous”.Probablytheremay be otherwaysof defininghomogeneity. In addition,giventheconceptofhomogeneity, theremay be other ways in which “HoughTransform”for binary/grey level imagesmay be extendedto color images.Theapproachdescribedin this work neednotbeunique.

References

[1] R. DudaandP. Hart. Useof the Houghtransformtodetectlines andcurves in pictures. Commun.of theACM, 15(1):11–15,19721972.

[2] J. Illingworth andJ. Kittler. A survey of the Houghtransform. Comp.Vis., Grapics,and Image Process-ing, 44(1):87–116,Oct.1988.

Figure 6. Extracted regions in Barrac kpore image(IRS-

1C) by K-meansalgorithm with�£� H

.

[3] A. K. Jain. Fundamentalsof Digital Image Process-ing. PrenticeHall of India,5th edition,1999.

[4] A. KesidisandN. Papamarkos. A window-basedin-verseHoughtransform. Patt. Recog., 33:1105–1117,2000.

[5] A. L. KesidisandN. Papamarkod. On thegray-scaleinversehoug transform. Image and Vis. Comput.,18(8):607–618,August2000.

[6] V. Leavers.WhichHoughtransform? Comp.Vis.andImageUnderstanding, 58(2):250–264,1993.

[7] V. F. Leavers. ThedynamicgeneralizedHoughtrans-form: Its relationshipto theprobabilisticHoughtrans-forms andan applicationto the concurrentdetectionof circlesandellipses.CVGIP:ImageUnderstanding,56(3):381–398,Nov. 1992.

[8] R. Lo andW. Tsai. Gray-scaleHoughtransformforthick line detectionin gray-scaleimages.Patt. Recog.,28(5):647–661,1995.

[9] C.R.Rao.Linearstatisticalinferenceandits applica-tion. JohnElley & Sons,secondeditionedition,1973.

[10] B. U. Shankar, C. A. Murthy, andS. K. Pal. A newgray Hough transformfor region extraction from irsimages.Patt. Recog. Lett., 19(2):197–204,Feb. 1998.

[11] V. Shapiro. On the Hough transformof multi-levelpictures.Patt. Recog., 29(4):589–602.,1996.