CLUSTERING ALGORITHM OF VEHICLE MOTION TRAJECTORIES IN ENTRANCES AND EXITS OF FREEWAY. Zongyuan SUN1 Dongxue LI2

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1 5th Internatonal Conference on Cvl, Archtectural and Hydraulc Engneerng (ICCAHE 206) CLUSTERING ALGORITHM OF VEHICLE MOTION TRAJECTORIES IN ENTRANCES AND EXITS OF FREEWAY Zongyuan SUN Dongxue LI2 Tongj Unversty, 4800 Cao an Road, Shangha, 20804, P. R. of Chna Northeast Electrc Power Desgn Insttute, 4368 Ren mn Street, Changchun 3002, P. R. of Chna 2 Jln Provncal Transportaton Scentfc Research Insttute, Jnhua Street 908, Changchun, 3002, P. R. of Chna KEYWORD: Freeway entrances and exts; Trajectores analyss; Hausdorff dstance; Clusterng algorthm; ABSTRACT: In order to mprove the research level of the ntellgent traffc survellance system, ths paper presents a new herarchcal trajectory clusterng algorthm n vew of the features of trajectores n entrances and exts of freeway. The valdty of trajectores s judged by means of the length of trajectores and vehcle speed frstly, and then the vald ones are encoded. The mproved Hausdorff dstance s proposed and appled to measure the smlarty of temporal and spatal characterstcs of trajectores. The fuzzy C-means herarchcal clusterng algorthm of trajectores s further establshed n whch trajectores are frst clustered nto dfferent paths accordng to the poston and geometrc shape of trajectores, and then trajectores belongng to the same path are further clustered accordng to vehcle speed. Fnally, the results of experments n true scene have confrmed the valdty and applcablty of the algorthm. INTRODUCTION As the accdent-prone areas, how to mprove the securty of entrances and exts has been an mportant research subject for freeway operaton management. Wth the rapd development of computer hardware and software and vsual technology, t s now possble to use the traffc control and survellance system to mprove the level of road safety and one of the most mportant efforts s to analyze and dentfy behavors of vehcles based on ther trajectores(valera & Velastn, 2005, Morrs & Trved, 2008). Through the analyss of trajectores n entrances and exts of freeway, we can not only detect the llegal vehcles, such as changng lanes frequently, speedng and retrograde volatons, but also can predct the tendency of moton, assess ther safety state n real tme and further judge whether they mght lead to accdents, f so, they mght be able to warn drvers before danger occur and thus reduce the number of accdents. Trajectory clusterng of vehcle s the bass for the subsequent behavor analyss and recognton. The satsfactory clusterng results can not only provde the tranng samples for the constructon of recognton models, but also affect the accuracy and relablty of trajectory analyss drectly. As the tme-varyng data seres, the trajectory has the characterstcs of dynamc, unequal length, hgh nformaton content and so on. Trajectory clusterng analyss ams at usng unsupervsed learnng method to explore hdden patterns from a large amount of sequence data. At present, the trajectory clusterng methods nclude: K-means clusterng(pan et al., 2009), herarchcal clusterng (Hao et al., 2009) and neural network based clusterng (Owens, 2000, Hu et al., 2004) and HMM(Hdden Markov Model clusterng(porkl, 2004, Sauner & Sayed,2005) and so on. K-means clusterng algorthm s smple, but the clusterng results are generally easy to fall nto the local optmal soluton. Although the herarchcal clusterng method s also relatvely smple, the tradtonal one s not adaptve to the ncomplete trajectory, and t needs to be mproved. The clusterng effect of NN and HMM s relatvely good, but the calculaton s complex and t s dffcult to meet the real-tme requrements. What s more, how to determne the number of HMM s stll a problem to be studed. In 206. The authors - Publshed by Atlants Press 42

2 addton, none of the above methods proposes effectve trajectory preprocessng method to overcome the defects of the trackng algorthm. Amng at the problems already exsted n trajectory clusterng algorthms; ths paper proposes a herarchcal clusterng algorthm based on the mproved Hausdorff dstance. Frstly, the valdty of trajectores s judged by means of the length of trajectores and vehcle speed and the vald ones are encoded, then the mproved Hausdorff dstance s proposed and appled to measure the smlarty between trajectores. Fnally, the fuzzy C-means algorthm s used to realze the herarchcal clusterng of effectve trajectores. Expermental results on real scenes show that the trajectory clusterng algorthm proposed n ths paper can get satsfactory clusterng effect and has good applcablty for vehcle trajectores n entrances and exts of freeway. Trajectory preprocessng Trajectory valdty judgment Snce the process of vehcle trackng may be accompaned by occluson, error, falure, and so on, the obtaned trajectores are often full of nose, dfferent from the startng pont and truncated to a number of short fragments. If the orgnal complex trajectory s not effectvely preprocessed, all the above factors wll serously affect the subsequent trajectory classfcaton, modelng and dentfcaton accuracy. Integrated varous factors, ths paper manly apples the trajectory length and vehcle speed to determne the valdty of trajectores. By preprocessng the trajectory, t can not only smplfy the calculaton complexty and reduce the amount of computaton, but also mprove the accuracy of the subsequent clusterng and recognton. The trajectory length To calculate the number of coordnates of each complete trajectory N and set a threshold T, f N T, then keep the track and record the correspondng trajectory by the subscrpt S. Through ths process, we can flter out a part of short trajectores whch are nfluenced by the nose n the trackng process and produced due to trackng falure, so t wll reduce the amount of calculaton and the error of further analyss and control the overall stuaton of the trajectores. Vehcle speed Because of the short tme nterval between frames of the vdeo sequence, and the ponts n the trajectory sampled at equal tme nterval, the vehcle speed can be characterzed by the change of the poston of adjacent frames. Assumng that the two-dmensonal coordnates of cancrods n the frame s( x,y ), + s( x, y ), Then the speed vector of the vehcle o at the tme s: v V = δ δ ( x, y ) + + ( ) δ = x + x x ( 2 ) δ y y+ = y ( 3 ) When the length of the trajectory s vald, the poston change of all adjacent frames n each tra- v V = δx, δy and the statstcal mean value of the characterstc values n the sldng wndow jectory ( ) wth length L X L Y are calculated n turn. Set the two thresholds T L x, T y and determne whether X > T Y > T and X Y > T θ are satsfed at the same tme, f the two condtons are satsfed at the L x L y L L same tme, t s consdered that the trajectory s vald; Otherwse the trajectory s nvald and removed from the samples. Due to the serous dsturbance of nose and the nfluence of the trackng error of the target, a large number of trajectores obvously ndcate that the speed s too fast or 422

3 change volently whch are not n accordance wth the laws of the movement of the vehcle. After effectve judgment of the speed, we can further flter out parts of nvald trajectores, and fnally get relable samples. Trajectory codng The purpose of codng s to create a concse and compact expresson for trajectory accordng to the demand of the clusterng method, and fnally get the sample lbrary for clusterng. From the nformaton derved from the regon-based vehcle trackng, we can acqure the tranng trajectores that are used to cluster. In ths paper, we use the smlar trajectory codng schemes whch are used n (Johnson & Hogg, 996, Stauffer et al., 2000, Sumpter & Bulptt, 2000). The orgnal trajectores are sampled at a fxed rate (once every V t frame). Gven a vehcle O, we represent the world coor- x,y. After samplng n tmes, we obtan a pont se- dnates of the cancrods at the th samplng as ( ) n quence T that s composed of n pars of world coordnates: n T = x, y, x, y, K, x,y, x, y, x, y ( 4 ) {( ) ( 2 2) ( ) ( n n ) ( n n) } v In addton, we use the prevously mentoned V = ( δx, δy ) to represent the speed of the movng vehcle at tme. Accordng to the purpose of ths study, the movement of vehcle O s represented by the set F n n, whch s composed of n flow vectors F = { f, f,, f,, f, f }, where f ( x, y, δx, δy ) 2 n- n =. It s worth notng that, the acceleraton of vehcle can be obtaned through the trajectory analyss, but takng nto account the nose and the effcency of the clusterng algorthm, here we do not consder t. At the same tme, n order to balance the relatve contrbuton between the poston and the speed elements n the calculaton of the flow vector smlarty, they all need to be normalzed. After transformaton, each component of the flow vector f wll be n the range of [0, ], that s ( x,y, x, y ) [ 0,] δ δ. By trackng vehcles, a set of trajectores S { F, F,, F,, F } 2 where M denotes the number of sampled trajectores and F l the lth trajectory. Trajectory Smlarty Measures = s acqured, In order to make a comparson between the trajectores and obtan the meanngful clusterng results, t s necessary to determne the approprate dstance metrc to measure the smlarty between samples before clusterng. Trajectory smlarty measure s manly used to measure the degree of smlarty between the two trajectores, whch s the bass of trajectory clusterng. The current commonly used trajectory smlarty measures nclude: Eucldean dstance (Eucldean), Hausdorff dstance (Hausdorff), the longest common sequence (LCSS), dynamc tme warpng (DTW) and so on (Xu, 2005). Eucldean dstance can only be used to deal wth the trajectory of equal length and s prone to the nose and sequental varaton; LCSS and DTW can effectvely measure the smlarty of the trajectory, but they are more sutable for the trajectory of the flexble object due to the shape change (Zhang et al., 2006). The Hausdorff dstance can't consder trajectory drecton, but n vew of the research object of ths paper s the vehcle trajectores of freeway entrances and exts whch are dfferent n length, but n the same drecton. Therefore, based on the comprehensve analyss of the advantages and dsadvantages of these ndcators, we propose and apply the mproved Hausdorff dstance to measure the smlarty between the trajectores.the tradtonal Hausdorff dstance s a measure of the smlarty between a par of ponts set whch consttute the trajectores (Junejo, 2004, Khald & Naftel, 2005, Atev, 2006). When there s a great dfference between the lengths of the two trajectores, the tradtonal Hausdorff dstance wll ncrease wth the length of the trajectory, and cannot truly reflect the degree of smlarty between trajectores. Therefore, gven the two trajectory F, F j, ths paper proposes and symmetrcally defnes the mproved Hausdorff dstance as follows: l M 423

4 ( ) (, ) (, ), (, ) D F F = mn D F F D F F ( 5 ) H j h j h j ( ) (,, ) D F, F = max mn d f, f,(,.) h j f E k jl kl k, fjl, (6) ( ) (,, ) D F, F = max mn d f, f,(,.) h j f E jl k lk jl, fk, (7) d f,f denotes the Eucldean dstance between flow vectors f,k, f j,l n feature Where E (,k j,l ) space. HIERARCHICAL CLUSTERING OF TRAJECTORIES BASED ON FUZZY C-MEAN ALGORITHM The am of trajectory clusterng s to classfy the smlar trajectores nto the same class. Compared wth the ordnary c-means clusterng algorthm, because the fuzzy c-means clusterng uses the fuzzy theory to gude the work, t s more close to the realty and often be done wth less workload and better results n practcal applcatons (Hu et al., 2006). Due to the complexty and varety of trajectory samples, the calculaton of dstance between the large numbers of trajectores s relatvely heavy. In order to mprove the effcency of clusterng, ths paper proposes a herarchcal clusterng method based on fuzzy C-means algorthm, whch uses the dfferent space and tme characterstcs of trajectores. As trajectores belongng to dfferent paths must be assgned to dfferent clusters, frstly trajectores are clustered nto dfferent paths accordng to the geometrc shape of trajectores, and then trajectores belongng to the same path are further clustered accordng to vehcle speed. Path clusterng The path s the space curve whch s characterzed by the poston of each successve pont of the trajectory. Although the path contans only the coordnates of the poston, t fully reflects the most mportant geometrcal and spatal characterstcs of the trajectory. Therefore, the correspondng paths for trajectores are clustered to obtan the prelmnary results frstly. In the path clusterng, only coordnates of the ponts on each trajectory are kept for clusterng and all correspondng samples are nput to the clusterng algorthm. The centre trajectores are used to present each cluster and the cluster results of orgnal trajectores are obtaned fnally. In ths paper, the path set correspondng to the orgnal vald trajectores s represented s = as { F, F,..., F,... F 2 l M } F, {,,...,,... l f f 2 f f n } =. The purpose of path clusterng s to cluster s nto K dfferent subset θ { θ, θ2,, θ j,..., θk} =, where θ j denotes the jth subclass and K denotes the number of cluster whch can be determned n advance or accordng to certan crtera. The above task s performed n fve steps: Step : Randomze the ntal K clusterng centers = F, F,..., F,... F and calculate the mproved Hausdorff dstance s Step 2: Input all samples { 2 l M } from each sample F l to all the K clusterng centers ( ) (, θ ) = mn (, θ ), ( θ, ) D F D F D F H l j h l j h j l l=, 2 M, j=, 2 K. (8) Step 3: Compute the membershps of each sample to all the K clusterng centers 424

5 R () t = θ lj K j= ( F θ ) H ( Fl θj) D, H l j ( D, ). (9) Step 4: Adjust each cluster center accordng to the formula M () ( (, θ )) R t D F lj H l j l= j( t+ ) = θ j() t + M = R lj () t (0) Step 5: Verfy the stablty condton of the cluster j K n { ( t ) () t } max θ θ ε j j + < () If the stablty condton s satsfed or the predefned number of teratons s acheved, then the learnng process termnates; otherwse, go to Step 2 for another loop of learnng. Correspondng to the clusterng result of the ntermedate trajectores, the set of orgnal trajectores S = { F, F2,, Fl,, FM} s clustered nto K subsets: {{ F } { } { },, },,..., F, M,..., F,,..., FM,..., F,,..., K FKMK s= (2) Where: M denotes the number of orgnal trajectores n the th path subclass. Speed clusterng Although trajectory pattern and geometrc path are smlar, there are many dfferences between them. Compared wth the latter, the former also contans the dynamc tme nformaton of trajectory, and ts external performance s speed dfference. For example, even f the vehcle s movng along the same path, they may also be attrbuted to dfferent trajectory patterns, as a vehcle may speed up and down or run normally. The purpose of trajectory clusterng s to dentfy and predct the moton of vehcles, and usng the tme nformaton to further classfy the trajectores wll no doubt mprove the accuracy of the above work. Therefore, t s necessary to use temporal nformaton to further s = F,..., F, =, 2 K. cluster the path subset {,, } M Snce each flow vector of the orgnal trajectory already contans the speed element, the smlarty between the trajectores belongng to the same path subclass s stll measured by calculatng the mproved Hausdorff dstance, and the fuzzy C-means algorthm s used to cluster each subclass agan. It s worth notng that snce the scale of each subset s s much less than that of the whole orgnal trajectores; the clusterng procedure based on the speed nformaton s more accurate and effcent than that based on the orgnal samples drectly. After speed clusterng, all ntermedate trajectores are clustered nto C clusters. Accordng to the correspondence between the orgnal trajectores and the ntermedate trajectores, the orgnal tra- s = F,..., F are clustered nto C sets of trajectores: jectores {, M, } s { F } { } { },,..., F, M,... Fj,,..., F,... FC,,..., FCM, { jm, j C } = (3) Where M j denotes the number of orgnal trajectores n the jth speed subclass. 425

6 EXPERIMENTAL RESULTS In order to verfy the valdty and applcablty of the proposed clusterng algorthm, we tested t n an entrance and ext of freeway scene whch both are parallel type and have two man lanes (as shown n Fg. and 2 respectvely). The mages are of sze pxels and sampled at 25 frames per second. Durng the 5 mnutes, 447 cars passed through the entrance and 352 cars passed through the ext. When the trajectores are preprocessed, the threshold value of each parameter s set as follows: T =5, T x =0.4, T y =.5, T θ =.732. Durng the testng tme nterval, 529 and 405 vald moton trajectores were produced usng our trackng algorthm, whch are shown as Fg. 3and 4 respectvely. Fgure. The freeway entrance. Fgure 2. The freeway ext. 426

7 Fgure 3. Trajectores from the entrance scene. Fgure 4. Trajectores from the ext scene Fg.5 and 6 show the clusterng results, respectvely, n the entrance and ext usng our algorthm. For smplcty, the results are represented by the geometrc mean of each cluster wth dfferent color. As shown n the fgures, the clusterng results not only have strong regularty, but also are consstent wth the actual moton patterns of vehcles at the entrance and ext of the freeway and reflect the spatal and temporal dstrbuton of the correspondng sample trajectores n the entrance and ext area. It s seen that the method proposed n ths paper has good applcablty for the clusterng of vehcle trajectores n the freeway entrances and exts. Fgure 5. The clustered result n the freeway entrance 427

8 Fgure 6. The clustered result n the freeway ext CONCLUSIONS Accordng to the features of trajectores n the entrances and exts of freeway, we present a new herarchcal trajectory clusterng algorthm. Frst, we use the length of trajectores and vehcle speed nformaton to justfy the valdty of trajectores and obtan the trajectory samples. Second, the mproved Hausdorff dstances are proposed and appled to measure the smlarty of temporal and spatal characterstcs for trajectores. Fnally, the fuzzy C-means trajectory herarchcal clusterng algorthm based on the mproved Hausdorff dstances s establshed. Through experments n true scene, the results have confrmed the valdty and applcablty of the proposed algorthm for the clusterng of vehcle trajectores n the entrances and exts of the freeway. REFERENCE [] Atev S, Masoud O, and Papankolopoulos N. Learnng traffc patterns at ntersectons by spectral clusterng of moton trajectores, n Proc. IEEE Conf. Intell. Robots Syst., Bejng, Chna, Oct. 2006, pp [2] Juyue HAO, Chao LI, Le GAO, et al. Movng object trajectory clusterng method n ntellgent survellance vdeo [J]. Journal of Bejng Unversty of Aeronautcs and Astronautcs, 2009, 35(9): (n Chnese). [3] Johnson N, Hogg D. Learnng the dstrbuton of object trajectores for event recognton. Image and Vson Computng, 996, 4(8): 609~ 65. [4] Junejo I N, Javed O, Shah M.Mult feature path modelng for vdeo survellance[c] Proceedngs of the Pattern Recognton, 7th Internatonal Conference on (ICPR'04), 2004: [5] Khald S, Naftel A. Evaluaton of matchng metrcs for trajectory-based ndexng and retreval of vdeo clps[c] Proceedngs of the Seventh IEEE Workshops on Applcaton of Computer Vson (WACV/MOTION'05), 2005: [6] Morrs B T, Trved M M. A Survey of Vson-Based Trajectory Learnng and Analyss for Survellance [J]. IEEE Transactons on Crcuts & Systems for Vdeo Technology, 2008, 8(8):4-27. [7] OWENS J, HUNTER A. Applcaton of the self-organzng map to trajectory classfcaton[c]: In Proceedngs of the 3rd IEEE Internatonal Workshop on Vsual Survellance, 2000: [8] Porkl F. Trajectory dstance metrc usng hdden markov model based representaton[c]// ECCV PETS Workshop [9] Qmng PAN, Yongme CHENG, Tao YANG, et al.trajectory recognton classfcaton and recognton of movng objects[j].fre Control&Command Control, 2009, 34():79-83(n Chnese). 428

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