PSO Algorithm Particle Filters for Improving the Performance of Lane Detection and Tracking Systems in Difficult Roads

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1 Sensors 2012, 12, ; do: /s Arcle OPEN ACCESS sensors ISSN PSO Algorhm Parcle Flers for Improvng he Performance of Lane Deecon and Trackng Sysems n Dffcul Roads Wen-Chang Cheng Deparmen of Compuer Scence and Informaon Engneerng, Chaoyang Unversy of Technology, 168, Jfong E. Rd., Wufong Dsrc, Tachung 41349, Tawan; E-Mal: wccheng@cyu.edu.w; Tel.: (ex. 5208); Fax: Receved: 9 Augus 2012; n revsed form: 7 December 2012 / Acceped: 10 December 2012 / Publshed: 12 December 2012 Absrac: In hs paper we propose a robus lane deecon and rackng mehod by combnng parcle flers wh he parcle swarm opmzaon mehod. Ths mehod manly uses he parcle flers o deec and rack he local opmum of he lane model n he npu mage and hen seeks he global opmal soluon of he lane model by a parcle swarm opmzaon mehod. The parcle fler can effecvely complee lane deecon and rackng n complcaed or varable lane envronmens. However, he resul obaned s usually a local opmal sysem saus raher han he global opmal sysem saus. Thus, he parcle swarm opmzaon mehod s used o furher refne he global opmal sysem saus n all sysem sauses. Snce he parcle swarm opmzaon mehod s a global opmzaon algorhm based on erave compung, can fnd he global opmal lane model by smulang he food fndng way of fsh school or nsecs under he muual cooperaon of all parcles. In verfcaon esng, he es envronmens ncluded hghways and ordnary roads as well as sragh and curved lanes, uphll and downhll lanes, lane changes, ec. Our proposed mehod can complee he lane deecon and rackng more accuraely and effecvely hen exsng opons. Keywords: drver asssance sysem; lane deparure warnng sysem; lane followng sysem; lane collson warnng sysem; lane model

2 Sensors 2012, Inroducon Lane deecon plays an mporan role n many drver asssance sysems such as lane deparure warnng sysems, lane followng sysems, lane collson warnng sysems, ec. [1 6]. A lane deparure warnng sysem manly deermnes wheher he vehcle s devang from he curren lane or crosses he lane based on he geomercal relaonshp beween he lane and he vehcle. When he vehcle depars from or crosses he lane, a warnng s gven for he frs me o draw he drver s aenon or he urn sgnal s auomacally acvaed when changng lanes; hs can effecvely reduce he ncdence of accdens. However, he lane followng sysem s usually used o monor wheher he drver s focused on drvng or no. When he drver s absen-mnded, he vehcle can easly drf o he lef and rgh. Therefore, he drvng saus can be known hrough a lane followng sysem. As for he lane collson warnng sysem, f he sysem does no know he lane locaon, mgh gve wrong warnngs by msakng he barrers on he roadsde as obsacles n he lane. Therefore, he lane deecon can effecvely reduce he rae of false alarms. From he above dscusson can be concluded ha lane deecon ndeed plays an mporan role n drvng asssance sysems. The commonly used mehod n proposed lane deecon mehods for lane rackng s he Kalman fler [7 15]. I s a hgh-effcency recurson fler whch can esmae he saus of dynamc sysems based on a seres of ncomplee measuremens conanng nerference nformaon. The dynamc sysem s expressed as a hdden Markov model and s saus s used o express he lane models and carry ou lane deecon and rackng. One of s advanages s s ably o speed up lane deecon. I can ncrease he lane search speed and accuracy n npu mages snce he sysem esablshes he area of neres wh lane models. Anoher advanage s ha can smooh he deecon resuls, reduce he errors and ncrease he sably of lane deecon. However, all hese advanages become problems n ceran road suaons, for example, dsconnuous lane markngs, lane changes and complcaed lane condons. Snce he range of area of neres lms he deecon, he above suaons can easly cause deecon errors. The soluon s o use he parcle fler (PF) o carry ou lane deecon and rackng [16 21]. The parcle fler s a novel echnology for probably-based rackng. I s a mehod based on he saus of dynamc sysem wh mulple Gaussan probably dsrbuon funcons, whch can sll effecvely complee lane deecon and rackng under condons such as dsconnuous lanes, lane changes and complcaed lanes. A parcle-based lane deecon and rackng approach usually sars wh parcle predcon, measuremen, and re-samplng [1]. Souhall and Taylor [16] presened a lane deecor based on a condensaon framework [22], whch uses markng pons as measuremen feaures. Each pon n he mage receves a score based on he dsance o he neares lane markng, and hese scores are used o compue he machng score of each parcle. The measuremen sep s consderably smpler han he Kalman fler, because usually consss of a comparson beween he parcle and he mage daa. In addon, many dfferen cues are used n he measuremen seps of he parcle fler [17 20] so as o ncrease he accuracy of he measuremen seps, for example, edge pons, color, emplae, sereo vson, ec. Danescu and Nedevsch [21] used sereo vson o help confrm he lane markng pons and used he condensaon parcle fler o acheve lane deecon and rackng. Even so, he parcle fler generally akes he parcle wh he bgges wegh or weghed sum of all parcles as he las oupu parcle. Therefore, he oupu resul s a local opmal soluon raher han a global opmal soluon n he problem doman. Ths paper proposes a new PSO-PF

3 Sensors 2012, algorhm by combnng he parcle fler and parcle swarm opmzaon (PSO) mehod. Such an algorhm s an erave operaon opmzaon algorhm ha furher refnes he global opmzaon sysem saus from he curren parcle fler sysem saus by usng he parcle swarm opmzaon mehod. The parcle swarm opmzaon mehod akes each parcle (saus) as an ndependen ndvdual by smulang he food fndng way of fsh school or nsecs, and can fnd he global opmal sysem saus under he muual cooperaon of all parcles. As a resul, PSO-PF can be used o search for he opmal lane model. In such an algorhm, he lane model s frsly defned. Each parcle represens a lane model and hus s known as a lane parcle. The algorhm can be dvded no wo sages. In he frs sage, he parcle fler s used for he predcon, measuremen and re-samplng of lane parcles. In he second sage, all lane parcles n he frs sage are aken as he orgnal parcles n he parcle swarm opmzaon mehod and he global opmal lane parcles can be obaned hrough calculaon by he parcle swarm opmzaon mehod. The remanng secons n hs paper are as follows: Secon 2 frsly nroduces he parcle fler and parcle swarm opmzaon mehod and hen specfes he new PSO-PF algorhm (PSO-PF). Secon 3 nroduces he lane model and how o use PSO-PF o complee he lane deecon and rackng. Secon 4 shows he expermens and resuls and he las secon presens he conclusons. 2. The PSO-PF Algorhm The PSO-PF algorhm hybrdzes a parcle fler and a parcle swarm opmzaon algorhm. The secon s gven over o llusrang he desgn of hs new algorhm Parcle Flers n Frsly, he dynamc sysem saus whn me s expressed as x R, = 1, 2,, N, wheren, he sysem saus conans he locaon, speed or range sze. The forecasng sysem of parcle fler s as follows: x = f ( x 1, w ), (1) n n n where f s he sysem ransfer marx from R R R, whch conans how o forecas he curren saus x based on he pas saus x 1. The forecased nose w s also added no he forecasng process, bu he nformaon s ndependen n me and s dsrbuon s no lmed. In he p observaon saus z R a me, z s a column vecor of p 1, conanng he observed saus resul. The observaon sysem s defned as follows: z = h ( x, v ), (2) n p p h s he observaon marx from R R R, he curren saus can be evaluaed as observaon resul z, and v s he nose durng observaon. The man purpose of parcle fler s o esmae he probably densy funcon wh he observed nformaon { z 1, z2,..., z}. In such case, D s he se of { z 1, z2,..., z}. Assume he poseror probably dsrbuon funcon (pdf) p( x 1 D 1) a me -1 s known, he poseror pdf p( x D ) can be deduced by Bayesan heorem. Ths process conans predcon and measuremen sages:

4 Sensors 2012, (1) Predcon: The poseror pdf p( x D 1) s propagaed a me sep usng he Chapman-Kolmogorov equaon: p( x D 1) = p( x x 1) p( x 1 D 1) dx 1, (3) wheren p( x x 1) s a Markov procedure. (2) Measuremen: The poseror pdf p( x D ) s compued usng he observaon vecor { z 1, z2,..., z} : p( z x ) p( x D 1 ) p( x D ) =, p( z D 1 ) (4) wheren P z ) s a normalzed em expressed as follows: ( D 1 p z D ) p( z x ) p( x D ) dx. (5) ( 1 = 1 The am of he PF algorhm s o recursvely esmae he poseror pdf p( x D ). Therefore, hs pdf s represened by a se of weghed parcles {( s, π ), = 1, 2,..., N}, where he weghs π p( z x = s ) are normalzed. The fnal sae oupu of he sysem s can be esmaed by he followng equaon: N s = π s (6) = 1 The basc parcle fler algorhm also needs o conduc he parcle re-samplng based on he parcle wegh n addon o he above observaon and forecas seps. The parcle wh hgher wegh π has more new parcles, and he oal number of new parcles s equal o ha of old parcles. Because of dfferen re-samplng mehods, many varable algorhms are proposed for he parcle fler. The CONDENSATION algorhm frsly proposed by Isard and Blake [22], whch s a parcle fler algorhm ha s easly mplemened and hus adoped n hs paper Parcle Swarm Opmzaon Algorhm Parcle Swarm Opmzaon (PSO) s a sochasc global opmzaon echnque whch has been shown o successfully opmze a wde range of connuous funcons [23,24]. The algorhm s based on a flockng of brds or a schoolng of fsh o look for food. PSO searches a space by adjusng he rajecores of ndvdual vecors, also called parcles, whch are concepualzed as movng pons n muldmensonal problem space wh wo assocaed vecors, poson vecor x k and velocy vecor v k, = 1, 2,, N for he curren evoluonary eraon k. The velocy of he ndvdual parcle n PSO s dynamcally adjused accordng o s own flyng experence and s companons flyng experence flyng n he search space. The former was ermed cognon-only model and he laer was ermed socal-only model [25]. Therefore, we ge: v k+ 1 = w v k + c1 rand ( x pbes xk ) + c2 rand ( x gbes xk )), (7) x = x + v k+ 1 k k, (8) where w s nera wegh facor (Hu and Eberha [26] suggesed usng 0.4~0.9), c 1 and c 2 are acceleraon consans. rand s random number beween 0 and 1. v s he velocy of parcle a k

5 Sensors 2012, eraon k. and x k s poson of parcle a eraon k, x gbes s he bes prevous poson among all he parcles. x pbes s he bes prevous poson of parcle 2.3. The PSO-PF Algorhm Ths secon wll nroduce he newly-proposed PSO-PF algorhm. To faclae he descrpon of algorhm, we rewre he parcle fler and parcle swarm opmzaon mehod wh a pseudo code program. Algorhm 1 shows a pseudo code program of a sandard SIR parcle fler. The algorhm conans he parameer seng and man loops. The parameer seng conans se P of N parcle sauses and se E of esmaed values of all parcles ha changes wh me. The man loop conans such seps as predcon, measuremen and resample of parcle saus, among whch he resample consss of he wegh calculaon of each parcle saus and he poson of new parcle n re-samplng based on he wegh value. Algorhm 2 shows he pseudo code algorhm of parcle swarm opmzaon mehod, whch also conans he parameer seng and man loops. As for he parameer seng, se P represens he se of N parcles, and se V represens he se of movemen speeds of all parcles n he k h eraon. Se P pbes s he se of recordng he opmal poson of each parcle, and se P gbes represens he weghed sum of P pbes of all curren parcles or he se of opmal posons so far. Algorhm 1. A pseudo-code for PF algorhm. Procedure ParcleFler() Var P[1 N]: Parcle se; E[1 N]: Esmae se along me; : me; begn = 0; Inalze(P); whle ( < T) do begn Predcon(P); Esmae(P, E[]); Resample(P, E[]); = + 1; end end Algorhm 2. A pseudo-code for PSO algorhm. Procedure ParcleSwarmOpmzaon() Var P[1 N]: parcle se; V[1 N]: velocy se along eraon; P pbes [1 N]: he bes parcle se along eraon; P gbes : he bes parcle of all parcle se along eraon; k: eraon;

6 Sensors 2012, Algorhm 2. Con. begn k = 0; Inalze(P); whle (k < K) do begn CompuePacleBes(P, P pbes [k]); CompueWeghBes(P pbes [k], P gbes [k]); CompueVelocys(V[k]); Updae(P); k = k + 1; end end As shown n Equaon (6), he parcle fler generally akes he weghed sum of all parcles or he parcle wh he bgges wegh value as he fnal oupu. However, boh oupus are approxmae opmal soluons or local opmal soluons. Thus n hs paper, we proposed a new PSO-PF algorhm by combnng he parcle fler wh he parcle swarm opmzaon mehod. Snce he parcle swarm opmzaon mehod s an algorhm o ge he opmal soluon, s used o furher refne he global opmal oupu from all parcle sauses afer he parcle fler re-samplng. Algorhm 3 shows he pseudo code of he PSO-PF algorhm, whch frsly nalzes all parcle sauses and hen uses he parcle fler o carry ou he predcon, measuremen and resample of parcle saus, and hen furher searches for he opmal saus from parcle sauses afer re-samplng by he parcle swarm opmzaon mehod. Laer, copes all parcle sauses afer he parcle fler re-samplng o he parcle swarm opmzaon mehod o sar he erave compung program. Snce he process of he parcle swarm opmzaon mehod doesn cause any mpac on all parcle sauses of parcle fler, can be conduced n parallel wh he algorhm. Algorhm 3. A pseudo-code for PSO-PF algorhm. Procedure PSOAlgorhmParcleFler() Var P[1 N]: Parcle se; E[1 N]: Esmae se along me; : me; begn (Parcle Fler) = 0; Inalze(P); whle ( < T) do begn Predcon(P); Esmae(P, E[]); Resample(P, E[]); k = 0; (Parcle Swarm Opmzaon ) Inalze(P = P);

7 Sensors 2012, Algorhm 3. Con. end end whle (k < K) do begn CompuePacleBes(P, P pbes [k]); CompueWeghBes(P pbes [k], P gbes [k]); CompueVelocys(V[k]); Updae(P ); k = k + 1; end = + 1; Fgure 1 shows he flow char of T vdeo frames connuously execued by he PSO-PF algorhm, n whch he upper par shows connuously npu vdeo frames and he lower he procedure flow processed by a dual core processor. A me, vdeo frame of frame() s npu and he core 1 frsly nalzes he parcle sae of he parcle fler, hen predcs, esmaes and re-samples parcles. Fnally, he parcle sae P s oupu o core 2 as he nalzaon parcle group P of PSO mehod and he parcle sae for he nex npu vdeo frame a me +1. When core 1 s processng he parcle fler for vdeo frame of frame(+1), core 2 s execung he PSO mehod of parcle group for vdeo frame of frame() and oupung he resul, P gbes. Therefore, PSO-PF algorhm can execue parallel processng. In addon, n he execuon, f fals o deec he lane, core 1 wll re-nalze he parcle sae of he parcle fler o connue deecng he nex npu vdeo frame. Fgure 1. The block dagram for PSO-PF algorhm. frame() frame(+1) frame(+t) Inalzed PF Inalzed PF Core 1 PF() P P +1 PF(+1) PF(+T) Core 2 P P +1 PSO() PSO(+1) PSO(+T-1) PF: Parcle Fler PSO: Parcle swarm opmzaon P gbes () P gbes (+1) P gbes (+T-1) 3. Lane Deecon and Trackng Usng he PSO-PF Ths secon llusraes how o use he proposed new PSO-PF algorhm (PSO-PF) o complee he lane deecon and rackng. Frsly, s mporan o defne he saus of each parcle ha represens

8 Sensors 2012, he lane model whch s also denfed as he lane parcle [21]. Wh gven parcles for N lanes, hen he PSO-PF algorhm s used o complee he predcon, measuremen and resample of lane parcle as well as search and oupu he opmal lane parcles, respecvely, as follows Lane Parcle General lane models represen he commonly-used sragh lne and curve lane models. Alhough he sragh lne lane model has a few parameers ha are easly calculaed, does no apply o he acual applcaon. Thus we adoped he curve lane model n hs paper. The ground lane model defned n hs paper s shown n Fgure 2. Fgure 2. Insallaon layou of lane models and cameras. β Z Y R C = 1 R α O β W X (X 0, Y 0, Z 0 ) Z L Gven he parcles for N lanes, he represenaon vecor of each lane parcle s shown as follows: T [ C, L, W, α, ], 1,..., N, x (9) = β = where C, L and W represen he horzonal curvaure, he laeral dsance from he vehcle cener o he rgh lane markng and wdh beween he lef and rgh lanes of he h lane parcle, respecvely. α and β denoe he pch angle and yaw angle of he camera. Relevan parameers are defned n he lef secon of Fgure 2. The rgh and lef drecons of he vehcle are shown n he X-axs whle he fron and back drecons are shown n he Z-axs, represenng he drecon of ravel of he vehcle. In he fgure, a par of double, hck doed arcs represens he poson of he lane markngs on he ground. The arc curvaure C s defned as he recprocal of he radus R of he correspondng arc. The rgh secon of Fgure 2 shows ha he es camera s nsalled n he vehcle below he rear vew mrror of he fron wndsheld whch s H cm above he ground. The camera faces he fron lane of he vehcle and s parallel o he vehcle body. There s a pch angle α wh he ground. Based on he assumpon of a fla ground, he pnhole camera s used o descrbe he relaonshp beween he camera coordnae and world coordnae. The pnhole camera model s based on he prncple of colneary, wheren each pon on he ground s projeced usng a sragh lne from he projecon cener o he mage plane. The orgn of he camera coordnae sysem s a he projecon cener of he locaon (X 0, Y 0, Z 0 ) wh respec o he ground coordnae sysem; he Z-axs of he camera frame s perpendcular o he mage plane. The roaon s represened usng Euler angles α (pch angle), β (yaw angle) and γ (roll angle)

9 Sensors 2012, whch defne a sequence of hree elemenary roaons around X, Y, Z-axs, respecvely. In addon, he drecon of he seerng wheel and he roll angle are no consdered n hs paper o smplfy he calculaon of he lane model. Fgure 3 shows he examples of he lane model and he correspondng projecon mage. I s assumed ha he vehcle s n he mddle of he lane, and Fgure 3(a c) represens he ground lane model layou of he lef bend (posve curvaure = 1e 5 ), sragh lne (curvaure s close o 0) and he rgh bend (negave curvaure = 1e 5 ), respecvely. The parallel doed lnes n he fgure represen he lef and rgh lane markngs (red lne for rgh lane markng, blue lne for lef lane markng) wh a 500 cm o 2,000 cm expresson range n fron of he vehcle. The nerval beween he wo crcles on he doed lne s 100 cm. Fgure 3(d f) shows he mages projeced by he lane models n Fgure 3(a c) hrough coordnae ransformaon, and he brgh spos n he mages represen he coordnaed pons a an nerval of 100 cm on he ground lane. Fgure 3. Examples of lane models and correspondng projecon mages lane model layous wh (a) posve curvaure, (b) zero curvaure, and (c) negave curvaure. (d f) are he correspondng projecon mages of lane models n (a c) (a) (b) (c) (d) (e) (f) 3.2. Predcon The purpose of parcle predcon s o forecas he curren saus x based on he pas saus x 1. In predcon, he forecased nose w s nroduced; herefore, he parcle predcon can be expressed as a smple dynamc moon equaon: x = Ax 1 + Bw, = 1,..., N, (10)

10 Sensors 2012, wheren A = dag ( I) and B = dag ([ α 1, α 2, α 3, α 4, α 5 ]). The forecased nose w can be expressed as a normalzed Gaussan nose vecor. Snce he sze of each parameer of he lane parcle vecor s dfferen, he forecased nose w vecor can be adjused hrough he B marx parameers when nroduced, so as o make suable o he sze of each parameer n he lane parcle. Usng Equaon (10), s easy o predc he nex saus for each lane parcle and o esmae he predcon resuls Measuremen The man purpose of he measuremen seps s o calculae each lane parcle and npu he machng degree of lane markng n he mages. As menoned n he above secons, he lane model represened by each lane parcle can be expressed as many coordnaes on he ground lane markngs (as shown n Fgure 3(a c)). These ground coordnae pons can be projeced on he mages hrough coordnae ransformaon (as shown n Fgure 3(d f)). Each pon n he mage receves a score based on he dsance o he neares lane markng and hese scores are used o compue he machng score of each lane parcle [22]. To complee he measuremen seps, we carred ou he lane markng deecon for npu mages. Snce he lane markng has noceable edges and characerscs such as hgh brghness, fxed wdh and drecvy, we no only deeced he edge resul bu also confrmed he poson of he lane markng based on he above characerscs. Fgure 4 shows an example, n whch Fgure 4(a) s he npu mage and Fgure 4(b) s he edge mage of he boom half npu mage. I can be obvously seen ha here also exs edges of oher panng lnes on he ground n addon o he lane edges. As for he lane markng deecon mehod whch only consders edges wll easly cause wrong deecon. Fgure 4(c) s he feaure mage of he npu mage whch s also he deecon resul of he edge mages based on prevous characerscs. For easer calculaon of he machng degree beween he lane parcle and lane markng, he dsance ransformaon s fnally used o ransform he lane markng mage no anoher dsance mage, as shown n Fgure 4(d). I s assumed ha he ground coordnae pon of he lane model of each lane parcle s projeced on he mage coordnae and can be expressed as ( u j, v j ), j = 1,, n, where n represens he number of coordnae pons as demonsraed by he brgh spos n Fgure 4(d). The wegh value of each lane parcle s proporonal o he measuremen resul. Therefore, he wegh value of each parcle can be expressed as follows: π = p( z x = s ) n 2 d( u, v ) j 1 j j p( Feaure ) exp (11) x = s =, = 1,..., N, 2 2nσ where d(u, v) represens he gray-scale value of coordnaes (u, v) of he dsance mage, ndcang ha he dsance from he coordnae pon o he neares lane markng. σ represens he sandard devaon o he Gaussan measuremen funcon. In he followng seps, he wegh value of each parcle s used o calculae he cdf funcon whch s adoped o deermne he poson of he lane parcle n re-samplng. Therefore, more new lane parcles can be obaned afer re-samplng near he poson of he lane parcle wh bgger wegh value; f no, less new lane parcles are obaned. As a resul, when he lane markngs n he npu mage are connuous, he wegh of he lane parcle near he lane s bg. Mos new lane parcles afer =

11 Sensors 2012, re-samplng gaher near he lane, hus he lane deecon and rackng can be compleed effecvely and quckly. However, when he lanes n he npu mage are dsconnuous, he wegh of he lane parcle near he new lane s small. However, here are sll a few correspondng new lane parcles afer re-samplng. Consequenly, afer re-adjusng he wegh of he lane parcle, he lane deecon and rackng can sll be compleed quckly and connuously n he followng npu mages. Fgure 4. Image measuremen examples of lane parcle, (a) npu mage, (b) edge mage, (c) lane markng characersc pon mage, and (d) dsance ransformaon mage and lane model coordnae pon projecon. (a) (b) (c) (d) 3.4. Lane Model Refned by PSO Based on he PSO-PF algorhm, he las sep uses he parcle swarm opmzaon mehod o complee he search for he oupu global opmal lane parcle. Therefore, he algorhm wll copy he lane parcle of he parcle flers as he nal saus parcle for he parcle swarm opmzaon mehod. Afer several eraons, he oupu global opmal lane parcle can be obaned, and wll be used n he follow-up lane devaon or ohers. Alhough he eraon of parcle swarm opmal mehod needs exra calculaon, he search process wh he parcle swarm opmzaon mehod doesn affec he operaon of parcle flers, hus can be operaed n parallel wh he algorhm. Fgure 5 shows he parcle dsrbuon map correspondng o he npu mage n Fgure 4. To show clearly, only hree parameers of lane parcle are shown n he fgure, namely horzonal curvaure C, laeral dsance L and lane markng wdh W. In hs example, he number of parcles s 20 and parameers w, c1, c2 are all se o 0.5, 1 and 1, respecvely. The blue dos n he fgure and green crcles represen he parcle dsrbuon of parcle flers and he correspondng oupu lane parcles respecvely. The mnmum dsance beween oupu lane parcle and lane s and he red asersk means he

12 Sensors 2012, global opmal lane parcle hrough he PSO-PF algorhm. The mnmum dsance beween he global opmal lane parcle and lane s 1.675, hus s clearly seen ha a smaller mnmum dsance can be obaned hrough PSO-PF algorhm (see Fgure 6 when usng 20 lane parcles). Fgure 5. Parcle Dsrbuon Example (N = 20). 200 Parcles The oupu of PF The ouou of PSO-PF Laeral dsance Xc (L) x Expermenal Resuls 1 0 Cv Wdh Horzonal curvaure (C ) Lane markng wdh (W ) In hs secon, we nroduce he expermenal resuls and envronmen. The equpmen used n he es ncluded one Inel 5 M GHz processor, 4 GB memory and Wndow 7 operang sysem whle he Malab sofware 2009 verson was used for developmen. The es road envronmen s composed manly of hghways, expressways and ordnary roads, ncludng sragh lne and curved lanes as well as up and down nerchanges. The es process also conans a connuous changng lane. Fgure 6 shows he comparson of measured resuls of oupu lane parcled beween he parcle fler and PSO-PF usng dfferen numbers of parcles as well as he dagram of he relaonshp beween he number of dfferen parcles of he parcle fler and he me consumpon. Each es resul value s he average value of 100 connuous npu mages. In Fgure 6, he blue crcle doed lne and green square doed lne represen he es resuls of he parcle fler and PSO-PF algorhm, respecvely. As shown n he fgure, f he parcle fler s used for lane deecon and rackng, he ncrease of parcle number wll resul n beer resuls, bu afer he parcles are ncreased connuously, he resuls wll end o be unchanged. However, when he parcle number ncreases, he requred compung me wll ncrease lnearly (see he red doed lne n he fgure). Therefore, f a hgher accuracy s needed, more parcles and more me wll be requred. On he conrary, fewer parcles mgh provde faser processng speed bu lower accuracy. The accuracy of PSO-PF algorhm for lane deecon and rackng s no affeced by he parcle number, and dfferen parcle numbers are adoped, hus he accuracy of PSO-PF algorhm s hgher han ha of parcle fler. The use of PSO-PF algorhm can ge he opmzed resul wh a small number of parcles. Snce he number of parcle used s small, he compung me and memory can also be saved. Alhough he PSO-PF algorhm needs addonal

13 Sensors 2012, compung me, s parcle fler and parcle swarm opmzaon mehod can be calculaed n parallel. When he sysem s mplemened, he acual me won be ncreased. Consequenly, he use of PSO-PF algorhm can realze he opmzaon resul by usng a few parcles, whch can effecvely mprove he effcency of parcle fler for lane deecon and rackng. Accordng o expermens, he execuon me of parcle fler under Malab envronmen s abou 0.7 sec/frame when usng 50 lane parcles whle ha of PSO mehod s abou 0.5 sec/frame. Therefore, under parallel processng for PSO-PF, he bgger value 0.7 sec/frame s aken, by whch can be known ha he me requred by PSO-PF algorhm s abou he execuon me of parcle fler. In praccal operaon, PSO-PF algorhm s mplemened on a dual-core embedded sysem wh C language and runnng speed of abou 15 fps. Fgure 6. Comparson beween parcle fler and PSO-PF by usng dfferen parcle numbers and mnmum dsances, and relaonshp dagram of parcle fler beween dfferen parcle numbers and me. 2.5 PF PSO-PF Tmes(sec.) 2 Measures or seconds The number of parcles The oupu lane parcle resuls of he successvely npu 800 frames (.e., he npu vdeo mages) are shown n Fgures 7 and 8, where he number of lane parcles s 50. Fgure 7 shows he comparson on he laeral dsance L of he oupu lane parcles beween he parcle fler and PSO-PF algorhm as he lane deecon and rackng (un: cm). The vehcle lne crossng warnng sgnal s also shown n Fgure 7. When he lef wheel of he vehcle crosses he lef lane markng, he lef wheel lne cross warnng sgnal s gven, as shown n he blue square wave below Fgure 7. When he rgh wheel of he vehcle crosses he rgh lane markng, he rgh wheel lne cross warnng sgnal s gven as shown n he green square wave below Fgure 7. I can be observed n Fgure 7 ha four lane changes occurred n he es. The frs wo are changes from curren lanes o lef lanes, wh he lef wheel lne cross warnng sgnal occurrng frsly followed by he rgh wheel lne cross warnng sgnal. The las wo are changes from he curren lanes o he rgh lanes. Therefore, he rgh wheel lne cross warnng sgnal occurs frsly followed by he lef wheel lne cross warnng sgnal. The duraon of he warnng sgnal s relaed o he exchange speed. In addon, accordng o Fgure 7, he oupu resuls of parcle fler s smooher han ha of PSO-PF algorhm, whch s manly because he oupu lane parcles of

14 Sensors 2012, parcle fler adop he weghed sum of all lane parcles, whle hose of PSO-PF algorhm adop he global opmal lane parcles. Furhermore, he camera shake also causes obvous changes n he oupu lane parcle resuls of PSO-PF algorhm due o he hgh-speed movemen of he vehcle. Fgure 7. Comparson beween parcle fler and PSO-PF algorhm on he laeral dsance of oupu lane parcles. 400 pf pf+pso ldw Laeral dsance Frames Fgure 8. Comparson beween Parcle Fler and PSO-PF algorhm on he mnmum dsance of oupu lane parcles. 25 pf pf+pso 20 Mnmal dsances Frames Fgure 8 shows he comparson of he parcle fler and PSO-PF algorhm on he mnmum dsance beween oupu lane parcle and lane markng (un: pxel). I can be clearly found ha he mnmum dsance of he oupu lane parcle by usng he PSO-PF algorhm s smaller han ha of parcle fler, especally when he lane markng s dsconnuous or changes. As for frames n he fgure wh frame numbers less han 125, can be found ha when he vehcle goes no he hghway from nerchange, he lane markng s shorened and dsconnuous, and he frame poson changes around 90 and 125 once for each me. The resuls show ha he PSO-PF algorhm can effecvely

15 Sensors 2012, mprove he resuls of he parcle fler, alhough n some crcumsances, here s sll lle dfference beween our proposed mehod and parcle fler, as frame posons around 265 and 380 show n he fgure. Fgure 9 shows he connuous mage of a lane change process n whch vehcle changes from he curren lane o he lef lane (whch corresponds o he second lane change shown n Fgure 7). In he fgure, an mage s dsplayed every 5 frames. The blue lne n he mage represens he lef lane markng and he green lne represens he rgh lane markng, as shown n Fgure 9(a c). When he lef wheel of he vehcle crosses he lane markng, he blue color on he lef edge changes o red and he lef wheel lne cross warnng sgnal s gven, as shown n Fgure 9(d f). When he vehcle cener crosses he lef lane markng, he orgnal lef lane edge becomes he rgh lane markng of he new lane, and he rgh wheel of he vehcle crosses he rgh lane markng. Therefore, he rgh lane markng n he mage changes from green o red and he rgh wheel lne cross warnng sgnal s gven, as shown n Fgure 9(g,h). When he vehcle complees he lane change, he rgh lane markng n he mage urns back o green and he rgh wheel lne cross warnng sgnal s cancelled, as shown n Fgure 9( l). The orgnal move fles showng he es resuls can be downloaded from hp:// Fgure 9. Connuous Images of a lane change example. (a) (b) (c) (d) (e) (f) (g) (h) () (j) (k) (l)

16 Sensors 2012, Conclusons In hs paper, we have proposed a new algorhm o mprove he effcency of he parcle fler, whch s known as he parcle swarm opmzaon parcle fler (PSO-PF). The algorhm combnes he parcle fler and he parcle swarm opmzaon mehod and has he followng properes: (1) he algorhm uses he parcle swarm opmzaon mehod o furher search for he global opmal oupu sysem saus from among he sysem sauses of he parcle fler, herefore, he opmal soluon o a problem can be obaned; (2) snce each parcle fler execued ncludes he predcon, measuremen and resample of he sysem saus, he compuaon s rapd. Whle he parcle swarm opmzaon mehod s an algorhm based on eraon, hus he compung process requres more me, he PSO-PF algorhm uses he parcle fler whch can compue quckly o search for he local opmal soluon or approxmae opmal soluon, and hen uses he parcle swarm opmzaon mehod o search for he global opmal soluon, henceforh, hs resuls n a beer effcency; (3) boh he parcle fler and parcle swarm opmzaon mehod are soluons based on he parcles, hus hey are easy o negrae and mplemen; (4) snce he parcle fler and parcle swarm opmzaon mehod don affec each oher, hey can be compued n parallel o ncrease he overall calculaon speed; (5) as shown n he expermenal resuls, he parcle number of he parcle fler s proporonal o he calculaon speed and also o he oupu accuracy, hus he parcle fler can ge beer oupu bu requre more me f more parcles are used. On he conrary, f fewer parcles are used, less me wll be needed for calculaon bu worse resuls wll be obaned. However, he PSO-PF algorhm can acheve beer effcency whle usng fewer parcles. Fnally, we used he PSO-PF algorhm o carry ou he lane deecon and rackng mmedaely and hen compared s resuls wh hose of he parcle fler. The expermenal resuls verfy ha he mehod can effecvely mprove he resuls of he parcle fler for lane deecon and rackng. References 1. Mccall, J.C.; Trved, M.M. Vdeo-based lane esmaon and rackng for drver asssance: survey, sysem, and evaluaon. IEEE Trans. Inellg. Transp. Sys. 2006, 7, Hsao, P.-Y.; Yeh, C.-W.; Huang, S.-S.; Fu, L.-C. A porable vson-based real-me lane deparure warnng sysem: day and ngh. IEEE Trans. Vehc. Technol. 2009, 58, Clanon, J.M.; Bevly, D.M.; Hodel, S. A low-cos soluon for an negraed mulsensor lane deparure warnng sysem. IEEE Trans. Inell. Transp. Sys. 2009, 10, Schuber, R.; Schulze, K.; Wanelk, G. Suaon assessmen for auomac lane-change maneuvers. IEEE Trans. Inell. Transpor. Sys. 2010, 11, Angkrakul, P.; Terashma, R.; Waka, T. On he use of sochasc drver behavor model n lane deparure warnng. IEEE Trans. Inell. Transp. Sys. 2011, 12, McCall, J.C.; Trved, M.M. Vsual conex capure and analyss for drver aenon monorng. In Proceedngs of he IEEE Conference on Inellgen Transporaon Sysems, Washngon, DC, USA, 3 6 Ocober 2004, pp

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18 Sensors 2012, Kennedy, J.; Eberhar, R.C. Parcle swarm opmzaon. In Proceedngs of he IEEE Inernaonal Conference on Neural Neworks, Pscaaway, NJ, USA, 27 November 1 December 1995; pp Eberhar, R.C.; Sh, Y. Trackng and opmzng dynamc sysems wh parcle swarms. In Proceedngs of he Congress on Evoluonary Compuaon, Seoul, Korea, May 2001; pp Hu, X.; Eberhar, R. C. Trackng dynamc sysems wh PSO: Where s he cheese? In Proceedngs of he Workshop on Parcle Swarm Opmzaon, Indanapols, IN, USA, 6 7 Aprl Parsopoulos, K.E.; Vrahas, M.N. Recen approaches o global opmzaon problems hrough parcle swarm opmzaon. Neur. Compu. 2002, 1, by he auhors; lcensee MDPI, Basel, Swzerland. Ths arcle s an open access arcle dsrbued under he erms and condons of he Creave Commons Arbuon lcense (hp://creavecommons.org/lcenses/by/3.0/).