FOR IMPROVING

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HIERARCHICAL NEURAL NETWORK SYSTEM FOR

IMPROVING EDGE DETECTIO N

Dy

@Ant ho ny WingKaySzeto ,B.Se.

Athesissubm itted to theSchoolofGrad ua te Studiesin partia l fulfillment ofthe

requireme nt sforthe degreeof Mast erofScience

Department ofComp ut er Science MemorialUniver s ity ofNewfou ndland

April,1991

st.

John's New found la nd Can a d a

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...

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A BSTRACT

Thisthesispresents a hiera rchicalneural uotworksyslt'l1Ifo rimpW\'ll1l-(1.11l't,d !!;\,IUI'a Slin ', mentsobtainedbyan edgeoperator.The neurulnotwork s)'s1t'mis,1"si!!:IU'dIIIilIlj llst1I11' ed gemeasurement sbasednuIhe informat ionprovidedby lll'iglihullriu/l;t·ll!!;.,s.TIll'"d"IIIt-,1 strategyis toanalyzet.he10('111edge pa t ternsto det ermine andrt';ll rnrl'l'l~ll\t'slrud llrl"swhilt' suppressing unwanted noiseanti false edges.ThelliCTardlj("iducnrulnctwork sysn-m islll.ul,·

I1p of fOIlTlevels ofsubncts.TIlesubnetillthe firstle n·]musis1.sofhiJ;Ii'lln l" T1Il' lITil 1lid s todete rmi nethe potentialiHljustmclIl011Lhedelllf'ntorJUII'fl'sLhy(l<'l.,..Lill~.,-dl\" nlllt"llfS accordingto the selectedprocessesinthelIe uTalnt~tsil ll.1till'illl'utI"ca lc',I~,']lall"tll.TllP secon dlevel consistsof a cooperative-competitiveuoural 111'1.111mI.·]to ,1.,trTmill"Lh,·urie-n- tation ofthestrongested gecontou rill thelo r,,]c,]w~IJilUNI1.Tlll~slll"u'lilltit.'I.iiii'll1"w,1 consists oftwotypes ofneuralnetmo.lds. Ahigll'I/nl"rlll'l1nl1ll1't;}Sf('rL.,ill.~1.1,..n,."liti"lls for adjus tingthegradicntmegnitudc011111rld,Nll1illl~~themnouutuf,uljusll1l1'lIl. l,,,1I11' Il,r;"li cnt magnitu de.A scmiliucarIccdforwardIICtis usedtoWIll I'UI.i~Ll l'~1I,~W,ulj llsl.",1,l?,l"illlil'lIl magnitudeanddeterminesifthe clementofilll,'rr~listo1!I~ .1II,,,I).!,!,d.'mt'lIl,ora1I1/II-r,, 11\1' elem ent.Tilesubnctinle vel fourisaseruilincarr'~flf{)tw.mllldwhidllslI~',ll",1l'1,l'rllli lH' the new ori entation fotthecleme ntofinteres t. Afast1"1Iruilll\"JI\"rir.l1l1lis ,1"v, 'I"I",r lto de rive suitablewe igh ts forthcneuralnets 1.0 performdrir:il'ul.ly,<llIl""rtI:r:t1y,Ilsillg L1H' hierarchicalneuralnetwork systemforeachclementilllhr~illl;lg.~,Ilil\lilyI'ill'ilildW"f:I~silil', can beachie ved . AniterativeapllToaf,hiurorpcratcdinto th,:lU:nT"I' ldwl/TksySI."lllhas ;.Is"

enabledtheapplicationofglobalanalysisintIJ'~ IJror..~ssof arljustillf!;ll,r~,~r1gr:11If~;~~UTl'lIWllt s, Asa result,thefina ledgemeasurementsarc more aecurute.

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iii

ACK NOWLEDGEMENTS

Iwislltl,':JI>r<...~Illylh llllh 10my superv isorDr.Siwl'i 1.11rorIIi,;ll"idancc,inlcrl.'llt•

•·.. "slt lldiVl:niticisIIIillIlll,,,lllllSi"-~III.Wili lOu thi,;cont ribution,itwouldheirnpcsaihleto .r;lvoolltisll"...isitscUW:llt ·llIlllity.

Iwnilid lik.:I"th,lIIktil.:Sysll'n~~SUI'llOrtlil llrr for provid illgalltile helpandas.sis t<lllcc ,luri nKti,,:t:oll.lud.urIllyI't...earch.

r11m alsowry gr"tc rul lt'the /\.llllillisLrativcstaffwhohavehelpedill oneway or another

III","'il,ioll,IwnuldlikeIuarkuowlt'(lge1I1l'financialsupportrtocdwdfromthe Depart.

1Ill'lIlllfGmllilul.-r S(:i.:nn 'illl,lt hcSchoolof GreduetcSIIlJil-s,

Spl,-iallllolllksan'11111'tilIllyfello wgrluilla t csludcll b: and goodIricnds,and ill part ic ula r

In'fiHilI\V;archa lTl,RenYiug,St-anIIn,;ao 1111.1HelmutRothfo r theirvaluablecomrnc nls ilTlllllJi('fulslI!Q!';C!itillll:t.1wouldalsolike10thankProf.JaneFo ltzantiPatriciaMurphyfor

Atlalit,hutllnlk-ast,Iwonldlike to t1lilnk PangI.iLeerOfher co ns ta nt encourage ment lila tkl1,t1111'&lIingt1,rtJUghu utIllygn dl1iltcstudies,l'Specially during thepre parationof lhisl1U'1'is,

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1'hi.~ ''' rfli.~i.•l/nli('llIrllIIJmy1I'lIfll/.~

/ur

Ihril· .~lItJ1lt>l"l'!lid nll'or,nr!/rll" '"/lIov" ,!/I,,,"1

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I.

II

12 12 1,1 14 15

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'1."

;'\cIITal~cl ""'IlTh. II;

2.4.3Coopcralin'-('1I11l\Wlili\'I-~t-llralX.'I!<. I!I

2.4..4Slrnc-tllTt'l1I';'t'ur;llNd~, \9

2.-4.5C(}llIjlll'xN.'uTillNt'I~.. :!U

Chap t er 3Gene r nt ingLocnlEdge PnU c I'1Jfor NeurnlNt't1111'111 11

3.1hurcductlou• '!I

3.2Comp uting\11t' Eligt'Mt·il ~ nn·lIlt·lIls. 21

3.3TIITesltol.lillg UII'E. lgt·""~gl'. ::·1

3.4Selecting Willt lm\'SiJ'.c, 2li

3.5Gcnl'r~lill,!l:1III'1ll"t'Clm s• . 2li

Cha p te r 4 Edge Contou r DetectionSulmct 2lJ

4.1Introduction..,. :!!I

4.2Information Con1ril.lIlillg10lIwlJd.'('tiul1l1( E,IP."('U111..llts, :!~ l

4,3SelectiveFunctiotlillExpallsiullMOIII'1 . :I!I

4.3,1Pro Cl'!iSf.'!ifurJ)ch.'CtifigIl,d ilin.'",E,I~,'(:IJII1.I,"t, :11 4,3 .2ProcessesfotIJdl'ClingJ\'1l1l,Syllllflf'lri"al!.i' w;ITE.IW:("mlullt, :11 4.3.3 ProcessesforIJcl<.'CtingCUf\,jlifwa rE,I I;'~O, r,IIJ1lr, :17

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1.304I't(J fl'SS I ~f"rI)cl edi ll gEdge Contours ata Corrwt., 1.3 ,5SIII)PP~ssiIlAFunctional Processes,

1.3.6Fum:liollillLinkwilliSdcdivcFuncticnn!ExpallsiollMOlle!. 1-1

1.1 IIYPllt.lll's i ~I ,<1I':d ~('l'a l.ll'f llS, 4S

1.!',I\rdlil l' dllrt'ofE,lp;(~COll1.ll\lfDetectio!lSnbuct. 19

CllIllltcr5 Ma ximumDet ect.ion Subnet 58

5. 1lntroductiou. 58

5.2MIIXillllllll lktedillllSuhnetDcsigu. 58

5.3 Ml·r\wllislt!of MuxhrauuIJd e clioliSubnct. 62

CII/Illtc r 0 Gradi cn tAdjus tm cntSubnc t 66

0,1Iutroductlou. 66

0.2 CoudltiouafurI~dgt,McusutcmentAdjustlllcn t, 67

6.2,1CllSC~(or Reinforcement . 67

0,2.2C'1SI'Sfor Snppn'Ssioll•. 68

0.3 ('umlit.iull'\s('L'rl"illllu'nlSubnct. 69

6.3.1Sl'll'rlin''lensorModel', 69

6.3 .1.1Ptllt'I'Sll('SfeeHt"illforrillg Gra,!i('lltMagnitude. 70

6.3.1.2 SUJlWt"ssi ngGrlldil'nt Magnitudo. 71

0.3,1, 3 FuuctkmalLinkwithlht,S("I('("1i\'(~Tensor~Iodd. 72

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riii 6.3 .2:\hyh.l 11islll llr \tlIl<lili" n'\sn -r1.1in uk·u' Sulom1•

Chapt er7 Orient at ionDctc rrnln a uouSubne t K2

7.1Illt rmlllcl iu lI.. s:!

7.4.1 Ca.'I(.'Sror/\rt i\'a tiun. :->li

7.4.2Cas<-~rurDe..Acth·lItiUlI.

Chapter8Ada ptingWeig ht sThrough Su pe rvised 1..·Mlliu g 8.1lnt roduct icn..,.. ••,

8.2~llItlilk.tJDellaRule1..~arl1illgAlgilritlllll. 8.3 ElTcctivl'Jles sor till:LCilnJiligI'rot (!Ss .

8.3.1 lmprcvlugHuto orLeilrnillg . 8.3.2Ellll<llldn g Getl(:ra lil,lltj"lJG1l.pal.ility, 8.4Pe rforming:'\cc~s1l.r~rTrllilling totill:SlIlmds.

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lUll Hll III.'",

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CIHlplc r 9CQlI du!i i ll u~nnd FutureRes e a r ch

0.1SlIIllIllar)'

fI r

(AlIIlril",l ilJ"~...

9.2Uiro,rt i..,,~rurFlIrt h" rU(~iIfrh.

0.2.:JIkl(~ ·till ~ r-.I"n~Cum Jlli~x EcJg(~Pauc ms.. 9.2.4Inqln ' \'iIlKIlIItill'SPCt~ JIIrLeartling . 9.2.5 IrJqlru\l ill~UtiOw"IJililyttlFurtherElimillllll'

!le(crCllce s.

AP l' t;NDl XA.• •..

ix

111

III lUi

IIG IIG Iii II i

IIi

us

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Lis t of Figures

rig ulcI.t ,\n(l\1.'f\'n,.worl,rUIKtsl'l1~YI'Ic-IIl . Figure 1.2 llicrarc!licalliLrlld ul"i.'

or

IWlIralllt"l w",kli)"lilt'lll••

Figure3.1 Elementsill11:1x:lwin.I,,", Fi&urc 3.2 SobelIIIl1sks•••

Pig ure3.3 I;;ightprjn r ip al 0'1,'1I1I\t iOIl!' .

•• ••• • • • • • • •• :!'.!

Fig ure 3..1 Thresholddch 'TlIlilllllioll lromgnuli"lIlllllll;t1it.u,I,·llilil"~riLlt1. :!!"I Flgurc3.5 A windowfort.heinjl ll luf lur;!.\.',lg"pnUnn. • :.!Ii

Figu re 3.6 EIIgcdellll'lll liill uwimlow .. '.!7

Figure.\.1 Ed ge contours.. :11

Figure-1.2 Local edgepltHe.'rn! •••• • •• •• • :t !

Figure-t.:I Non-sym mdriclll edgepaUcrns . :I!",

FigllTc-1.-1 CmvilincarC(lgcCO/llUlll'1l.• •. :I!I

CornlTCllgcraU(~I1 !1••••••••• ••••••••• • ••• • Figure4.6 Pat ternfor5u pprl.'$singeent ralco-lged'·IIlI'l.l•.• • Figure-1.7 Schematici1Il1~lnlli ol1or"sdN:liwfunrl ionllll'xl mllSimt

modelrorthenor thoril"JlllltiolJ . Figu re-t.8 IIEPs forthe northorielilation. Figure4.9 HEPsforthellorll H ~iLliturielltatlllli. Fig ure4.10 Architectureof selec tivefunctional.link Ile lsin

EdgeConto urDet ecti onSuh nd.

Figure4.11 Characte ristics

or

sigrnoid1!.1acfivationfllrlf~lihll.. Figure5.1 Laterallyinterconnec ted neurons.

Figure5.2 Schematicrepresenlation orlateralj"h~rar;ljfl". . . ••.

!ifi

!i!J fjll

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xi

Fil!;lln ~.'i.:l Ard lit' -rlll reofMa xiurumDetect lou Snhn c r. . 61

Fil!;"n~r•.1 Cltll rilr.1.wi sli ,~~orInucrlon'4>' . 6·\

FiJ.!,IlI"6. 1 Sdu~Ill;\t i<:illlls 1.T/,tioli orItselectivetense r model. 73 Fi.c,lIl'<·I;.;! Ardlil.' d llrcofGOlld it ioJlAscertai nm ent Subnct . 74

Fit:IIl'(·Ii.:l CII;lrad l'rislicl!or (!luetioll'/1. '. 76

j:i/l,lIr, '(i.1 Arc hi1.'!(:1.lIworGr;,J i(~IILComput atio nSubuet.

n

Fi.c,lIl'<·^(i}j Chil, r~l<"to:ris1. icsu(flltlct.io/l'op'. 79 Fi","I""lUi Cl"mu:1.I']'isl.icsoffU/lct ion'1/,', 8\ Fi",un -i.1 Art:lLill~·l.lIn-ofOriclitatiollDctcnnluattonSubnct. . 83 Fi"'I1""7.:1 CIt'II'al"l,·ris tj,·sor fund ioll'lJI' . 86 Fil',uI'('x.I lla kor1t';\l'lliligfort11(~r~d gcCnillollf Iletocti on Snbnct. \02

Fip;un'x.~ 1·;t1,(t,-l'at.lI~I"Il S_ 10,\

Fi.c,un-!1.1 [)q~r;ublundlIuisl'corrupted gray-lev ellmegc. 115

l-'i.l;lIl'l'!I.:.! E, IW ~ illm~l'-hdor( ~precessingbyneuralnetworksyst em. •115 Fi.c,ul't·!I.:l 1IllI'I"m'('11('.lg( ~iUliIgt' - afterprocessin gbyneuralnetworksyst e m. 115

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Chapter 1 Introduction

Animpor tant probleminimage processingisthe dctccrlon(Ift',lgc'liill II1';1\"1'11il1la.t\t·.

Edges arc the consequences of changesin somephysical;111,1slIl'filn'prt1Iwrli,'s, sud,;111 illuminat ion , geometry (orientat ionor depth]orn'{l('d;mn'.AIlI'llg!'inlll/!;t'""11\" ·Y.~mustnf theimpor t nnt scene informa tion as therearcdlrcct,'ofH-Iodinll!!Iwl,wI-"1l1111',·,I':;I-!! ;11\,1t.ln- physical prope rtiesofa scene. Edge detectionis,111 ('SSI'lltiJll pM L<Iftunuyrullll'"I.corvisioll systems asitplays akeyrolein earlyprorcssitlg.The('c1gt~,I,·t, ·tt iolll,nH'(·.~:lSillll'lili.'S tht·

ana lysisofimagesbydrastically reducingtheamouutof.],d,at.u I.epmn 'SSf'lI, wllill'utthe sametimepreservingusefulaudimpor tant str ucturalillfol'!II;llilJlIahcut.1II1jl'('lIUJllIlllilri('S.

Itishardto ovcr-c-np hasizethe importan ceof e\lgr'dd,f'dioll illilJH1~('lllJ,I('r.~1.alldill~.l\l,,~l modulesin a visionsyste m depend ,directly orindirectly ,OiltheJmd"rlJl" IIl"(~"ftln-(' IIW !- detector,Edgedetect iontechniq ues havevarious;lppIiCld.i(Jll~suchil~pa ll l!rt1ff1'''~lIil, i''lI, robotscene analysis, andimagecoding.

Accurateedgedetectionis adifficult task[PeliIUIII~Iahdl1!JH2;Ba llardallliIlrowli 1982~1and therehasbeen a subst antial effortto(Jev(~IHJI th(~'irl,~;d 'f.~J~f!,1l'1.1 ',:lfJrsur"I"' r- ato rs.However,cadi of these edge oper a tor s usually(~ll1horly .~rwdli,;(:,Igf ~11H"I,.[s ane]Hlay performbestonly underspecialcircumstances. Fur exam ple,SOf fit:('IH~rll 1.'>r~HHlY filll imllst edges but alsorespo ndtonoise, whileothers maybo1II1is,~-ill~'~/Isiliw:hutlrIis.~ S'HtH~r:nlf:ial

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,!,IW!s.Ilt;rlf:'), HlflStl)r1W!npcruto rs willglnlc r ally produce impe rfect result s.There fo re, oon·

si,ll'ri ll~til,) lIverHllfli""rseapphcatlo nsforedgede tec tio n and the performanceofcurrent 1~.I)I,I~npemlurs,it isbetter1,0improve

tuc

resultsof anedge opera t or ra therthan to develop lIll :'iell'a l' l'(!W:opera tors.

Thf~rc'1I"~ dilrl~re nt tr~ d lll i(I Il(''l;(or improving edgeoperator measur emen t s .Tedmiques Ilsill grdax"li(llllal ,ding aroros n-lctedhythelimitedcapacitytoaccurately repr esentedge- IJru,',~s.~c.~anddiffcTl~1I1lilJ.d illgS. I\s<I,result,these techniq ueslack the abilitytodetect runny,Iilfl'j"l'lltandlIlOWcomplexedgepatterns.Sometechniques usccon te xtinfo r matio n (PHiltil"im'lg<' ll11 LUH~yI<lrkaccuracy asstronguclsoisalsoenhancedalongwithvalid ,',II!,"'~'Otlll'r1,1'(:lllIi'[Il1'sIIsing1;01lLo1lrfind ing to improve the detecte dedgespe rform poorly illnoisyilllil~I'S,

I\s r-urre-nttct:!l1lillUI'Shavu limitedca pa hillty toperformgood and accurate edge do- tccricnfernoisecorruptedi~lIddegrade dimages, th is thesisprese nt sa newtechniq uefor ill11ll"Ov illgl.Il el'dgl~nu-asurcmonts . Edgemea surementsinclude: (1)the amou ntofedge sl, rl'lI~l lliISt'I'rl"lil1cd1IyIlII'l1slIril1g the degreeof abruptnessin cha ngesin inten sitiesalong 1,11l'I'd,!!;l'and(:.!)111l!directionsofthesecha nges ill intensit ies.A hierarchicalneural network s.\·slt' lIl isJlmpusl..lto'U"I'llllllllish thefo llowingtas ks: (a)toreinforceorenha nce true edges;

(11)10H'C)\ Wll1issill~edges:(I")to SUPllrcssfalse,spuriousedges;and(d)to eliminatenoise.

Tin'ucuraluctworksystt'lllis,,111c ttl achievefo ur veryimportantobjectives:

l.IJilf(' rl'lIt. lyp\'s of('tlgecontours (c.g. cur va t ure,linea r, corners ,etc.) canbe accurately IIdl"·l,,d.All \'(!geWiltouristheoutlinetha t definesan edge.Anedgest ruc t ure on

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theot he r hand is an edge construc t ion through till'arraugcuu-ntIlf!.lll' sllb n'llll ' Ullt' lds (ed geclements]or1111edge.

2, Mereglobalinfommtionismade il\'ail ah ll' fu r,uTllr.lll'l~l gl'dt'l I'd iuH,iUh'T! w la l,ilul andnoiseelimination.

3. llighl y parallelprocessingcnableshighcmupuf.ationspcedful'rcul.tin«-'l!.plinlt iun ,

goodgene\·a1izill;oll.

Theadjus t mentoftheodgc measurement isfOrtllula h 'fl ill.111);111111'1"suchrhat.iUll',I).!;,·"II' mont mayha veitsgr<ldiclil1llag llil lH.lcandnrientntlouitl'rali\'l'lyill1.I'n' d in;1p;rH 'II11'lI twith

ea chiteratio na'IJthenew valuesarcfedback 1.0tIll:ueurnlnetwork SySI,l' UI fllrrllrl1wr processing .Thisiterat iveapproachenableslireul iliZll1.ilHi

or

g110111I1illf" fillat,ioll1l.~tilt'ill format ionis'propagat ed'1.0surro u nd ingcleJ nl~I ILsilltire1~lgl' im;'g'~"n.<'r",,, ,11 il.,·ral.i"Il.

1.1 Or g anizat ion of t he System

TireIlow cher tinFig.1.1 giVCl;all overviewflftJll~PWlltlSI'<!sysl.t·ll l.11Iit.inll'llw,11IO';u.;un~

mcntsarc ob tained llsillg tllr:Solidupc ruturs[Il<tll;~rd<tu<I11l'<lwllI~JK'l" I.Ag;11.1,;,lthr.'s h" I,1 algo ritlJmisused todisti ng uishedge elcnmuts .T111~illfHrllla tirlll(tl l'~"ri'~lIl,llt.i,,"anrlLIi,~

gra d ien tmag nit ude)isinputto thehierarc hicalneuralnetwor ksy:.tt:ltl whichit'~ri~t.i"I<~ly adjusts theedgemea surement ofeachelementutiliIconvergenceisalta iur'd.'I'llillis ,I,rll'~

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l~d W'~<1ft:ddl~(;ll~lliHllll' lIll illlred,missingedgesor edgesnotdete ctedby theedg eOpe rators arerl~:oVf~r.~,],IalsoIlllf!spuriollsedg(~sdete cted hytileedge operators arc suppressedand

Improved Edge Image

Figllre1,1 A11overvie wofproposed system

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1.2 Struc tureofthe HierarchicalNeur alNetwor k Sf-sf.em

Theneura lnetwork system consists uf(ollrmajorsulHlI'lswllit"h\lI·rf,lrnisp.·("ili."~ull·

tas ks inorde r toaccomplish theoveralltaskofimprtl\' illgtil<'l" ! ~"11ll''lSU Tl·lIl . ' uls. 'I'ho int erconnecti onsbetween thesesubnctsarcIashloned illa lli''Tard lil"lIltnutuu-t.'1'1...sl1hnd inlevelonedetectsthestrengt hsofctlgc contoursacro rdlugtil lilt'gradh-ntlIl;\gnit.u,[I'!IMill or ie nta tion sofneighbouri ngL'tlgc de me ntsinthelocal edge llal,lI'rll,III1.'\'1'11,1\"11,l.llP SlIll1l1' t.

de t erminestheorient ationof tilestrongestedgeccntonrilllilt'l' lI'alt'{!gt:pattern usin gt.lll' inputfromthesubnctinlevel aile.TheslllllldinI.'vel lIlr"f'USI'S Ill!'inr"rlllali"lIpm Y;I!t',1 bytheeubnct;1\leveltwo toadjustthegrllt.lieul l11ngllil1Hh~uf lIw ..rlgt't'h'ulI'nl.11.willllll!t>

signaltothe sub netinlevel {our tomodi fytheoriclll.lll.i unofllw {:I'ulnlr-h-tueuf..'I'll"11l1hlld inthefinalleveldetermines theneworientation {orthet'{lg.\dt'lI\t'l\lwithllll';nf" l"ll1aliuu fromtile subnctsinlevels twoandthree.Thehierarchicalstrurf.ureufLln-m-urallld,wurk systemisillustratedin Fig, 1.2,

Eachsubnc tismadeupofone ormoreleycrsofnodes.Tilellil'r;lrr,llit'i11neural1lt'l,wlJtk syst em has for ward and/or lateral connectio ns betweennodesII I('111"1,If'v!'l{ItI" yl'r Inlilt, forwardconnections, theoutput o( nodes at c.l<:11level(urlaY'~r)M'nt:!! II.Silll'"llu1.111:nu'/"s onthenextlevel(orlayer ) intileneuralnetwork.InUICI"kr;d l:mlllt'{:ti"l111lId-w,'{'u1It1111:S, theemphasisison lateralinhibitionor cxcitntloubetweenn'HI"sOiltlwS;H!II:layor, 'I'll{' firstlayer

or

thesubnetinle velone isthe recept o rll\yt ~rIIIJ'{~n~ivl~lIminpul11;11.1' .

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A(ljlls ll~dGradicnt

Mugnitudc New Orientation

IlIr'ltImage (Gra dientlIl..gnilllrle;Orientation)

\:igure1,2lljcrcrchicnlstructu re ofneuralnetwork system

Tltl'output

(lr

1111'subnet inlevelthree isthe newadjustedgradientmagnitu de

o r

theedge ..h-nu-ntamlthesign illillllirali llgwhetherthe clementis anedgedement oranon-edgede-

11Il'lI t.Theoutput ofthesubnct inlevel fourgivestheneworientationfor the edge clement.

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1.3 Organizationof theThesis

Th isthes is isoeganized iutc ninecltaptc rs.CIJ1I p lt' rtwo illln..lm',,\<1',dslinF;1o,-lllIi' llIl~

foredge detectionendcnIUUln..nlC'ul ancl,lbol'C\'icwstl1O'rllrrt' II 1n....·arr\.0111.1i1I'I,!i'·i1lillll.

ofdifferentneuralnetw orkmock,l"Chapter1I1rt'Cc1,'snibl'!lhowIll\'ill l'll l .lala111 1111"hi,'r- archicalneural networ ksyste m lire gcm'rat ed ami fnrlllilllc"d,IIIClmp leT f"lIf,I!II' .ksil!.ll, architectu re andmechanismo(thesuh nl'1inI"VI,IOIl(-'nf1111'1ll'l lI'lIr kan'll ,',.;c·rilll"li. Till' funct ion fin d purp os e oftil('lluhllt'larcalsotli.~c ll ss t'<.l.Chilp terIiI'" dl'SlTilll'lllhl' NlIlIIll't in the secondlevel.Thedesig nandrOUn'lllarcilduptc,.1IromIhl'iIIwlu~r10 L11l' M"lup;in ll neuron.Thethird subnctintheIIcuralnetworkisf!,'Sc,tih"flillCh"pll'rsix.ThiNsll l"ll't consists ofahigh -ofd e r rllllcliollllllinkt'<.!lIcUflII IlCIfur df'(-j, lillglIu' llpl'"'l'riilh'...ltIfliliOIl~

fo rco.Igc measurement il.djudlTlt'l111ami ascllli liucllr rc't'Clrurwllfll'wtfurtnUllifyilll;tI...~r,,' clientmagnit ude.Cha p lerseventlcscrihcsaSCllli1iIlCar rl"\,l forwa rII IlPlfur.Il·tl'nllilli ll~LIM' oricnta lio u of the edgedement.Afa.'\llcar nin g algorlt h l1lrurdlllllSinl,;Illlil .,I,\c,w.·i" l,lli.,fII,..

neuralnelsis describedin Chaple reight.ThedilT(~relltNitlliltiun~ ilrl~alllllyz'''I1IIIfill.1filii whet hertra ini ngforthe neu ralnet sisrequir ed ornot.C:1I" 1''''r "iUl'~iVf'llL1wf"I"lf"Ju!lifJll~

amipossibledirccricnsrorfllrll,crr~/\rc!l.

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Chapter 2 Survey of Edge Detection Techniques and Neural Networks

2.1 lnlrn.ilill:l mn

IIIIllis C"hliJlll'T, 11IHidoverviewofl~lg(~dotcctlon l(~dl/liqIJCli,ed geenhan cement tech -

"i'IIl('1iunciJ1(~mulnl'l wo rhispn~l·nl.cd.This discusstonincludes theprinciple sadoptedin th{'.~1"l,'Chllil p IO'S,tllci r s1.wngl115 and wCilknc!i!K'lI,l\Swella!!Focaslngon techniques which IlLili~t,t~lg('iufurtnat.ioutoenhancethelodgeimage.Fin ally,t.hedesignconcep tsand appli- C"ill.iO llSuf thedilkrcntneuralnetworkmodelsarcdiscus sed.

2.2 EdgeDet e ction

T echniques

TIII~rt·hils111'1'11In 'IHI'lulo111lr<--:warchin thean'lIofedgedetection in an auc rn ptto create the'{deal'('il~,..uprretor. '1'11('followin g lirere v iewsoftlll'typical «lgc detectionalgorithms.

2.2. 1 DiITcrcntinl Operato rs

l\1\l~Loftilt'l'arlicredgode tectiontcdmiq uc semployed firsturdordifferen c eoperators. IJilr"I'I'lilialoperatorsindndctheltobcrts2 x2 pixl'loperator,thePrcwilt3 x3 pixel op- erntor ;lIull.lll'Suhd

a

x:1pix el operator[Ball ardandBrown 1982..

1 .

TheseoperatorsscL

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suitab leweigh ts over a convenient neighbourhood~iZl'10I'.dimill.,Sl" l ll'sill 1lu-'J';,nd'.!I' directi o ns. First. order dlffcronti...1oper-ators,lr('filS\ ('clg " dl'l(','!i' lII11I" ' ri,lnn<.Tlll'}'nlli!ll sharpe nthe edge contours,hiltalso luadvenc ut.ly ('l1h,l,,,"('1I1('Imi sl'.TIlt' !.;ll'bu· ia llofC: ill l~' sianop e rator[Mart -Hil drethmc t borl]is lISt,1!10tll'1t''''!.l'IIKt'Saltlu-IU" atiuli Suf1111'Z" l"U crossings[~IarrandHildreth19801.However,z,'ro,rrosliillKsdulltltlllwilYSrUrrl'l<lhllUIttl edges, TheMarr-llild rothmethod alsohas poor lll('a)iz "tion prUIll'flit,satu]illlrulllIt't'Su bias illthe edge location eslirna ti oll lUt'rzins 198,1;Nalwil alill Biuful',II!Il"li].'I'll.'slI1ont.h i l1~

operation wit h the Cnnsslonmask It'lll ls1(1 l.l lIrwonkI'tll;<'s\IIM,lli"kilwl l,t '" l!)lltlj,lind furthermore,the prese n c e u]inlpulseno ise illtrilusmiu,"t lil11ilg.'Srunsl'liull.~l.v,1"I!;nul<'tilt' perform a nce of thesmo othingoperator,Al\llt.1l(~rdilrl'f('l l1.i'llupe-ratnr,(~i1 l1l1Y... I!!;I'ul,('ril l,l lr {Canny!!}86!,usesth efirslderivativeofthefilt eredilll " !;I!flllll·ljunaOlitshasisrur1·<Ip;.' detection .Optimal edgeopera torsarcthender-ivedfo r.lil rl'r<'1l 1.l'dl;l'IJrulih'!i,fu rI'Xi'ltIl'!(', step edge or ridge edge , The se opera tors arcoptirnillilltil"SI'II~t~ufjuilltlyllIaxitllizill~

thesignal-to-no iser...tioanda-localizaf.io n rrile rillllwit hf"tJllst r ailll"IIn"lIti!, I.,n'~I'0llst's, IIcrc, smo ot h ingis use d10 offsetthedr(...:\ ~oft1oil«!IwftJfl!l'Jlg' :ddl'diull,'I'll.!l'lrrd,s(If smooth ingblu rsweakedges. Anotherdri\wlJ,lt:kim~)l v(.'liretnrniIIg(alsl'",lg!'sI'll~rll"tJt.ldy shadedsurfaces.

2,2,2 Temp la te MatchingEdgeOperat ors

The popular edgete m plate rna-tellingtJl":rat(lfSan:l tU!Kirs.:hrnil~k.~[lI;dtard ;lllllllr"w/l 1982.1,theRobinsonma sks [Robinson1!J77],the Nt:vati."lla llll masksINr:l"id,ia;w.1B'lIJ1l

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10

I!JHfJ],/lJIIItileCCllI1p a SSGradient masks [Park and Choi198 9 ].Bydetermini n g the largest n~SJJU!lSf!fora I'dof masks,the edge orientat ionandma gn it udeca nbera pidly estimated.

1I11wf!Vf'r, tmllpJalcmaskmethods giveriseto large angularerrors and<10notgivecorrect Vill ul·.~forL/ICgra-licut.Anothertype oftemplatematching techniqueis basedonthesum of ah~fJlllt,:I'rror.~[St rickland,Draelosand Mao!!)!JOj.Thistechnique is effectivein detecting

l~dW'swherethe (orll1ofthe edgestohe detected is known.Ilowcvcr,tilerearc disadvantages

with thisled llliq u().Firstly,thetechniquerequires smoothingtllremovenoise before the

",IRellt'led ioll,whidlarrlJdsthodetectionofweakedges.Theperformanceis alsoaffected

ifilllJlulst·rmi~l.'i~ prl.'~Nltillllic lnrage.Secondly,tile formoftileedgestohe detected must II(' huwl!ill advlLnre.This^1TI^('^t110dalsoinvolvesthe expensivepixel-by-pixelcompar ison in

2.2.3 Imnge Filter ingTech niques

Liul'M filleringtechniqueswere some oftheearliest flltcriug techniquesusedforedge tldt·t'I,iull[Modestineand Fries19iiJ.Inthistechnique,a stochasticmodelofedgestructure isPrullo~('dandtheedgedetectionproblem is formulate das one ofleast mean-squa respatial lIIl,·ring.1·~lgt·xillnoisyIligit 1l1 images are detectedusingtwo-dimensionalrecursive digital lilte ring.IIIeddition10thenoiseim munity,therecursivenatureofthefilteringoperation 1t';lIls It) signilinLlllrompntationnleconomics.However,linea r IIlteringtechniques are goner- ally wry romph-x and hawachieved onlymoderatesuccess.NonlinearIiltcnn g(c.g.median lilt t·rillg.enh-r sl'lt ixlicsfilt:-rillg.andnoulincar meanmler ing)is able to removecert ain

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11

~cnmeasure the mean ofth l· \umilHult\,.If tilt',Iillpl'ui"nIIft1...hlln illilll...•will. iuIh.'lilh-r extent isgreaterthanIIccrteln lh n:'l'hold.tilt'("t'nkrIIflin" lilh'T,' xli-III is.1,,,,1..,...1astllO' edge poin t (pita sand VCIlC llUltlltl'tl ll l051986\.Slid ,c',lgt'.1,·ln'lnt1'l11ll\1'Il...."ldlilTil,·h-ri."Ij,-~

onlyin thepresence' of1I1lifUTml)"di~lrillll ll...1 lluiM'.Arlm' lluf1l"..liilu-IYlH·lillt'TllIN,"wu, Heinonen lind Defee1987:Ncuvn,Nicmincnlin,IIlt-inOlll'1I 19Si l ,'Ul1Ihil1l':<lilt'uHllml<IfII number

or

linear spa til\lfiltersand1111'mcdinu0lll'ra liunto,1"' 1'('1,t.11<',·dp;o'll.TIll' n,w

However, the lineslntwo-dimenelcnalilllitgl'll tiuIIl1tsun-in-IIII'rilt"rill~I'TOn'llSIS'lil "041..1 Cunningham 1990].

2.2.4 St a tisti ca lTechniques

Ast a tisti calclassiflcafionh..clmiquc[K un du 1!t!KJIi!l1l~.'(1til.I..t...·t LIll'~t.·I.illI,lli'lI"ilr edges.ThistechniqueishaliCd011two(h a.ra.eh·rist i f~fI(II..tu rlll,..Ip,."S:OJL]...l'i lC"I~'l<'iH the steporlinearedgescan hedass ifin lilltot\\"(.'lPil rl y("I"ifl~rull"swith,Iill.·,.·"tilVf·ti lj('·

inl ensity values, and(2)the"K.'Jnh.~tsof(~a chgrolll'show stmu" sl';ll ial'·" rr<·l'lli"u.TIll"

edgesarclocated atpointswherebothlhcs(~CUlJ(lil ~llI!4a,.,silli.~li"flwith.~lnlll~.~lillislif'ill evidence,TIlewea k edges arcnotblurredbe cause 1111srn""Lllil lgi~ill\'"I\l(. I,II1IIw....·r,11" 1.illl edge clementsarcdetect ed.Anothe rIl'fhn i (llll~.!.a sl·11IIU1,1..•likd illlJ",1tali"t,,-stilla l\i""'11 smallneighbourhood,derivCllII.decisionrn ll:tud.~d,J.~wl.. ,tlwt tl..~wbilII':111;",ilI",illl, a comeredge,or justasmoothrcg iou[HuangilliflT!I(:"~I!I.lSIII.:-'1I,r"Ij,:risjulirul.'!! filII

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12 lJ(~.1,·ri Vl~,tform{m~mmr,lil:i.t l.-'1lsitu a tions (neighb ourhoods], but they arc eom putatlo n ally

2.3 Edge Improvemen t (Enhancement)Techniques

TII"r.·11mt1ifr.~rl'lItledlll iqut'S for improving tile'raw'edgein form ationobta inedby the

""w'

.ld tdio ll. TIll'fullowingis a sum maryof Lhesctechnlqu esfo r improvingthe edgeimag e.

2.3.1 Hcla xlltionLabeling

PruhalJili s1.krcli. xa liullisIIuxhnlqnefor labelingimageentities.Itrelicson iteratively 1I1,,]nl,illgthedistr ih uti on ofavailableprohllhili ly over IIlabelso t.A su pport functioncom- hill,'S('Vi,II'Iln'S (WIllthecontext-co nveyi ng neighbourhoodandincorpo ra tespriorknowledge llftill'stnn-Lure oftlll~labelingtask in-hand .One of the earliest,prob a b ilistic relaxati onle- 1ll' lillP;1l1l't1lod WilSint roducedby[Zu (."kt'r,lIumrndandRosenfeld19;;;HummelandZu cker

1!I~al .Itn"l'lin~thesl'llin gofmanycompatibilityweights. Theupdat ingprocessem ploys

onlya singl(!fllrlllu la forallthevario us, differ ent edgepau crn a.Con ver gencecanbevery ,lilli " lIlt~i lln'Inilll.Vvaeiablcs mustbe0IJLi rni7.Cdshnultanccualy . Withtheheur isticnatu re of tilt'IlIJ(lilt,~procedu re.therearcoftt'ninterna llncon slstonciesinthespcclfication ofthe rt'l Olxal iulIscheme, ami alimitedca p acity10accuratelyrepre s en tedg e-pr ocesses .Anot her

\'t'rs iunufrt·la xalilllllabeling[Prage r10S0)allows(or morecomplicatedadjustmentform u las hutoulysix inlllH..li.lh'(adj .l ('{'Ut)neighbouringpixelsarccon s idered. lloncc,it docsnot pfU\' i,I,'~ufli('il'lIlinfonnnfiouforiImore accu r atein dication ofthepresenceof an edge or

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noise.Animproved applicati onofproba bilistic maxatillilto"11';1'lalwlil1t:,[lIa l1nlt-k allli Kitt ler19901uses areprcscnti\lioll orthecdgc-pTO<"t'lll'(.'>I.Hy.'i1l<'riryill1tIII<'l.ru haJ.ili"t ir frameworkusedtorep resentthewortll lflO(ld.illlcrnalnlll"i"t t'Il (")"ilIl·Il"ur' '' 1.Fur,'arh"I.

jed,priorknowledge of thest ructure isrepresented hy a,lirtKlllilryof1;IIII'lillr;Ilt,s"iMlilic'll fortheentirecontexl -conveying neighbou rhood.UClilrirtillu"1111II...rt'pTl"SI'nlaliunal("'1"11"

ity of the schemearcavoided.Thi"dietionery-bnscd appmad lisI'al,ahll'"f,·I1II;uu-il1,l!; ",1';1' st ruct ures in thepresenceofnclsewithoutfillers,hilltil('dil'l iuu a r}'ruu1'1' l' ul1I l'veryliltll"

l\.Sthe application task ismade morecomplex.AIIUlllNlypcof prllh;lb ili"t.icrl·lm.:ntiullis ba.sroonan automatonapp roac h(~Ianda}'am,Tlliltllill:ll1tr/lUll SastryI!1~(;1.'I'll('IIm"••I,i1- it yupdat ingill accom plishedthroughlearningautomatn.FordiUl·n'lIl.t)'lll'Sofsil Ualillll!l, the IC&fningalgorithmcanbed,oiPoCndCJlelld illgent1wIlrohlt'lIIitl hall,1(Tllatllarll'"ill,,1 Sast ry 1985}. Thelcar ninr; 11l1tomAl.a. alr;oritlllnsarcvery silllilk'tilIJI'r furm<Il1ll ll(',,«·tlll'y canbehard wareimplemented.Howe ver , their ahllltytoaa:llrat d ytl:l'ro,;,11llilt:,liIf"rl'ut lab clinge isw~rylimited.AstodlUlicrelaxation~licllle{C'.t111lt.1lan,1GI:lllall I!IH-ljisitiml-e1 atincorporatinr;obser vationalinformatio nby rer;lIrdillgll,e1.,IJI'lingtusk asUliIllilll'llllII po~terioriprobabilitycstimetion. This!«;hernei1dollt~it lIityl'Siilllapp ro",dlt"it'Ili"ri\f' chical'stochas ticmodel based onthe Gihbsdisrribution.AIIC:Wrl'!;l'/Tatilll1 al.I!,uritltHlfur com puting the maximumaposteriori(MAP)cslillliltiflll

oru..:

ifll<lg'~jsIJIISt..,]1111sludl1lst i<:

relaxationandannealing.Theschemegenerates aHCfllJelll:cIIfirnllW::IllHitr.<Jllv,:rW::Iinnil app ropriat e sensetc the10.11\1>estima t ion. TilealgorithmisIliglllyI'lLralida...1 l:XjlllJils theequivalence betweenGihhs dislr ibuLiolls alld)'Iarkovrando mnd,ls.IraIl1 Vt~rgell<:f:is

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14 slow,1I1<~rd;~:<1t lio/lschemeis comp ulati ona llyexpensivebecauseJT1l11ryim a ges have to be

2.:1.2 Coutcx tDep en d en t Edge Detect ion

Il;L'i", 1fin localctlW~coherence,context informat ionofthewholeima geisusedinthe edge

,JPlt~djoliprocess [Haralickant]Lee 19901.The edgeevalua t ion is formu latedas aBayesian

flf·,·j.~illlJprobk-m.Tlll~monoto nically increasingpallISbeginat anypixelslocated athound-

Mi,'s illt11 '~iHl;lg'~ilIJOVf:till:selected pixel , passthrough tile selected pixel,andendat some pixI·lslond, I',1al houlida riclibelowtheselecte dpixel.Apixel is Msigncdto an'edge' staleif till-1'11,1;1'prohl1hilityufthehest 'edge'pathis higherthanthe averageprobabilityof the best '1ICH·,lgp'pillhs.Thistechniqueis computation allylessexpensivethanotheredge detection tvrhniqur-slIsingrclnxation bbcliug.However,thepath with the highest prob abilit ymight nut C"OITI'rll}'depict1111'edge'path as thepixels in thepathcouldbe thelo ca tio ns of very st.tullg Iloisl'rnl.hcr thnu edges. This techniqueconsidersonlythepixel valueson thepath, without,ftJnsideri ngifthose <He'edge ' pixel s or 'noise' pixels. Manypa t hscanbe gene rated hnl lintall ofUU: S l'pal,hl> representvalid'edge'paths.

2.3.3 Det.ecti ngEdg esbyusing Mult ipleScales

1\11algorithmforlinding11singlegoodpaththronghtheset ofedge pointsdetect ed us- ill~lltl'gmdicntofthe Gaussian operatorwas proposed by(Willia ms and Shah1990J.The algurithm\lSC'Sonesca le for findingcontours andthe nexte ndstomulti ple scalesto produce

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improveddetectionof weak edges. Aweightassigned at each l'llgl'Iloin\i"h;\~I...1ou flnlr factors :11 measureof noisiness,a measureof curvature,co utonr1,>n!~I,h,;111,11,1,,' I;radil'lIt ma gnit ude. The edgepoiUlwiththelergcstaverage weighl, is rhUSI'llH~tIll'"c1gl'l'oiUI Ull the contour, Inthe multiplesca le algorithm,thesearchfor a rontourI'r<ln...'t[~<IS fortlu- singlescale,usingthela rgest scale tolocatetileLJI'llt pilrt illle-outour,11l('11f.,l1ol\,,>.lb)' till' nextsmallerscaletoloca te the next bestpa rtialcontour.Thenlgnri Ulillis ;1],1.. toiIlLprm't' detection ofedges Illatarcdose togetherawlint er actsnllirlll.'.~whidlun'larg.'l'IIUII~htil removenoise,lIS well asalsoillJII!"o vingthe dd"diol1ofweak ...II\'·s.110\\"">"[', UIl' all-\orit,11I1l is 1I0table 10detectcJgcelementsUralarcapart, 1l"lll'C\llll'S\>"111;1'"will Ill' lostali LIIl' algorithmsarcnotable tointerpolatewell.Sincetill'nlgoritlllllis;,1.1.,1,0 ,1t'1.(',"\ WC'llk 1"ll\l's only iftheyarcwell-defined,tire 110twcll-dcfilll~dvalidw,'.~k f~dg""will Ill'lust,

2.3,4 Con t ou r'I'racing

Conto ur traci ngfrom a set ofedge pointsistackledby

, l

mmhill<ltiullClf,.<I,1!,f~lillkillg.

polygo na lapproximation,thinning , and nclghbcurhoodsto 11 routours"gllrt'lJt/11<'11awl PHil 19901.A contour is storedby encodingthedirectionfrom onecdg«o:!f'lIll'ntI." itsrll'il{lrhul1t, using an eight-va luedFree ma nchain code scheme.Togefl(~r;LlI~(~I.l!proutours,nu".I,I!,f~il! rilW~

isrecursi velypro cessed untilthecontour is closedor1l1l1i1 allpixelsWIlirecdW:1t'1V('IIl~~rr pro cessed .Araiseisolat ed edge contourcouldbe mistakenfllrIIVilli.1(,Ip;I)nmllJllr!l.~.>ad r edgeclementisin dividua lly processedand several,wighhollrillg'~llgl~dl~lJwlllsg"lwnale,lby st rongnoise mayhavethesame ori entatio n hydri1nr;(~.Alrif~ratdli<:alaPIJTUllf:1rforra.'itI'M'

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16

alld"rl)l:f~ssillgof chain-c:odah\l:contours [Mecr,Shcrand Rosenfeld 1990}isbase donthe chai nflyrarni,!forextractingand analyzingcontours. Thechain pyram idemploysthe chain f:OfI(~rqJHos"lll,alionconcept (FN.'Ctrlan1974j andthe contours arc represented aslinked lists.

AIn.:a! connectivityalguritlltllisusedto generatethe linkedlists represe ntingthecontours.

Aprll h" hilisl ir. allocationalgorithmisthenusedtola bel the st ringofcontour pixels. A I;:lJlhriltgingalgoriUlI1listhen usedtofill thega ps in the contours. Thetechnique allows r;l.~lparallel processingoftilecontours,however,itcannotdealwithno iseor contours th at arc moretll<lllthree pixels wide.Therefore,inorderto uscthechainpyramidtechnique, I'Tl'pfOl'essillgmusthedoneto eliminatenoiseandthecontoursmust bethinned.

2,4 NeuralNetwork s

ThereliaS been iucreaslng interestin arti ficialneuralnetworks (ncura l ncls), due to new 11;..1topologies,learningalgorithmsandmassive parallelism[Lippmann1987).Neural net Illll'.Id s exploremany computing hypothesessimultaneouslyusingmassivelypar allel nets composedofmany computntioualclements(nodes)connectedbylinks with weights.A neu- ralrlt'lis specifiedhy thenet topology,nodc characteristics,andthetraining or learn ingru le.

Thepotcnrinl benefitsof neuralnets ext endbeyond the high computationspeedprovidedby massivcpnrullclism.Nt.'llflllllChalsoprovideagreat degreeofro bustn ess or fau lttolerance 1I",1IllS1'there nrc ma ny processingnodes. Damage to a few nodesorlinks may notaffect IIII.'overallperformanc e of tilenet significantly,

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2.4.1 Multi·LnyerNeuralNets

Current ly ,multi-la yer1Ld~arcone oftile mos tpopu la r neural11l'1,moch-la.Tlu'~"lid"

employhidd e n nodesconnected1.0bothtilein putand out put!II11lc'!! [B u llwlhart..Hhuou andMcClelland19861.Theout putfromtilt·!lmlt'sin(,ildllnyor isf.·t!tu 1lll'lH"ksillI ILl' next layerthrough weightedfccd forwa rdintcrcouncctlous .TILl' (·,lll;.hilil.i.·.•(If1I11111.i·IIl.\','r netsstemfrom their abilitiestoformcomplexdecisionrt'giulis,11111tu1'1' trilill(',111I1I111l'1.

hart,HintonandWilliams19861. Two-layerlidsf;HIh.~trnlucdtofurlllh,,1.11,'''l1W'Xalld disjoint decisio nrcgion s , and three-layerlidscallIll)tr aill('(l t oform arh it ra ry,·orlll'l('.~,I.··

elskmregions[ll uilligandLippman1988].Af()lIV(~X(k-..lslcun-gionisarl'l!,i"l1WII<'I,.·I,y theboundary betweentIledistr ibutionsofpop ula liOllsis Sllloothundsilllp],·.(~"II\'c'lst'ly, a com ple x deci s ionreg ionha s a comp lex boundary.•lisj uinLdcclslonrq~i(JlIs1ll"".1....isi,,11 regio nswhicharc part.iticncdanti do lIotoverlap .However ,thereureIlruhkrllswitll,I lIIult i, layernet . Firstly ,whe ncomplexdecisionrcglous<In)rcquircd,1:<11lverw ~nn:lill WrunI", exce ssivel ylo ng.lie nee, learn ingillamulti -layernet isslow.S,!<:u llllly,1.11,~JlIIIll I"'1"Ilfm,d.,s mustbelarge ('houg htoformitdecisionregion.III/wever, ilIllllst notlw su1M,!!,' >th;l1.t11f~

weightscanno the, reliablyestimatedfromthe available ll"1lining.J;lta. TIII)T<-r"n:, ".11'1,lI<:lis only cap ab leofperform inga speciflctaskanti any expausicnof tlw()ri~i llaltaskr<~'lll i l<~s

ill '

extensivemodification tothest ructureofthenet.An(Jtl ll~rprnl,I')lIlis Uwdillit:ullyillIJJn vidlngthehiddennode s with a trainingsignal.TIJCrcarea1I111n],,:rofr:lilrllll"'1;q'l' linLli"ns formulti-layerneuralnets suchasclassifieat lou[Wid-ow,Wiute randBlIxt, :rI!JHH;(;up1.;<, Saychand Tam mana1990;Kho tnn aadand 1.11I!J901, 1nofldiugf,i{Jltlgi,~dClJIIII'f:us ;,I,,,ry'~Y'~

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18

"",li,,,,

IF..

ndli,U"I.lm l...1111Sdlllll.lJOlk!!)90).feat ureextractionILinskcT1988 ;Dupagu ntla.

au.1V"f1l1ui1!»I91.flwI"I\l lc rn/cl ,ara d cr rcco gnilKHl (KammererandKupper1988;Wa.ibel, Jl" JIl':tolwa ,IIIill.)!.Iii!.!;I.CCIIIl,IIO<';(.-r,cI.ill.19891.

2A.2 !..!!.gh·OrdcrNeuralNets

Tll!'rc~MI~var i l/ IISW.,ySofincorpofal inghigh orderc/Techint oa neur alnetbeforeinput lotil<'nude :'~iglll;l-J1i'IHlil sIlllllncllHHt,Hintonand McClelland19SG],'meta-connections '

[i'UIIWrll 'llliI!IS7],1I11l1nonlinonrcombina tions of pa ttcm element s[Klasse n,PaoandChell

I!1l'il'lJ.Jlig h unle Till\~,lvl.,);tile Simll llalll-'OllSul ilizat ion oftheinputsforproces s ingbytile ,11'11 £111lid.'I'heIlla ju f,lra w hlU:kof thehigh-o rderapproachisthe combinatorialexplosio n

fir

l.i,;I,·nnlf.'f terms (Minsk}'andI'arcrt19S8].However,therearc variousmethodsfo r deal- ill';witht1li~pn,l.k·llI:Jlrio r rcslrictionsofhigh-orderterms,reducedinterconncet ione,and IIsin,;Ilriorknowledg e oftheproblem domain Laselcetonlythose termswhichare usefu l.

Ili,ltI.-t",II'rncurallleL.I.aveilllllrCllllivccom pu1inll, stor illg,andlearningcapabililies[Giles

;11I11Muwd l1987]. whilelllnin1;l.illingsimple architectures[Paoand Beer1988]_ I1illh·order Ill'l.r"ltwlill("orporalill~nonlinearlin kshasshown fast lea rn ingca pa b ili tyandalso enha nced l·UIllIIll!;,l ioll .ll capa hililJ'duetothegcno rntiou"fenhancedcombinations offeatu res[Scbajie I!ISS].TII('mcmoi-y rnpacityuf nhigh-cnlctuct isalsoimprovedthroughthe introducti on uf Iligh,'rordr-r1lI('11l0r~'f"nctionswhichenhan cetllcpatt ern discrimina t ingcapa bilityofthe 11('UTllllld[Lee,Doolen, ct al.H1SG),Despitethela ck ofmorecomprehensivesimulat io ns, IIII'('lllpir i('a ltI'SlI ltllshowthathigherdiuensionalitlcsandhigher-orderedcorrelationsin the

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IB arc hitecture ofthencuraluctdo imkc,l improvetlu-11"'1 11"1 )'l';'I'Mi' r"fIii,'In''ISimps"n 19 90],

2.4.3 Coop erative-Compet.it.iveNe\lr~ 1Nct.s

Accopcratlvc-compc rltlvc neurallid nlusis(s(Iflab'rall)'inl.l'rrumu "'!.",1 1""1",,,'1'1",iu-

fromIInodetoitselfanduoga tivcinterac tion(n'lIll' diUv,,) £1'0111il U" d"I,u its,,,'i!!.ItIo"lIr,,,1\

cooperative-competit ivenetcan be used,I"ac''lltl'llt.lltl.lr,,,,,s,,101.,IIIl' m " ,") '(",,"'tll'iatil'l'IlU' II I ory)[LapcdcsandFarber1!)8uiXIIandTsaiJ9!JO],TIll:11"l'fid.1,wtlll" llli,'ldI!lS'I;11"llli.'I,1 an d Tank 1986Jisacoopcrfltivc-oolllpclit iv':!let dcsignedl;lwrifit:;,lIyas""" "1." 111.-,,,1.11-,':<,0,;;01,1,, memory.\V hcn co op ern tive-ccmpotjtiveucurn]lid sarcll",-~II'"1:l", I"'I,1.,;"I ,ln~.o,;a l ,I.'menr- ory ,thenum berof paucrnsthatCfI lIIll'storedi1tul/,ccur" td y1'''m ll,,,1is l;"\'l'n·lylimilo·,1I,y the largenum berofnodesrequiredforthereeognit i,mof a1'c1i1tivdyl;' llilllllulIll...r..( I','l te r ns.Ccopc ratl vc -compc tiviv c neura lnelshaveIouud'lJ>pli<:il1.i" lISill1"l":" l;lIi;-:illJ.\lIIulll l'l., groupingsof data [Coh enand Gros sb erg1!18 7 j,weakpa ll efllsillnoisyiUI'III.l;pl"tI,I!JX!JI, and rccog nialngcatego ries[Ca rpe nterand Grossh, )rg1!JH7,I!J!JIJI.

2.1.4 St ru ctu r e dNeur alNels

Structur edne ura l networks arcarelativelynewapproachtu1I",m dI",t111",1.,1,1. 'Si ~1I [Fehlman ,Fa utyand Goddard IUMB]. Astructured nournllid mudd ':" "I,,~vj"w r:<J".~"

synt hesisof twolraditi Olla llyOPPUS()r]approa che stoi1rl ifkialifll,,:JliJ';CII<:".S"'/If'O:lLrlyAlill-

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20 Vf'~li~ill,,,r~f,,<:uwt/"IItllf' pnTaliclisf/Ifln']rnhua t ncssof hiolngical brainsandex plor edwaY6of g,'w,ralill,l!, l,hishi",11rWl'r"rwalll:eillnon-biologicalne t wo r ks. The oth e rgroupcon centrat e d urIlI", <ld ..ile, l "lrlldllr<:oftasks anrl algorithmsandexpressed them inconvent io nalcam- 1'111.,,1'lI" tUti OJl.St.ructurerl noural'I<'{m", I d.~atlcmpLto capturethe bestofbeth pa radi g ms.

2.'1.5 COl~~lcxNcurlll Nels

Tlwft'al"'-"th"r'"'lIrallid mlHldswithmore cUlllplcxarchitectures[Fukushi ma\988;

(:;lql<'l ll".'andGIOl<sl...rg 1988,I!J90].These modelsarccomposedofhighly parallel build- ill/!;]'I,,('k~'.halM"ill1.<'fCOIIIII,cl" dto constructhighlycomplexsyste ms . These systems arc usuallylIIm;si vd ypariliid andt~IIJpg(,,1ill 11 mululovcl cr hierarchically fa sh ion.Each of

lh,'~ ,·lids t:lJllsi...1.sofIlHIIIYlayer" of nodes .Tilenet hASfor wa rd ,back ward and/orlatera l

n'l1Il<'l·l ioll.'],('l\\''' I'1I1I01!c S, Some of tile connectionsarc variablewhileothersnrc fixed.

'I'll"\"Miahlceeuucct.ionsarc trainedtoenablethe nodesto acquiretheabilityto lear-n to [ln r"rrlln'rr.'C.t,ly.SIlIlH'of1I1e cnnncct.inns arcexcil.a lo rywllilcother connectionsarcin- hih it.u r.v,CnlllpkxIll)Uf1111lcl.modelsarcspecificilltheirtasksandcanperform very wellror 1111'ir;1s><iglW"tusk»,hut. thesenet slackmodularity.Enha ncem ent to theneural not usually i\l\'"I\',·s('xl ,l'lls;v"tllOtlificlllinli s tothestructu re.

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Chapter 3 G enerating Local Edge P a tte rn for Ne u ral Ne t Input

3.1 Int ro du ction

described.An edgeclementi,Apixelin "amall ,m'awln-rel1u'Im"1I1p;nl)'-ll'~'I'1v.,lm'Kan' changingrapidly ina monot onicway.These('dgl ' dt'lI M'lLlsn,llt'r t i\,.·ly nms l rllt"t ...I~t·11m- tours. Therefore. anedge image isanedgema r) orlhf~origillalr;ray.Jt·\'f·!jlll'l gl '.All,..1';1' operato ris able todetectthe presenceof "loral('flgl'd"II1f'111lIymll lll ll l i llP;ib p;r,uli"lll magnitu deand determin ingits orientation. The griulic nl IIII1,r;uilIll Jc 'UIl}tiM' uri " lIlil.lj,,"uf tbc edge clement can intum beusedLa improvethe,!ch...\l'.11~1.r;.~,illl<'TI",lalc Illi!l!liu,r;

cdgC3,OTremove noiseand falsecdgl':'l.

3.2 Computing the

Edge

Measu rem ents

Theedge image is generated(rom an originalinput illl/lgcl.yIlsingllll~Solid(Jlwra lt,r [DudelindHart1973J.TheSobeledgeoperatorcomput eslIw m..~nilllfl'l1tIl,l lllf·,litl1:1.illll ofmaximalgray-levelchange.TheSobeloperat oris desigrwdto"1I"ruxiflmll~1I,edjSr:tr:ll~

gradie ntfunct ionby computationof the approprialeImri'.(JIIlnla",1vI'rtir:1I1r:u1fl1~'f"·lIh.

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22 UUIIh.:"'l,ardl!.1"-~a r.oml.iuatiunuftwot;radicntmuk,(Figs.3.2A,3.2b), onefor the lJ.,ri;r."/lb.l directionandtileotherfor thevertica ldirectio n.

u h c

<I e

r

- i -I -

~ h i

-1 0 1

-2 0 2

-1 0 1

-1 -2 -1

0 0 0

1 2 1

1'i~llr,::1.1EI"lrIl:nlsina:1,,:1window 11)'rilehorizontalcom ponent II)The verticalcomponent Figurc 3,2Sohdmll~ks

Till'I;HHli"llt mar;llilll<l.:i~IIlJlaillO...Jfromtile two ortiJOgo ni'l1maskoutputs,Tile ho rizo ntal alllithe\~'flic:AI('I)lIlIKl1ll'lll~arede notedby'Sr'and'5,',respectivelyandarcdefinedby (f,•.:1.1),

87

=

(c+2f

+

i)-(a

+

2d+g),

5, = (g+2h+i)-(a + 2b+c).

The gr;ulicnlmaguit ndeatthecent ral point,'9:,isdefinedby: (3.1)

(3.2)

9. =

/ 5':+ S:.

(3.3)

'l'hcdirectionillthe n'l1trlll lloin1(denotedby'0;)isdeterminedby:

o ,

=

arclllll(~) .

^(3..1)

The ,lirl'Ctioll11.1point'c'is ceded intoeightprincipalorientations accordi ngtoFig,3.3, wlu-rc',,'tll'notl"llnorth.'"",'denotesnorth-west,'s e'dmo tcssouth -cast,etc.

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:~'~: w--:--"* , -"-_:

I

, _ :'~-

c 0°, 360°

---- - -- . -- -

HW : S : se

__~_L L _

Figure 3.3Eigl11 principilluri('\\l,lti OllH

The orientationofeach edge clement isTepreSC'1I1t'1III.\,<I.~.'I,uf11itl~·t.iollvIlIlII''( :

wherethe superscr iptsdenotetheprincipaloril'ntaliolls.

Each clement in theset of directionvalueshasbinaryV;lrll(~'0'fir 'I',wJwn'111l~v,llul'ilssiWIl·,J is dependentontheorientation of the edgeelement.l'or(~XiLIIIIII(~.if11I1.-.1",,·"II'lIJl' lIlhols a north orientation,the directionvalue'([In)'isset to 'I', andtheuUll't,Iin'd,ioll viLlilf'1'l, na mely,'cfl·l, ••,d C>. )'arc set to '0'.lienee , 1I1C:!let(Ifdiro-dio llV;llll(~Sfur this('fIg':d'~IIIl'JlL is :

{d(nl,d('),dlej,dew),dCne),fP""',rl("wl,dfor)} ::: (I.n.n.u.n.n,n,n). CUi)

For anon-edgeclement,since theelementdoes!lotllavelUI orilm1.at.if"I ,lllt~st:1. flfdjrf~l:lifln val ues forthe clement consistsof'u's.Thatls:

{d'"', ...,d''''} = {O,•. .,O}. 1'1.7)

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24

3. 3 ThresholdingtheEdgeImage

Tllrf~sll"ltIitigi~ Ilsf~1to simplify an image while retaininginformation about shapes and

W~(Jllldric:structures, Tlltcs hotdingis performed on thegradientmagnitude inorderto

There:Metwokindsof thTL'l;holding: hilcvolandmultilevel. ln the bilcvclthresholding I<M n 1!J78;Kittlerand Illing wo rth 1986; Abutalch1989].thehistogram of the image is hilllOtlaland the thresholdisdlOSCIias II value betweenti l epeaks orthe two distributions.

111tlu:lI,ullilcvdthresholding[Wang andHar alick 198<1; Boukharouha,Hebo rdao lind WCIl- dd 1!ll!fi;1I1lrl zand Schafer19881,the histogram has severalpeaks,andtileval ues oflire t.hn ·sholds art:set to l!Cllaralcthese peaks.

The 1I1T1'1illl1Millg technique usedinthisthcsieisa globalthresholdalgorithm.Thisat- gorithmscnrdl{':;forthevalley betweentwo peaksin the histogramof gradientmagnitude.

Thevalleybetweenthefirstand second peaksdeterminesthethresholdvalue'T'fordis- tiuguishing non-edgeclementsfrom edge clements(Fig.3.'1).Anclementwith a gradient lIlagniLJI(lc'9,,'git'lIlerthan orequa lto the thresholdvalue'1"isinitia lizedto an edge

clt' I Ilt 'II LOtherwise,thedementis initializedto a non-edgeclement. Thatis, jfJ(c;)isthe

thresholdimage then

{ g., if

s« ~ ^r f l' ;)

~

go otherwise,

(3.8)

where'/';' denotes1iI1clement inthethrcsholdcd edge image,'ge,'denotes the gradient runguitudc of the clement,'go' denotesthe gra dientmagnitude for the non-edgeclement.

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No.orpixcl~/dcmC't1ts

prob a ble T Ilon-ec!!:c elements

JlrobOlh\f' edge e1<'1II1·11t!i;

Fo r manycom plex real-world images, IIgrullal tlm -:;hul.JIIrsd urLllr''!II,,,I.lswillyi,.1.!

unsllUsracl oryresultsdue to noise,grad ua lvariatiulJsillgray.I'~Vl'I[II;,I1;lr,1ill,,1 Hrllwil1!IN2~1 or non-uniform light ing [Her tzandSchaferI988J. III}WCIII~r,with1I11!i.pplil:nl i"n ..rtlu~

hierarchica lneura lnetwork system toprocessthe~Igl~irrlltge,anilHprolll!,II:.JW~ ilrlilW~with verysa t israclory resulls can still be obtained.

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26

3.4 SelectingWindowSize

Tlw'UI:all:<IA(~patternto heinp ut totheneuralnet worksystem isiI5 x 5 windowinthe

,~dI!Pilllag':(Fig. :Ui).The r.elltrll.\pixel (<<enot edby'X' ) in tilewindowis thepixelunde r f:Ollsidl~mlil)lIalllibuthits urientatioll and gradientmagnitude ca llbe adjas tcdbythe

• , 1" ,

. ,~, . ^"

I l ' "

, I. , .

, , I , "

!"igllrea.5.Awindowfor theinput of local edge pattern

hii'm rd lindneural network system,Anappropriatewindowsize has to he selected.Irthe windowis too 51110111,thelength of theed ge contourinthelocal edge patternwillbetoo shuttto Ill'ofany sign ificance,whichmakes thene uralnetworksystemless effective. Onthe othe r hand.11.la rgewindowallowshet terinterpolation ofmis sing edge clements butresult s illmorerul1JplirilLl~1localc.lgcpauemsand a very complex neural net design.

3.5 Genera ti ng Input Vectors

A ucurnlnct processestileinformationfromthe input patter n in a vectorform. There are threekindsof input vectors10theneural network.Each compo nentina vectoris associated with,\rurrespondlugc1cmcnt/pixelin a window.Input vector'G'containsthe norma lized

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:!7

gradientmagnitudeoftheclementsinthewindow,(G = {gIl.j = :!!q.Tllt" 'i}\htst'b ofdirect ionvectors,'il(;I'(il(;\= {d~;) },~· = 25.iE{lI,...,.•f'l ).n'rrt '''ptl lll ittl

nil'

eight edge orienta tions.Anexample isused toiIlllstr at e IIIlWttl ,!l'ri\"\' lilt' ilillut,\in~,tillil

westorientationwhilethe other c1e menlsarenon-edged,'lIlt'llls.

• ^I ^,,

^,^~

^' ^~~

²

^"

^, ^,^,.

^{, ,}

^I¹ ^I'

Figure :1.6Edge clements in a window

Thesetofdirectionvalues for'el'Is :

The set

or

directionvaluesfor 'C1' is :

Thesetofdirectionvalues for'ca'is :

{I, a,O,O,o,o.o,f1}.

{O.O,O,I .o ,lJ.o,rJ}.

{O,a,O,f1,f1,O,f1,f1}.

(:I.")

(:1.111 )

(:1.11)

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28 IJPllf:l~,till:ill jl1Jlvector'!J(""associated with the northorientation is describedby:

(3.12) (I,D,O,D,D,I,O,O,O, ...,O).

Silll:lld(~!lI{,1l1s'(:1'and'1:1;'have anorth orientation,theirdirect ion valuesassociatedwith lIn~ll/JrUloricruut lonaro 'L's.Forclements'C1'and'Cll', sincetheyh.wc an orientationwhich is1101.north, thd r directionvaluesassociatedwith thenorth orient ationarc'O's. The other l'I"IIW1l1sIwv('dired iollvaluesof 'O's becausethey(10not have any orientat ion.Similarly, 1.1willputvecto r 'f)(v,j'ussccin tcd with thew<.'Storlontarion isdescribed hy :

(3.13) (0,0 ,0 , 0, 0, 0, I, l,a,...,O) .

[o'llr l,11.,iIlII1l1 vc doT,'J)(i^j"(f) (;"

=

(dfil'}, 1

=

25,iE{n ,..,se}),lllccomponc nlsin vector'/J(' )',cout ninthccomplomcut valuesofthecompone ntsin vector'/J(i)'.For cxample,

(I, O,O,O,O,I, O,O,O,..,0) . (D,I,I, I, I, D,I, I, I ,..,!).

(Ul)

(3.15)

'nil'

1"'d OfS'( ;' ,•Oli)',lind'/J(;)',whereiE[n, .. , sc]arederivedandusedasinput pattern

\'t'clursforthencuruluct.

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Chapter 4 Edge Contour D e t ection Su'bnot

4.1 In t r oduction

In Chapterthree, thecomputat ion ofthe initiall'llg \' lI\\' i\l\\1t( 'llll'1l 1 Wll !\,I,.,;,'ril.1'l1.'1'111' gradient magnit ud e and orientationforapixelin111t~inputill\a~eisohl"im"!11.1'l1~il\~t.lll' SobelOp erat or.A globalthrcsbcldal~orililUlis 1111'11lIs, ~Jiu:.q!jrt·p;aLo-,>,I!!.,·"]" llU'lIl,sIrom non-edge clement s.

Inthischapter,the subnct in1IlCfirst level

or

tI,,· hi.'rard,irill,wufillnetworksysu-m, called the EdgeContour Dctec tlcn Sulmcl,ist!c licri l.l..l.Thi~!lIl h lw ln"("(·; vl";IIIPlll,10,11, generated bythe edge operato rand detects the1'f''''''IIC'Corl'l'[tllCUlil U ll niillv;,rium lund edge patterns,The EdgeContollrDetect ion 5uhnl1.call Iu·cur ...tdydl'l' ..1f..I~,·r(",ltllIrsI.y simulta neouslyutilizingallavailableillrormatioll,

4.2 InformationContributing tothe DetectionofEdgeCf)Hlollr~

Threesourcesofinformationcont ribute totheIlcll~li() 1lIIfallI~.I K' ~f:l1l11"lIr;tIld111'11':'- affecttheadjustmenttothe edgemeasurementoflht~ft:1I1ml(:1[11;(:dl~ll)('tl l,Theyan! :

I,The gradientmagnitudeofthe neighbouring{,'1lgt:dt:lrll:lltsill/lIU/"id(~IW~ pll.ltf~rlJ,II collectivecon siderat ion ofthe gradie ntrnagnihlflc of nl:i.E:liI l1.urjll~''fI~I:d'~II"'I.lsI'MI provide a goo d indicationof thepossibilit y oftt,,'!prl~I'IIr.c~llflUIf.'/I~.~f"JJlllfJtJ t,

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30

2.TilelJri.~nlali{J1ltlffI(:ighhollr ingedge clements.Iftheseedgeclements1I"...e the same

"rif'IlLAlio n,thisi~it.good ind icatio n thatthey would emst ructAn edge contour.

:I.'1'111:relati veI~jlio,,~or appropriatenci,!;hl)Ourinr;pixels /edgeclementsinthe local l!t.lgepattern, Thilli!l,thelocAtionsof neighbo uring edge clements whicharethe 1~llnstilllcnlsofanedge contour.

'1'111:in fo rrna l jo llprovidedbythegra die nt magnitud e and the orient ati onof appropri at e

1~llgeebrwnlsill Lhelocalotgc patter nmusthe utilized simulta neously toachievethecor-

n'd detection of anedgecontour. Therefore,neighbouringedgeclements which havethe SiIIlle!uril!nl al ioll amiha velarge gradiclitmagni t udewillgiveaverygoodindicatio n tha t till:rml ri'lledge clementliceon thedetectededge contour.

4.3 Selective Fun ct ional Ex pa n si on Model

III the Iunetionalcxpe ndo nmodel, a sd offunctions(/1,12,.• •

,1..)

maps an inputpattern illtn alar~erpa Ltl"l'lIl1pa cc.Suchnonlinearcom binaLionsofpatternelementsareintroduced rueitfUIlcti ullallink.~A.(hinputpallcrn is exten dedbysomenonlinea r trans for mationbe- fort,it is prcscutcdto thenod einthe net.lienee,thefunctionalprocess esgene ra t edbythe fUlldi(lllilllinkenabletheenhancem entoftheinputpatternto higher -orderterms,

TIlt'genera lIuuc tiounlex panslon model generalesallthepossibleIuncvional processes.A majurdrawlmck ofsuch nchililtle combin a to rialexplosio nof high-ord erterms{I\fimkyand 1)"pl·rtI!JSS).IIIordertoavoidthis,thefunct iooa l-lin knetsfortheEdgeConto urDetec- tionSuhl1darcspecially Ilcsignl'\l andarc rcfc rcd 10 asthe SelectiveFunction al Expansio n

(47)

Mod el.Usually,funct ionalprocessesbeyondthe!\('('(Iudonh-rtllll}'han-asmall I" l!...~i"ilit), ofhcin! useful and donotsig nifica ntl y OOlltri blllctothelid outp ut11'.' 0l!ls..~:1'.",I!l$!)..[.

Fur t hermore, notallsecond order (ullc l ionalproCt'5!1('$need tohenlll~i.I,"n'Cl111dl.lril.1e'ri l'A' VAlidedgepatterns. In ordertoadjllslthe edge1ill'i\.·ulrt'lIl'nl.lIl'\'t'lltype'lltlfruufti" lI<tl processcsarc selected(ortheIunctlcnalli nk.The'p','q'. 'q",''I"',','i11l.1·.~·I),p"lln"T·!t!t4'S areusedfordetectin g various validedgeconto ursinlocal edgellaU<-'rIL~audlu'urv,ut',,!<C..I (orrclnforclng the edgemeasurement. The'h'lype IlfOn'l;!t0111111'ut.ln-rhandi!tus,..1 fur detecli ng Oleabsellceofv"lidloca ledgepatt e r nsandh"III'('i~lIsl..1rorsllppn':iSillll;tlll'.'c1W·

measure ment.

I

^{.., X}ÎÎ^{. .}^.Î

·

^.

I'li

ÎÎ^/^X^..^. ÎÎ^X^. ^..^..

a)Rectilinear b) Non.symmet riul c}Clltvilin('u

Fi~ll re'1.1Edge c:vnlm l l'1l

4,3.1 Processes lot'Detect ingRe ct ilinear EdgeConto ur

A rectilinearedge contour (Fig,4.1/1,)is <:har ader il'.I:dlIy the"1'tYrll~rllllf:liulli,1JlrWI'SS.

The 'p'lypefun ct ion alprc ccssshasIourdifferentfJrof.(:S.~(~.~.IlltlTldy.J'~~~" 11~;~, ,.~;~" alld p!~!n .where'k'denotes theorlcntat ion,kE{rt.... ,....~}.A',.'lY/,I~pm rl<SNiNi\.Ns"riall..1 withtwoedge clementsonthe rectilinea r edgeconto urin lheIOf.al1:llgcpaUI'W,l.;adl

f.r

(48)

32 theM)r:dWl dcltlf:nlsiskicetcdOTiopposite sidesofthe edgecontour which isdividedbythe centralelement'X'.For example ,forILre ct ilinear edgecontour(Fig.4.1a ),the two edge d':/nenl slL~~f)r:illlcdwit hit.'p'type process,P!~~,arc theedge clementsat locationsindexed Ily'i i'mulIi)'intile local pattern, the centralcleme nt'X'issituatedbetweentheedge dl'lIll'llls atlocations'ii'and'ii',The'p'type processesarc:

("

d !; ) *( 4 ;)

«s« «s« (1.2)

Pi"j,

11!~~ ^dl~)^..c1~l

..

gi, ..gb (1.3)

1" d!:J *~;) ·9;.^*9i, ^(1.1)

Iii.'; ,

("

d !;l '" i;l .. s....

Yj, (4.5)

T1i•.h

wlll'n:

ill;),

d}~)denotethe direct ionvaluesandgi"~9j,denote the gradient magnitudesof the two edge cleme nts indexedby'i.'and'j]',In ordertodotccta rectil inearedge conlo ur, all

ofl'lll:hprocessisdependent onthedirection values.

11 ^/.

_{a) Paucm}

^.

¹

^{,/0 , ,} ^" ^, ^'

^I^X

^. ^, ^/. ^, ^,

^I_.

^/0

!

^,

^I

^, ^, R ^{I, ,}

_{b) Pattern}^•

^,

^I

^,..;: ^"

⁷¹^X^•

^, ^{, , ,}

^...,.

^{' /o}

^"

^,

_-_II^I

^,

Figure ,1.2 Localedgepauems

Fur examp le, a rectilinearedgecont ourwit h a north-cast orientation in alocal edgepattern (Fig.·L~il.)i~rhnra ctcrizedbythefollowing'p'type pro cesses associa te d withthe north-cast

(49)

:1:1 orient at ion.

luI crl~'1•~6d~g~^-gill lUi)

Pu e

(,101

J1u) ,

J~<I_g~.glO _p_.i)

Pi "

I •• )

dl.~'1-I~~<)-9<.,-gil; (-I.:\) h.16

(".) ,~,'<J"J~'I.!/!l'g7U. (I.") Pi '"

(,,<)

I.I- gs- Y.<; (-LIllI Pue

(~I I-1.ys"g» 1·1.11)

Pl,20 I" . )

I"I .!J<J-gl6 (<.121 h,le

~~

^1,,1"^99"^9», ^lUll

Allthefunctionalprocessesassociatedwit h anorth-l,.,~loril'lIlatioll fllrtllO~n'f:t ililll"ar1..1~,~

contourare activated ,However,if111eorientationofan(~I~ed"lIl1 mtis,liff"wll trmllllIw associatedorientation oftheprocess,thenL1lcrurrc;pondillgrUlidiml,.1"run~sswill1.,:,I'i·

ectlvetc d. IIIFig.1.2b,edgeclements allocat io ns'9' 1\1Id ':lO'illtll(!lur.;,1,:d~, :llilLt,"r11du nothavca north-cast cnc ntaticnandas suchtlL(~irdirecLiollV;illl'~~itr,: 'II's.'I'11l!fI:r,m!,

r".,

Pl ,20

1·'·95·!JIII=!1~·[1Ir.

1-0-95.!l1O

=

⁰

11.") (1.1.1)

(50)

0 ..I "!}<J* YJG=0 0 ...0 "!J'J" Y20

=

0,

(4.16 ) (4. 17)

IIIll li~^situatlon,onlyprocessP~~I'J^is^{activate d}while processespi~,~~I'J,

pt;J

are de- activated.Therefore,iftlmrnarcmore neighbou ringedge clementswithtilesame orienta - liun,ll~ln~functionalproCCNSCSarcactivated.Ontheot herhand,ifthe local edge patte rn

llI H'1Inut form anedge contour,tbe functionalprocesseswill not be activated.

4.3.2 ProcessesforDetecti ngNon.S ymm e tri calLinear Ed ge Conto ur

A neu-symtuetricalliucaredge contour(Fig. 4.11» is characterizedby the''1', "/',and 'q~'typr' flllldiOlialprrrces scs.Fo reachof thesethree types of processes,there arcfourdil-

q!~I:;",q~~tQ"

,,!:fQ'

andq~:::e' The''1',''1''and

'qU,

type processes arcassociatedwith two edge clementsallthenon-symmetrical linear edge contour.Eachof those IXIge clementsis loc<ll.cllon opposite sidesofthe edgecontourwhichisdividedbythe centr alclement'X'.

Fur example,[oraunn-eymmctricalllncar edge contour(Fig. '1.1b),the two edge clements

t·,tl\'~t'l"l1lt']]lsatlocat.ionsindexedby'7111'and 'nl' in thelocal pa t tern. TIle cenl ralclement 'X'is situated betweentheedge clements atlocation s 'ml 'and'nl" The'q'type process is uftlu- second order;\..'1two edge clementsarc considered .The'q"and'{ ' typeprocessesare orthethird orderas eachor thesefunctionalprocessesinc orpora testhreeedge elements.

(4.18)

(51)

: m

(·I.:.tn

The'g"and'q'"typepro cessesarc similar to 111c'q'typoproeesa c'xn 'plll,,~ltil\'

'1/'

tYlll' pro cessalso takes111eorientation ortheclement.(rldillljiH"Cnl1.0tlll~n~lIl.ril l,·, I~pdC'rrll'llt int o account.Whereas forthe'q'" type proces s,11l1lnri('ntal iullortl1l'l"I'lItr;II,~lw~dl'm"111 (dx )isconsidered(Fig. 1.lb).Fereacll'q"ty/,cprocess, a<:Ul"m~rlo"ding'f('tYlmpm n'ssis usedto countera ct th e effec tsof each ether,TIle1Il1~iI!·;ur(·lIlllIl 1orllj(~n~ntra ll'rlw' d('rrll'nl'X' shouldnot be st rengthene d,beca use theclement

'I'

isallolgce]l'rrwlIland itc:(jllll'ldl"~tlll!

edgecontour,increasingtheedge measurementofclement'X'willUl il:kl~n t"c~I~IW~runtonr, orcreat efalseedge clcmc»; s.

a)A'complete'edgecontour

II

^•

,

^I

·"

^{• -}^{, - , . .}

,

-, -" X I I

Il)All'incomplet e'mlgrlCIIlIt fH,r F'igUfC4.3Non-symmctricalndgcpa tt e rns

(52)

36

Furexample,inthe {unctio nal-linknelilSsociiloowiththe eMl orientation(Fir;.4.3&),l.hc dind io"valuf:ll'~~",.•",

't4.1'

havethevalue,,',Therefore,

(1.30)

(1.33)

111'nn:,thoIunctiona lproccs scsdcscrlbcdinexpressions(>1.30.~.3.1)areactivatedtoreinforce tlwl"l'lIlrall'{]g{:clement 'X'.Howev er, Minceedge clement ' S ' existsand completestheedge contour, cflgcdl:rncli L'X"5110uld noLhereinforcedbecause theedge contouris already 'ouIIIlIl'lc',Therefo re,thecorrespo nding'q"type processes must. be activated Lacounter theTl'l'jlIlIlS('!lOCtheadivatcd','lypepro ces ses.That is,

~~~

=

l- t-I '99*911

ql~J

=

I.t -I '910 'gI2' (·1.31)

III tlrtll'T11>offsetthedTcelsoftheadivalcd''I'type proces ses bythe', "typeprecesses, a I'llsili\,!,wL'ig!llill assignt'1l tothe'q'typeprocess,whileAncgAtiveweightisassignedtothe ('Oft l'Xllllll1ling'f/"type(lfocexs,The absolutevaluesoftheseweig htsarc equalandthese wt'i~hl('dprocessescHCconnected to thesam eneura lnode.Therefore ,ifa's'typepro cessis O!c'th'41I('d;\I1e1thccdgcrlc mc lll'8'(Fig,4,3<\)comple testheedgecon tour,t h ecorresponding ',," tY11l..'I'rot'l.,.,.~belseactivatcdto nullifythedrccls orthe'q'typeprecesses.Ilcwevcr,if ,'ll'l1ll'lt'S'Illk'llnotcompletetheedgecontour(Fig..1.31».the'q"typePPQCf,'SSCSwillnot

(53)

be activated bccaus-thedirecLionvaluefo r eletueut'S'(d~'I)is'0',TIIt'n 'fun', ulllythe

'11'

ty p eprocesseswillbeactivatedandtheresultantcITedis aIlositin ' tlutPllthOI1ltlH'''I't~'Pl~

processes.

Neighb ouringclementswith orientationsdiITcrclitfromtill!or i<'lIlat.iollhandll'll10)'lilt' functional-linknetarc usedtosuppressthecentraldemcu tinLIH~Illf all'lI/?;I'11,1LtI'rll(cldails concerningsuppressionarediscussed insection1.3 .1.5),Dnetothculrsd. ti llgC'lfC'I' huf1I11:

'q'type and'q"typ epro cesses,acentraledgec!e ITlt'uLillthl~valid(~Ig,~willlll1.illlllll·lyhe elim inatedbythesuppression,Inorder to preservetheel ' lll mlva lidl'il,;{'C,II'lIl t'lll.but not thefalseedgeclement,'q '" typeproces sestAke illl "an' oullltilt)Oril~lIt;ltitl llufthofl~lltal edgeclement Fo r example,inFig,t3a,if edgecktlwnl 'X'haslUII!itsluric'l lll,nUIl,it s directionvaluewillbe'I' andthereforethefollowingIlro('(~s~c'!IwillheM·t.ivaLc·11:

q~:~

=

1*1 ",1 *fh'*911

(1.'11)

Byconsideringth eorientationof the central clement,ifthecl'lilr illdt~IIII~lIlisaIl(JJH',I~(!

clement, noneofthe'qff'typ e processeswillbe activn\c'(1andtlris willprl~w~IJLtill'rrcatlon offalse edge clements.

4.3.3 Process es (orDe tectingCur vilinear EdgeContour

Acurvilinearedgecontour(Fig.tic)is characterized hythe'r 'typeflllll:LiulI illl,rlWl~S . The'r'typefunctio nalprocesshas four different pmcussca , namely,r~~;'J" r~~:~.,T~~~!"and

(54)

38 r~~~!.,where :

(lJ

'k'am]'I'denotetheorie nta tions,and(2)'U l', '112' , 'VI'and'V2'index the

l(j(:;~tioll!loftI,e edgedementsinthe localpattern.An'r' typ eprocessisalsoofthe second

order milljsassociatedwithtwoedge cleme nts on thecurvili nearedge contour inthelocal cdW:Imtt erll. Each oftheseedgeclementsis locatedonopposite sidesofthe edge contour whiehisdividedhythecentralclement·X'.Inorde rtodetec tacu rvili nearedgecontour, allf\Jllt'r'typeproCCSSL'Sarcconsidered:

rt~:'!, d~:..d~~)..9~1..!lv, (~.1 2)

r~~~1 d~:

'"

d~l^..9~,.. 9"" (1.13)

l·t~~J, d~!..d~l*!J..,*!lu, (~ M)

r~~~~ d~!..d~)..

s,• ..

9112' (4.45)

wherc :(i) ifk=='fl'thenIE{nc,nw}; (v) ifk=='uc'the nIE{n ,e };

(ii)ifk=='.~ 'thenIE{" r., 3W}; (vi) if~'

=

'mv'then IE{n, w};

(iii)ifk

=

'e' thenIE{nc,se}; (vii)ifk='JW'thenIE{s,w};

[lv]ifk='w'the nIE{nw,Jw};(viii)ifk='ee'the nfE{s.e].

TIlt'ar1.i\'illiolloTau'r 'typeprocesslsdepen dentonthedirecti onvalueswhich arcessoci- illl,.1 willI dilTl'refiL urielltations,lIence,this activationrequire ment foran'r'typeprocess i:>dilT{'rclltfrom tha lToreit hera'p','q', 'q" ,or'q'"type pro cess,A'p', 'q' ,'q",or'q'"

l}'11t'prun'ss isactiva tedonlyifall the edge clementsassociat edwiththefunctionalprocess havethesa meorientation astheorie ntat ion handledbythefun ctionalprocess.However, in IlrclntilM!i\'ateilll'r 'typeprocessinIIfunct ional-linknet.anorie ntationdilTerent from