Applying graph theory to automatic vehicle tracking by remote sensing

0 0 Appying graph theory to automatic vehice tracking by remote sensing *Caros Lima Azevedo Nationa Laboratory for Civi Engineering Department of Transportation Av. Do Brasi, Lisbon, 00-0 Portuga Phone: + Fax: + 0 Emai: cmazevedo@nec.pt João Lourenço Cardoso Nationa Laboratory for Civi Engineering Department of Transportation Av. Do Brasi, Lisbon, 00-0 Portuga Phone: + Fax: + 0 emai: jpcardoso@nec.pt Moshe Ben-Akiva Massachusetts Institute of Technoogy Cambridge, Massachusetts 0 United States Phone: + Fax: +0 emai: mba@mit.edu * Corresponding Author Word count: 0 + Figures + Tabe = words Submitted the st August 0, revised th November 0 TRB 0 Annua Meeting

0 Abstract The estimation of driving behavior modes reies on the access to detaied traffic information such as vehice trajectories. Recent deveopments in vision-based technoogies have aowed an increased coection of vehice trajectories around the word, with an emphasis on aeria or high observation point imagery methods. Severa computer agorithms have been proposed using images of different traffic scenarios with the specific aim of detecting and tracking road users. Very recenty, mutipe-object tracking based on constrained fow optimization has been shown to produce very satisfactory resuts. Generay, this method uses individua image features coected for each candidate vehice position as main criteria in the optimization process. Athough these methods are very effective in controed scenarios, adverse conditions such as dynamic view points and wider observation areas with ow ground samping distances are known to encumber significanty the vehice trajectory extraction task. In this paper we present the appication of a k-shortest disjoint paths agorithm for mutipe-object tracking using a motion-based optimization based on dua graphs. A graph of possibe connections between successive candidate positions was buit using speed and ane connectivity. Dua graphs were constructed to aow for acceeration and ane-change-based optimization criteria. The k-shortest disjoint paths agorithm was then used to determine the optima set of trajectories (paths). The proposed agorithm was successfuy appied to the vehice tracking in the A suburban motorway, in Portuga. Vehice positions were detected by image processing and.% of the trajectories were successfuy and efficienty extracted using the proposed method. TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva 0 0 INTRODUCTION Vehice trajectory data has been one of the most important sources of information in driving behavior modeing and caibration research (,,). In recent years, the progress in sensing technoogies and image processing agorithms aowed for easier coection of such detaied traffic datasets (, ). Aeria imagery is the most common process for coecting the base data (), and severa vehice detection and tracking agorithms have been depoyed for different traffic scenarios (). A key step in this process is the vehice tracking step, where the time-independent vehices detected in successive images, are inked together to reconstruct observed trajectories (see FIGURE ). One of the most common approaches reies on the segmented regions or contours properties identified in each frame and uses Kaman fiters (, ) to reconstruct motion tracks. Region-based tracking is computationay efficient and works we with short image view fieds and free-fowing traffic (). However, under congested traffic conditions, vehices may partiay occude one another, making individua bob identification much more difficut. Feature-based tracking is another approach based on tracking of points which have a particuar texture in their respective image positions. These interest points have been ong used in the context of motion, stereo, and tracking probems. A desirabe quaity of an interest point is its invariance to changes in iumination and camera viewpoint. These points (features) are then grouped considering spatia proximity or simiar motion patterns aong the reevant mutipe image frames. These agorithms have distinct advantages over other methods: they are robust to partia occusions, they don't require initiaization, and can adapt successfuy and rapidy to variabe ighting conditions, aowing rea-time processing and tracking of mutipe objects (). However, specia requirements have to be met as regards to camera caibration and objects with simiar motions (). Knowedge-based methods (), which empoy a prior knowedge to decide whether the identified object is a road user of interest, and optica fow based methods (a dense fied of dispacement vectors which defines the transation of each pixe in a region) have aso been used (). Each of these methods has, however, presented some weaknesses, such as frequent identity switches or non-simpe tuning of its mode parameters (). Graph theory has been recenty appied to the vehice tracking probem with success (). Typicay, every region in a frame is represented by a node in the graph. A ink between each region in two consecutive frames is generated and abeed with a discrete variabe representing the number of objects moving from inked nodes. Trajectories are then extracted using goba optimization using a mincost fow agorithm. Linear Programming can be used to ink mutipe detections over time, and therefore sove the graph probem (). However, the computationa compexity of the dynamic programming approach can be prohibitive when the frame or/and vehice number is higher. FIGURE The tracking probem TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva In FIGURE an exampe of how candidate positions are inked when constructing the graph is presented for a sma image set. In each image, three vehices are captured by the camera. As an exampe, the possibe inks from position a at time t and position f at time t + are shown with arrows. Recenty Bercaz et a. () reformuated the Linear Programming (LP) probem as a k-shortest disjoint paths probem on a directed acycic graph. In their study, the area of interest in the image sequence and the time interva of the recording were discretized (as nodes) and inked considering possibe object motions, resuting in a directed acycic graph. Two additiona nodes (source and sink) were added to account for a consistent number of trajectories (fow) in the data set. These two nodes are inked to a the nodes representing positions through which objects can respectivey enter or exit the observed area, such as occusions or the camera fied of view, and to a nodes in first and ast image. Any path between the source and the sink nodes represent the fow of a singe object in the origina probem aong the edges of the path, hence a trajectory. The node-disjointness constraint is needed to assure that no ocation can be shared between two paths (see FIGURE ). 0 0 FIGURE Generic mutipe object tracking (adapted from ()) In () the optimization function depended on the margina posterior probabiity of the presence of an object in each image, which was obtained previousy during the object detection task. When the extraction of object features from the detection agorithm is defective, either due to poor image quaity or to ow ground samping distances, feature-based optimization may produce unrea trajectories, which is a known imitation that has to be addressed whie extracting vehice trajectories data. To overcome these imitations an aternative approach using vehice motion parameters as optimizing function is proposed. THE PROPOSED FRAMEWORK To account for different motion reated criteria, the agorithm proposed by Bercaz et a. () was extended by integrating the use of dua graphs, based on the assumption that any driver has a motionbased optimizing function, i.e., that any trajectory is subject to on a set of motion-based objectives of the driver. Ideay, compex microscopic driving behavior modes and Kaman-fiter dynamics mode may be used in this optimization process using arge number of variabes and parameters to reconstruct trajectories aong with the k-shortest disjoint paths agorithm. Due to the specific nature of the current appication, a simper approach was considered. In free-fow conditions, it was assumed that a driver tends to reach and maintain its target speed; when reaxing the free-fow constrain, the driver tends to minimize changes in acceeration. These changes are even smaer if observations are more frequent, due to vehice dynamics imitations. Regarding atera movement, a simiar approach can be formuated with the incusion of ane change tags: when the atera acceeration (regarding the ane axis) is constant and different from zero for a onger period of time, a ane change might be tagged. In the next paragraphs the graph construction task is described and the k-shortest disjoint path agorithm is presented. TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva 0 0 0 Graphs Construction Simiary to the approach proposed by (), our optimization probem was expressed as a graph probem. Instead of dividing the area of interest into possibe ocations that may or may not be occupied by a vehice, a prima graph A was buit inking acceptabe candidate positions aready detected in the vehice detection step. However, dua graphs () were constructed representing different motion reationships (speeds and acceerations) between the inked positions. The dua graph of G is constructed such that each of its nodes correspond to an edge of G, and each edge to two neighboring edges of G. Prima Graph The prima graph represents a connections between acceptabe candidate positions in successive images. This graph is constructed based on bounding imits for speed and ane connectivity. Each detected vehice position candidate i t K t, where t T represents the image from the fu image set T; and i t, a node (candidate position) in the prima graph A. For any ocation i t, et N i t K t+ denote the possibe positions of i t at the next observation time t +. To mode vehice positions over T time, et us consider a abeed directed graph with t K t nodes, representing a candidate positions in the fu image set. Its edges correspond to admissibe vehice motions between successive image shots. For i t and j t+ (denoted as i and j for simpicity) to be connected with an edge e ij, its computed speed shoud satisfy eq. (): 0 V ij = X j X i Δt ij V max () where X i and X j, {ong, at} are the ongitudina and atera vehice positions reativey to the ane center ine for the position candidates i and j, respectivey. Eq. () is aso used to assign the ongitudina edge costs c ij = V ij, where V ij represents the ongitudina speed from two consecutive positions i and j. A ane change tag c c ij = {0,}, equa to if ane i = ane j and 0 otherwise, can aso be computed for each edge e ij. Lane connectivity was ony used to reduce the size of the prima graph. Its information was extracted from existing geo-referenced ane axis data. Every detected position was projected to the nearest ane axis and inked positions associated with unfeasibe ane changing maneuvers (e.g.: different directions) were fitered out. Dua Graphs After constructing the prima graph, acceerations might be computed from adjacent edge cost (speed) combination. These combinations produce a new cost for each pair of adjacent edges in the graph, simiar to turn costs in route panning graphs. These new costs cannot be stored easiy with the edges nor nodes of the prima graph, but they can be attached to a inear dua graph. This can be achieved using inear dua graphs, where edges in the origina graph are repaced by nodes, and pairs of consecutive edges by edges (). Given a prima directed weighted graph A N, E, the graph B N, E with the foowing properties is caed its compete inear dua graph: For each edge e ij in A there is a node n ij = d(e ij ) in B. d is an objective function so that d (n ij ) = e ij. For each pair of consecutive edges (e ij, e jk ) in A, there is an edge e in B between the corresponding nodes n ij = d(e ij ) and n jk = d(e jk ). A cost function f c : E R. The number of nodes in B equas the number of edges in A and the number of edges in B equas the number of connected edge pairs in A. TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva A first dua graph representing the acceerations, caed B, may be obtained by performing the above procedure once. A second dua graph representing variation of acceerations, caed B, is obtained by performing a second iteration, using the foowing cost transformation functions:. Acceeration Dua Graph B : cijk c cijk = a ijk = c c c ij c jk = V jk V ij Δt jk +Δt ij. Acceeration Variation Dua Graph B : cijkm c cijkm = Δa ijkm c = c ijk c jkm = a jkm c a ijk where, i, j, k and m are the node indexes in the prima graph A. These transformations are represented in FIGURE, where the prima graph A is represented in continuous grey ines, dua graph B by dashed grey ines and the fina dua graph B by bod dark nodes and edges. () () () () 0 0 FIGURE Dua graph construction Additiona acceeration-based criteria were used to fiter out edges in the Acceeration Dua Graph. Using minimum and maximum ongitudina and atera acceerations, a edges not satisfying eq. () were eiminated from B : a min a ijk a max () The majority of shortest path agorithms take as input a singe edge cost vaue. To avoid the use of muti criteria optima path probem, a cost function to integrate ongitudina and atera vehice movements must be specified. In our appication, a simpe inear optimizing function was considered. For any edge e ijkm (noted as b for simpicity) in the fina dua graph B, its cost cb was computed as: cb = ω cb + ω c cb c () where cb is the vaue of cb normaized to [0,] and cb c is equa to ( cb c ). ω and ω c represent therefore the weight of the ongitudina acceeration variation and a ane change factor. It is worth mention that this simpified approach is acceptabe for non-saturated motorway traffic, but does not however, represent a true drivers' trajectory optimizing function vaid for a traffic fow conditions. The ane change factor, for exampe, considers that a driver tends to stay in the same ane, underestimating the effect of strategica ane change in drivers' trajectory optimizing function. TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva The k-shortest Disjoint Paths Agorithm After the graph construction, an extension of the k-shortest disjoint paths agorithm proposed by Suurbae () was used to compute the best set of trajectories. Suurbae's agorithm reies on the iterative augmentation of signed paths and on a generic shortest path agorithm using modified costs. In this section a short description of the extension of the Suurbae s agorithm proposed in () is presented, and one shoud refer to both artices for further detais. Interacing path and Augmentation A signed path is a sequence of sign-abeed edges connecting them in order to form a path in a directed graph G, where each edge is assigned with a positive abe or a negative abe. An interacing path s, is a specia type of signed path inked to a path set P, which satisfies the foowing two conditions: An edge is common to both s and P if and ony if it has a negative abe; A node is common to both s and P if and ony if it is on an edge with negative abe. Both conditions are essentia to achieve both edge and node-disjointness. The augmentation of P and s may be viewed as the addition and subtraction of abeed paths, where adding positive abeed edges of s to P and removing negative abeed edges of s from P. The augmentation process is iustrated in FIGURE b) e) and f) for a simpe graph. 0 0 FIGURE Suurbae s agorithm genera framework The path set obtained in b) composed by a singe path {i, j, k, m} is augmented by the path {i, k, j, m} showed in e), resuting in the disjoint paths set i, k, m, {i, j, m}. Graph Transformation To account for signed paths and augmentation in the origina graph G, Suurbae () proposed two transformations to a path p on G to obtain an interacing path equivaent s: Node spitting: to account for the above-described two conditions, the node-disjointness criteria is reaxed to an arc-disjointness by node spitting: for each node i, introduce an auxiiary node i, reassign a outputs on i as outputs on i, eave a arc engths unchanged and connect i and i by an auxiiary ink e ii with cost c ii = 0 (see FIGURE ). Path inversion: To account for signed abeing, the direction and agebraic sign of cost for each arc (and auxiiary arc) of p is inverted. This transformation represents a transformation from signed paths to directed unsigned paths. TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva 0 0 0 The two step transformation is iustrated in FIGURE for a simpe path. In c), nodes j and k in path {i, j, k, m} are spit into j, j and k, k respectivey. Finay, in d), source and sink nodes were not spit to aow mutipe fows (paths) from these two nodes. A edges direction in path {i, j, k, m} were reverted and its cost signs inverted. In short, the Suurbae's agorithm (aowing negative costs) performs the foowing steps:. Find the shortest path p from source to sink in G using a generic shortest path agorithm.. Spit every node i in p and reverse the direction and agebraic sign of a edges in P, according to the previous section.. Find the shortest path p in the transformed graph G E using a generic shortest path agorithm.. Discard the reversed edges of p from both p and p. The remaining edges of p and p form a sub-graph with two edge-disjoint paths from source to sink. Cost Transformation As the number of vehices passing in the observed area is unknown, one aso needs to optimize the number of paths k. Bercaz et a. () formuated the genera optimizing probem by estabishing an equivaence to the LP formuation. As discussed in their paper, the equivaence of the LP and the k- shortest paths formuation by Suurbae resuts from assuming a convex function of the path set tota cost with respect to k. In fact, when assuming that path costs are monotonicay increasing at each iteration n, cost(p n ) cost(p n+ ), being p n the shortest path computed at the n t iteration of the agorithm, the n tota cost function for the fu path set P n at iteration n, (costset(p n ) = cost(p n )) is convex with respect to n. Therefore, the goba minimum is reached when cost(p n ) changes sign and becomes nonnegative. In our case study the foowing transformation of the aready combined cost ca (see eq. ) for the acceeration variations and ane change tags was used: cost a = og c a ca Doing so, the cost(p n ) is concave with respect to n, and sets the stopping criterion of the agorithm to obtain the best P k trajectories as: cost P k cost P k cost P k + () Genera Framework The genera agorithm for vehice tracking and trajectory extraction from the processed images is summarized in FIGURE. THE CASE STUDY The proposed approach was used in the coection of trajectories aiming at the fine caibration of an advanced micro-simuation too for safety assessment. Vehice positions were extracted from a sequence of aeria images using advanced computer vision techniques. The piot area ayout, systems configuration and image processing agorithms are shorty presented in this section, but the reader shoud refer to () for further detais. System Configuration and Piot Site Layout Network of interest was the A road in the region of greater Porto, Portuga. It is a two-ane urban motorway with ess than km and main interchanges. It represents one of the main south entrances for () TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva the commuters iving in the south-western region of greater Porto and to heavy vehices heading to the main nationa port.. Construct the prima graph A.. Compute the dua acceeration and ane change graphs B a, B c.. Compute the dua acceeration variation and ane change graphs B a, B c.. Compute the transformed combined cost graph B T.. Iteration : Compute the shortest path p on B T using the Beman-Ford agorithm (, ).. Iteration n: a. compute the transformed graph B n T using Suurbae's transformation steps (see FIGURE ). b. compute the shortest path p n on B n T using the Beman-Ford agorithm. c. compute the interacing path s n from p n. d. compute the fu path set P n by augmentation of s n on P n. e. if costset P n costset P n, then return P n. 0 FIGURE Genera framework A ight aircraft overfew the A eeven times (fight runs), between : and : AM (see FIGURE ). Fight characteristics were optimized considering the atmospheric conditions on-site and a desired ground sampe distance of cm. Images were orthorrectified using a D terrain mode, the camera and ens characteristics and the precise fight positioning data recorded through differentia GPS. Images were coected at an average rate of 0.Hz, triggered by the fixed maximum image overapping rate of 0%. Vehice Detection The vehice detection was carried out using coored background subtraction (see FIGURE ). The reader shoud refer to () for the detais on the vehice detection agorithm:. Images were ocay rectified to minimize the terrain mode and main orthorrectification errors. Each image was divided into grids, scaed and referenced automaticay using the SIFT (Scae Invariant Feature Transform) method (). The key points in successive images were then matched using the RANSAC (random sampe consensus) agorithm ().. For each fight run over the A a coored background was constructed using the median fiter. A foreground of moving objects was extracted through background subtraction.. Shadows were fitered from the foreground using a spectra ratio technique and non-shadow moving pixes were used in a region-based anaysis to extract bobs out of connected pixes and the vehice candidate positions. TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva a) Average traffic fow in the A (back) and on the existing (eight) oop sensors (grey) Fight Run b) Average speed in the A motorway (back) and on the existing (eight) oop sensors (grey) FIGURE Loop sensor data coected on-site and fight run periods a) rectified image b) background c) foreground d) spectra ratio e) bob anaysis f) position extraction FIGURE Image processing steps (adapted from ()) TRACKING RESULTS In this section, we present the resuts of the cost function caibration and the statistics of the extracted trajectories for the A motorway case study. TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva 0 Cost Function Caibration The agorithm parameters ω and ω c = ω that represent the weights of the ongitudina acceeration variation and a ane change factor in the simpe driver mode used in this case study need to be tuned. Different combinations of weight pairs were tested against a manuay reconstructed trajectory set with dense traffic situations. A set of specific measures of performance (MoP) were computed for both the manuay extracted trajectories and those reconstructed by the proposed agorithm: mean (μ), standard deviation (σ), skewness (γ) and inter-quantie range (iqr) for speed, acceeration, headways, time-tocoision, ane gaps, etc. A few exampes of the obtained root mean square percentage error (RMSPE) of a set of MoP are presented in TABLE. A description of this goodness of fit measures is presented in (0). TABLE RMSPE for different weights combination and MoP ω c = ω Detected Speed (%) Headway (%) Acceeration (%) trajectories (%) μ σ γ iqr μ σ γ μ σ γ 0.00 0.... 0. 0..... 0.0. 0.... 0. 0..... 0.00. 0.... 0. 0....0.0 0.0. 0....0 0. 0.0 0..0..0 0.00.0 0....0 0. 0.0 0.0... 0.. 0.... 0. 0.0 0.0.0.. *0.0 0. 0..0.. 0. 0.0 0.0... 0.0. 0... 0. 0. 0. 0....0 0.0. 0... 0. 0. 0.0 0.... 0.. 0..00.0. 0. 0...0.00. The proposed method achieves very good resuts for higher weights of the ongitudina acceeration. However, the ane change aso brings a non-negigibe enhancement to the estimates of the mean (μ), standard deviation (σ), skewness (γ) and inter-quantie range (iqr) of ongitudina motionbased variabes. ω and ω c were respectivey set to 0. and 0.0 for the vehice tracking of a fight runs. Tracking Resuts With the proposed method a tota of trajectories for a fight runs were successfuy coected. Leves of service remained between A and D, except for the weaving area in the South-North direction, where eves of service F and E were observed during the first two fight runs (see FIGURE and the trajectory sampe from fight run nº in FIGURE ). FIGURE Sampe of vehice trajectories extracted using the proposed agorithm for the eft and right anes in the South-North direction of the A motorway For the specific purpose of the simuator caibration, key traffic variabes from smoothed () trajectories extracted using the proposed approach were computed. In FIGURE, the empirica TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva cumuative distribution functions (CDF) for some of these variabes are presented. Speed and headway may be approximated to a truncated norma distribution. It is worth noting that for the eariest fight run (fight run number ), ow speed vaues were sti coected in some sections of the A, resuting in a bimoda nature of its distribution (see FIGURE a). Acceeration and deceeration foow a haf-norma distribution with the typica ow upper and ower range vaues for non aggressive manoeuvres. a) Speed (m/s) b) Headway (m) Fight Run 0 c) Acceeration (m/s ) d) Deceeration (m/s ) FIGURE CDF of motion variabes for the different fights CONCLUSIONS AND DISCUSSION The trajectory reconstruction of independent object detection is a known difficut step in the road vehice tracking probem. Recent deveopments in the appication of graph-based agorithms to this specific probem have brought severa computationa and forma advantages against previous optimization soutions. By extending the k-shortest disjoint path agorithm to motion based optimization, we show in this paper that the integration of dua graphs in the genera k-shortest path agorithm can provide a formuation free of image-based patterns and characteristics, by incorporating motion dynamics in the optimization probem. The proposed approach reies on the specification of a motion-based optimizing function, which can be easiy modeed for different traffic scenes. A simpe mode based on ongitudina acceeration and ane change tags resut in robust and fast resuts, even with images coected from a moving observation point and with ow ground samping distances. Besides the agorithm parameters, the performance of the proposed method sti depends on two key inputs: the vehice detection resuts and the image shooting frequency. The vehice detection used for the candidate positions generation () sti acks for an overa performance assessment for different TRB 0 Annua Meeting

Lima Azevedo, Cardoso and Ben-Akiva 0 0 0 ighting and weather conditions, and image acquisition system configurations. The infuence of different image samping rates on the optimization parameters shoud aso be assessed in future works. Finay, it is worth noting that the origina specification of the Suurbae agorithm appied to dua graphs may not aways converge to the true optima soution. In fact, if no dependence is created between graphs, the approach aows for node-joint paths in the prima graph for the fina soution as a transformations and shortest path cacuations are made using the dua graph. A possibe soution is to use an Integer Programming (LP) formuation, as proposed by Bercaz et a (0), instead of the graph-oriented formuation of Suurbae, ensuring that the constraint matrix exhibits a property known as tota unimoduarity, but at the expense of higher computer processing time, especiay under dense traffic conditions. Future work wi focus on additiona enhancements to the proposed method to account for graph dependence, on different motion-based optimization criteria and on testing the agorithm to different image sets. ACKNOWLEDGMENTS Research contained within this paper benefited from the support of Prof. João Pauo Costeira, Dr. Manue Marques and from the computationa resources of their home institution: the Institute for Systems and Robotics of the Instituto Superior Técnico, University of Lisbon, Portuga. The authors woud ike to thank InfoPortuga S.A. for the coection of the raw aeria images. REFERENCES Hranac, R., R. Margiotta and V. Aexiadis. NGSIM Task E.: High-Leve Data Pan. Pubication No. FHWA-HOP-0-0. Cambridge Systematic, Inc., Cambridge MA, USA, 00. Kesting, A. and M. Treiber. Caibrating Car-Foowing Modes using Trajectory Data: Methodoogica Study.. In Transportation Research Record: Journa of the Transportation Research Board, No. 0, Transportation Research Board of the Nationa Academies, Washington, D.C., 00, pp. Punzo V., B. Ciuffo, and M. Montanino. Can resuts of car-foowing mode caibration based on trajectory data be trusted? In Transportation Research Record: Journa of the Transportation Research Board, No., Transportation Research Board of the Nationa Academies, Washington, D.C., 0, pp. -. Laureshyn, A. Appication of automated video anaysis to road user behaviour. Ph.D. thesis, Lund University, Sweden, 0. Lenhart, D., S. Hinz, J. Leitoff and U. Stia. Automatic traffic monitoring based on aeria image sequences. Pattern Recognition and Image Anaysis, No., Vo., 00, pp. 00 0. Hoogendoorn, S. P., H. J. V. Zuyen, M. Schreuder, B. Gorte and G. Vosseman. Microscopic traffic data coection by remote sensing. Transportation Research Record: Journa of the Transportation Research Board, No., Transportation Research Board of the Nationa Academies, Washington, D.C., 00, pp.. Ange, A., M. Hickman, P. Mirchandani and D. Chandnani. Methods of Anayzing Traffic Imagery Coected From Aeria Patforms. IEEE Transactions on inteigent transportation systems, Voume, Issue, 00, pp. -. Cheung, S. and R. Kamath. Robust background subtraction with foreground vaidation for urban traffic video. IS&T/SPIE s Symposium on Eectronic Imaging. San Jose, CA, USA, 00. Yimaz, A., O. Javed and M. Shah. Object tracking. ACM Computing Surveys, No., Vo., 00, pp.. Veeraraghavan, H., O. Masoud and N. Papanikoopouos. Computer vision agorithms for intersection monitoring. IEEE Transactions on ITS, No., Vo., 00,pp.. TRB 0 Annua Meeting

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