Automatic Freeway Incident Detection for Free Flow Conditions: A Vehicle Reidentification Based Approach Using Image Data from Sparsely Distributed Video Cameras

This paper proposes a vehicle reidentification (VRI) based automatic incident algorithm (AID) for freeway system under free flow condition. An enhanced vehicle feature matching technique is adopted in the VRI component of the proposed system. In this study, arrival time interval, which is estimated based on the historical database, is introduced into the VRI component to improve the matching accuracy and reduce the incident detection time. Also, a screening method, which is based on the ratios of the matching probabilities, is introduced to the VRI component to further reduce false alarm rate. The proposed AID algorithm is tested on a 3.6 km segment of a closed freeway system in Bangkok, Thailand. The results show that in terms of incident detection time, the proposed AID algorithm outperforms the traditional vehicle count approach.


Introduction and Literature Review
Traffic incidents have been widely recognized as a serious problem for its negative effects on traffic congestion and safety [1].Under heavy traffic condition, one minor incident could result in gridlock and hence serious traffic congestion.In addition, traffic injuries are likely to be more severe if incidents occur at higher speeds (e.g., under free flow condition).Statistics also suggest the high chance of a more sever secondary accident following the initial incident on freeway [2,3].An ability to detect incident in a timely and accurate manner would allow the traffic manager to efficiently remove the incident, to notify the follow-up traffic of the incident, and to better manage the traffic for minimizing the negative impact caused by the incident.Therefore, considerable research efforts have been dedicated to the development of automatic incident detection (AID) algorithms by utilizing the traditional detectors (i.e., inductive loops) over the past few decades (e.g., the California algorithm series [4] and McMaster algorithm [5]).The underlying assumption of these algorithms is that the aggregated traffic parameters (e.g., travel time and traffic flow) would change dramatically when incidents occur under congested situation.By comparing the real-time traffic data with the incident-free data, one can determine the likelihood that an incident has happened.Based on the above-mentioned principle, various advanced data mining approaches (e.g., neural network [6], Bayesian network [7,8], and principal component analysis [9]) were adopted for detecting the abnormal traffic delay or abrupt change in traffic flow pattern.However, most of the existing incident detection algorithms are specifically designed for congested traffic conditions and may not be applicable for free flow situations.
Under free flow condition, a drop in traffic capacity due to a traffic incident (e.g., one lane blocking) may not cause any traffic delay or substantial change in traffic flow pattern.Therefore, it is no longer feasible to detect the incident through analyzing the aggregated traffic parameters.
To handle the aforementioned challenge, research attention has shifted away from the data mining approach based on macroscopic traffic data, towards considering the continuous tracking of individual vehicle by using the microscopic vehicle data (e.g., vehicle trajectory and individual vehicle feature).The rationale behind this idea is straightforward.For a closed freeway system, if one can track all the vehicles along the designated points, a disappearance of any vehicle movement (or nonmoving vehicle) between consecutive points can be classified as a potential incident.Based on this principle, various emerging technologies, such as GPS technology [10] and cellular phones [11], has been utilized for collecting the Lagrangian measurements (i.e., individual vehicle trajectory), which eventually could be used for identifying the "incident" vehicle.Despite their theoretical simplicity, the successes of these approaches heavily rely on the high level of market penetration (in principle, 100% of penetration rate is required) of the in-vehicle equipment (e.g., GPS device) and the driver's willingness to provide the location information.To compensate for this, Shehata et al. [12] conducted a study to detect the nonmoving vehicle (i.e., caused by incident) from the fixed video camera (i.e., Eulerian measurement) by using image processing techniques.Although this method appears to be theoretically sound, the deployment of such system requires the installations of cameras at all key locations along the freeway, which may not be feasible due to the limitation of public resources.In practice, the fixed traffic sensors (e.g., loop detectors and video cameras) cannot cover the entire freeway system and are generally sparsely distributed [13].In this regard, Fambro and Ritch [14] conducted a pioneering study to trace and identify the "missing" vehicle through analyzing the vehicle count data obtained at two consecutive loop detectors, which is also referred to as the vehicle count approach.Given the vehicle speed at upstream, the arrival time window at downstream could be estimated.By comparing the vehicle counts in this arrival time window with the corresponding vehicle counts at upstream, one may be able to identify the missing vehicle (if any) for incident detection.However, it is also noteworthy that the overlapping of arrival time windows of different vehicles would lead to a significant increase in the detection time (this will be discussed in more detail in Section 3.1).To further reduce the incident detection time, much attention has been paid to track the vehicle by utilizing the emerging automatic vehicle identification (AVI) systems: automatic number plate recognition [15] or Bluetooth identification technology [16].Although the AVI technologies enable a more efficient tracking of vehicles across consecutive points by accurately matching their unique identity (e.g., plate number and media access control address), privacy concerns may arise as the consequence of this matching process of vehicle identity.In this case, the vehicle reidentification (VRI) scheme, which does not intrude driver's privacy, provides a tool to devise a more practical and effective incident detection algorithm under free flow condition.
Generally, vehicle reidentification (VRI) is a process of matching nonunique vehicle signatures (e.g., waveform [17], vehicle length [18], and vehicle color [19,20]) from one detector to the next one in the traffic network.On one hand, the nonuniqueness of the vehicle signature would allow the VRI system to track the vehicle anonymously at two consecutive detectors [21] and, hence, identify the "missing" vehicle due to an incident.On the other hand, this property of very nonuniqueness imposes a great challenge on the development of the vehicle signature matching method.To improve the matching accuracy, Coifman [22] proposed a vehicle platoon matching method such that the lengths of vehicle platoons were compared.To further consider the noise and uncertainty of vehicle signature, Kwong et al. [23] introduced a statistical matching method in which the vehicle signature is treated as a random variable, and a probabilistic measure is calculated for matching decision making.During the past few years, the authors also developed a VRI system [24,25] by utilizing the emerging video image processing systems [26].Various detailed vehicle features (e.g., vehicle color, length, and type) were extracted and a probabilistic data fusion rule was then introduced to combine these features to generate a matching probability (i.e., posterior probability) for reidentification purpose.To account for the large variance in travel time under dynamic traffic condition, the proposed VRI system also introduced a prior (fixed) time window constraint, which sets the upper and lower bounds of the vehicle travel time, to rule out the unlikely candidate vehicles.However, it is noteworthy that the aforementioned VRI systems were specifically designed for the purpose of traffic data collection (e.g., travel time).To our knowledge, very few studies were explicitly conducted to investigate the potential feasibility of utilizing VRI system for incident detection.Also, as the existing VRI systems cannot guarantee an accurate matching due to the nonuniqueness of the vehicle signatures, the mismatches between the upstream and downstream vehicles may potentially lead to false alarms when they were applied for incident detection.To sum up, the current VRI systems are not readily transferable to the field of incident detection.
To this end, this paper aims to propose a VRI-based automatic incident detection algorithm under free flow condition.The revised VRI system is based on authors' previous work [24] with several major changes to cope with the purpose of incident detection, which eventually give rise to the incidentdetection-oriented VRI.
(i) Note that in the work of [24] a unified and fixed time window constraint is imposed on all the vehicles.However, the vehicles would maintain a relatively stable speed under free flow condition, which allows for the estimation of a flexible time window for each individual vehicle.Therefore, this incident-detectionoriented VRI would introduce a flexible time window to further improve the matching accuracy and reduce the incident detection time.
(ii) Rather than finding the matching results between two sets of vehicles (i.e., upstream and downstream sets of vehicles), the incident-detection-oriented VRI attempts to make an instant matching decision for each individual vehicle such that the "missing" vehicle can be identified promptly.In this study, the statistical model regarding the vehicle feature is built up, and the matching probability for each pair of vehicles (i.e., the posterior probability of each potential match based on the observation of the vehicle signatures) is explicitly calculated.(iii) Last but not least, a screening method (i.e., thresholding process), which is based on the ratios of the matching probabilities, is introduced to screen out the mismatched vehicles for reducing the false alarm rate.
The rest of the chapter is organized as follows.Section 2 describes the traffic dataset collected for the algorithm development and evaluation.Mathematical notations are also provided in this section.In Section 3, the overall framework of the proposed automatic incident detection system is introduced.The description and analysis of the incidentdetection-oriented VRI system under free flow condition are proposed in the following two sections (Sections 4 and 5).
In Section 6, simulated tests and real-world case studies are carried out to evaluate the performance of the proposed AID system against the traditional vehicle count approach.Finally, we close this chapter with the conclusion and future works.

Dataset for Algorithm Development and Evaluation
The test site is a 3.6 km long section of the closed threelane freeway in Bangkok, Thailand (i.e., the green section in Figure 1).At each station (i.e., location 10B and 08B in Figure 1) a gantry-mounted video camera, which is viewed in the upstream direction, is installed and two hours of video record ( Hue and Saturation values are then exploited for color detection, whereas  (value) information is separated out from the color space.Second, a two-dimensional color histogram  is formed to represent the distribution (frequency) of colors across a vehicle image.To be more specific, the hue and saturation channels are divided into 36 and 10 bins, respectively.Thus, a color feature vector  with 360 elements is obtained.Each element of the feature vector is calculated as where   is the number of pixels whose values fall within the bin  and  is the total number of pixels in the image.

Vehicle Type Recognition.
Vehicle type feature provides the other important information to describe a vehicle.The template matching method [27] is utilized to recognize vehicle type.This method uses  2 distance metric to measure the similarity between vehicle image and template images.Specifically, vehicles are classified into 6 categories.For each category, the corresponding template image () is built.Finally, the normalized similarity value between the vehicle image () and the th template image () is given by where G denotes the maximum gray level (255); M and N are the dimensions of the vehicle image.Thus, the vehicle type/shape feature  is a vector that consists of the similarity score for each template.Detailed implementation of the VIP systems to traffic data extraction can be found in [24].A formal description of the dataset obtained from the video record is presented in the following subsection.

Dataset Description and Notation.
VIPs provide a large amount of traffic data to develop and validate the automatic incident detection algorithms.Let  = {1, 2, . . ., } denote the  vehicles detected at upstream station during the time interval. = {1, 2, . . ., } is the set of downstream vehicles.
In addition,    and V   are the associated arrival time and the spot speed of the th upstream vehicle, respectively.Accordingly,    and V   are the corresponding arrival time and spot speed of the th downstream vehicle.As discussed above, for each detected individual vehicle, the intrinsic feature data (e.g., color, size, and length) are also obtained.Let    = {   ,    ,    } denote the signature of the th upstream vehicle, where    and    are the normalized color feature vector and type (shape) feature vector, respectively.   denotes the normalized the length of vehicle .Similarly,    = {   ,    ,    } is the signature of the th downstream vehicle.To sum up, dataset from the VIPs during a time interval consists of the upstream vehicle dataset {(   , V   ,    ),  = 1, 2, . . ., } and the downstream vehicle set {(   , V   ,    ),  = 1, 2, . . ., }.In order to quantify the difference between each pair of upstream and downstream vehicle signatures, several distance measures are then incorporated.Specifically, for a pair of signatures (   ,    ), the Bhattacharyya distance [28] is utilized to calculate the degree of similarity between color features: where  denoted the th component of the color feature vector.The  1 distance measure is introduced to represent the difference between the type feature vectors: where  is the number of vehicle type template and is taken as 6 in this study.The length difference is given by

Overall Framework of Automatic Incident Detection System
The basic idea of incident detection under free flow condition is to track the individual vehicle so as to identify the missing vehicle due to an incident.Owning to its computational and theoretical simplicity, the vehicle count approach [14] is the most well-known free-flow incident detection algorithm.Thus, it is necessary to revisit this method in detail.counts data, cannot promptly detect the incident (i.e., delay in incident detection).In general, the incident detection time would significantly increase with respect to the increase in size of vehicle platoon at the upstream detector, which increases the number of overlapping in arrival time intervals at the downstream detector.

Vehicle Count
To reduce the detection time, this research proposes a novel incident detection algorithm by incorporating the vision-based VRI system.As shown in Figure 2, vehicle   and   are detected and their detailed feature data (e.g., color, type and length) are also extracted.Once a vehicle is detected at downstream site, the proposed VRI system is performed to find a matched upstream vehicle based on the vehicle feature data.In the case that vehicle   is missing, if the downstream vehicle could be matched to the vehicle   based on the vehicle feature, an incident alarm would be triggered at time    +   , as vehicle   is not reidentified during time window [   +   ,    +   ].As shown by this "toy" example, the additional VRI component could potentially reduce the incident detection time to some extent.However, it is also observed that the concept of VRI is not readily transferable to the field of incident detection (mismatches of VRI may trigger false alarms) and several modifications should be made regarding the vehicle matching process.
(i) First, instead of finding the matching result for upstream vehicle, the incident-detection-oriented VRI attempts to match the vehicles at downstream site such that the proposed AID algorithm can be implemented in real-time.
(ii) Second, once a vehicle passes the downstream station, the incident-detection-oriented VRI should be capable of making matching decision immediately such that the missing vehicle (i.e., the vehicle that does not appear at downstream) could be promptly identified.Therefore, this study calculates the matching probability for each pair of vehicles on which the following screening method could be imposed to further reduce the false alarm rate.
The overall framework of the proposed algorithm is presented in the following subsection.

AID Algorithm
Based on VRI System.The detailed implementation of the VRI-based incident detection system is summarized in the following flowchart (Figure 3).First, the system will initialize the timestamp, , and check whether a vehicle is detected at upstream and/or downstream station.If a vehicle is detected at upstream detector, the expected arrival time window of this vehicle at downstream station will be estimated based on the historical data.The record of the detected vehicle at upstream will be stored in the database as unmatched upstream vehicle.On the other hand, if a vehicle is captured at the downstream station, the system will perform incident-detection-oriented VRI subsystem to check whether this detected vehicle match with any of the unmatched upstream vehicle.The time window constraint is utilized to identify the potential matches for this vehicle detected at downstream station.Once the match is found, the matched vehicle data will be removed from the list of the unmatched upstream vehicles.
After the previous two steps for handling the detected vehicles at upstream and downstream stations, the system will proceed to determine whether there is an incident occurs on the monitored segment.For incident detection, the system will screen through the list of unmatched vehicles.If the current time () is out of the expected arrival time window (i.e., greater than the upper bound of the arrival time interval) of the unmatched vehicle, an incident alarm will be issued.If not,  will be set to  + 1 and the system will move forward to the next time step.It could be easily observed that the performance of the incident detection system is heavily dependent on two critical components, that is, flexible time window constraint and incident-detection-oriented VRI system.
For the aforementioned framework, the following three comments should be taken into account.
(i) First, the detection error is not considered in this study.In other words, it is assumed that all the  vehicles cross the video cameras will be detected.This is achievable under free flow condition, as there is no occlusion between the vehicles and, consequently, VIPs perform generally well and are able to detect most of the individual vehicles.(ii) Second, under free flow condition, the traveling behavior of the individual vehicle is more predictable.This phenomenon enables the estimation of the flexible arrival time window for each individual vehicle based on the current spot speed and the historical data.It is expected that the accurate estimation of the arrival time window could potentially lead to an improved matching accuracy of the VRI method, and hence reduce the incident detection time.(iii) Third, it should be noted that the proposed VRI cannot guarantee an accurate matching because of the nonuniqueness of the vehicle signatures.Instead, the proposed VRI scheme in this paper can only provide the matching probability between the downstream and upstream vehicles.Therefore, some of the mismatches resulted from the matching probability could potentially lead to false alarms.To handle this, a ratio method is introduced to screen out those mismatches for reducing the false alarms.

Flexible Time Window Estimation
Under free flow condition, each individual vehicle would maintain in a relatively stable speed (i.e., low variance in travel time).In this case, the arrival time of the vehicle at downstream station could be estimated based on the spot speed and historical data.Let   represent an upstream vehicle detected at time    , and the associated upstream spot speed is denoted as V   .The expected arrival time Arr of vehicle   is given by where  is the distance between the upstream and downstream detectors; V   is the estimated vehicle speed at downstream detector based on the historical speed database.To account for the error in estimating the downstream spot speed, the upper and lower bounds of V   are provided by the following equations: where V  ub and V  lb are, respectively, the upper and lower bounds of the vehicle at downstream detector;   is the current average speed of the upstream detector;  ub ≥ 1 and  lb ≤ 1 are respectively the associated upper and lower bound factors;   hist (  ) is the historical average speed of the downstream detector at time   .The time   is chosen such that it is matched with the arrival time, which is estimated by a linear speed profile of the modeled section, at the downstream detector.The estimation of downstream spot speeds can be viewed as a prediction-correction process.First, the historical average speed   hist (  ) is adopted to predict the speed of this vehicle at downstream site.Then, this prediction is corrected by the factor V   /  for the better representation of the current traffic condition.Finally, the upper and lower bound factors ( ub and  lb ) are applied for determining the upper of lower bounds of the downstream spot speed.With the estimated downstream speeds, the corresponding upper and lower bounds of the travel time of vehicle   can be calculated as follows: However, it should be noted that the proposed incident detection system is not confined to the above method for estimating the time window.Any other estimation methods are equally applicable to the proposed AID algorithm.With the estimated time windows, vehicles on the monitored freeway section could be "partially" tracked and reidentified in a timely and accurate manner.

Incident-Detection-Oriented VRI
As explained previously, the proposed VRI system is devised based on the video image data provided by VIPs technology.By applying myriad image processing techniques, the detailed vehicle feature data (e.g., color, type, and length) could be obtained.The vehicle matching process is then performed by comparing these vehicle feature data.In this section, the methodologies involved in the incident-detection-oriented VRI system are presented.

Vehicle Matching Problem.
For a vehicle   arrives at downstream station at time    , the vehicle signature, denoted as    = {   ,    ,    }, is then obtained from the VIPs.A search space, S(), which represents the potential matches at upstream station for vehicle   , is determined based on the calculated arrival time window.Specifically, S() is given by where   represents the vehicle detected at upstream station; [  ,   ] is the associated travel time window.The vehicle reidentification problem is to find the corresponding upstream vehicle for   through the search space S().
Herein, we introduce the assignment function  to represent the matching result; that is, where () =  indicates that vehicle   is the same as   .Recall that for each vehicle   ∈ S(), one may assign to the pair of signatures (   ,    ) the distances  color (, ),  type (, ) and  length (, ) based on (3), (4), and (5).In this case, one simple method (i.e., distance-based method) is to find the matched upstream vehicle with the minimum feature distance.However, it should be noted that the vehicle signatures derived from VIPs contain noise and are not unique.Therefore, the distance measure cannot really reflect the similarities between the vehicles.Instead of directly comparing the feature distances, this study utilizes the statistical matching method.Based on the calculated feature distances, that is,  color (, ),  type (, ), and  length (, ), a matching probability (() =  |  color ,  type ,  length ) between vehicles   and   is provided for the matching decision making.

Calculation of Matching Probability.
The matching probability, also referred to as the posterior probability, plays a fundamental role in the proposed VRI system.By applying the Bayesian rule, we have where ( color ,  type ,  length | () = ) is the likelihood function; (() = ) is the prior knowledge of the assignment function.To obtain the explicit matching probability, the denominator in (11) can further be expressed as On the basis of ( 11) and ( 12), it is easily observed that the calculation of the matching probability is dependent on the deduction of the likelihood function and the prior probability.In this particular case, the prior probability is defined as (() = ) = 0.5, which suggests that the matching is solely based on the comparison between the vehicle feature data.The calculation of the likelihood function is completed in two steps.
(ii) Second, a data fusion rule is employed to provide the overall likelihood functions, that is, the term ( color ,  type ,  length | ()) in ( 11) and ( 12).

Statistical Modeling of Feature Distance.
Without loss of generality, only the probabilistic modeling of color feature distance is described.In the framework of statistical modeling, the distance measure is assumed to be a random variable.Thus, for a pair of color feature vectors (   ,    ), the distance  color (, ) follows a certain statistical distribution.The conditional probability (i.e., likelihood function) of  color (, ) is then given by Likewise, the likelihood functions for the type and length distances can also be obtained in a similar manner.

Data Fusion Rule.
In this study, the logarithmic opinion pool (LOP) approach is employed to fuse the individual likelihood functions.The LOP is evaluated as a weighted product of the probabilities and the equation is given by where the fusion weights, , , and  are used to indicate the degree of contribution of each likelihood function.The weights can also be calibrated from the training dataset.By substituting (12), (13), and ( 14) into (11), the desired matching probability for each pair of vehicles (  ,   ) could be obtained.For the sake of simplicity, let   denote the matching probability between the vehicle   and   .In this case, we may obtain a set of probabilistic measures {  |  = 1, 2, . . ., } to represent the likelihood of a correct match between   and the vehicles in the search space S().The final matching decision-making based on these matching probabilities, becomes the major concern in the following subsection.

Ratio Method for Final Matching
Decision.An intuitive decision-making process (i.e., the greedy method) is to sort the matches via the matching probability {  |  = 1, 2, . . ., } and choose the vehicle   with the maximum matching likelihood; that is, However, it is noteworthy that the proposed VRI system is utilized for incident detection purpose, the final matching decision would produce significant impacts on the performance of the AID system.Based on the greedy method (15), the potential false alarms would be triggered.As shown in Figure 4, the downstream vehicle   arrives at time 10:39:39 a.m.  and   are, respectively, the two candidate vehicles with the largest and second largest matching probabilities with the downstream vehicle   (i.e.,   = 0.9295 and   = 0.8392).Although vehicle   actually matches with vehicle   (based on the manual matching), the greedy method yields the matching result () = , which could lead to a false alarm at time    +   .To reduce the false alarms mentioned above, a ratio method is then introduced for the final matching decisionmaking.Let {  |  = 1, 2, . . ., } denote the set of matching probabilities in descending order.The ratio method proposed in this study involves two major steps.First, by imposing a threshold  on the value of the ratio between the neighboring probabilities in the ordered set {  |  = 1, 2, . . ., }, one may be able to screen through the search space and rule out those unlikely matches.The screening process is described in Procedure 1.
The underlying implication of Procedure 1 is that if the ratio (i.e.,   / +1 ) is sufficiently large, then it could come to a conclusion that vehicles { + 1,  + 2, . . ., } are the unlikely matches due to their relatively smaller matching probabilities.Otherwise, if the ratio   / +1 ≤ , then we may declare that vehicle  and  + 1 are not distinctive from each other and a matching decision cannot be made at current stage.Upon the completion of the above screening process, unlikely matches could be ruled out and the search space is further reduced.The second step is then to make a matching decision based on the remaining search space S  ().Let S  () = {  |  = 1, 2, . . ., } (clearly  ≤ ), the matching result is then given by It is obvious that vehicle   is matched to the vehicle in S  () with the smallest upper bound in the predicted arrival time window.The rationale behind this approach is that a matching decision could not be made based on the matching probabilities (as the matching probabilities for vehicles in S  () are not significantly different from each other).In this case, the vehicle   is matched to upstream vehicle with smallest upper bound in the predicted arrival time window to avoid the potential false alarms.As a matter of fact, the second step could be viewed as a standard vehicle count approach in which only the counts data is utilized.
To sum up, the matching decision-making process of the incident-detection-oriented VRI is a hybrid of the vehicle feature matching and the classic vehicle count approach.The overall procedure for the matching decision-making is given by Procedure 2.

Test Results
In this section, the performance of the proposed AID algorithm is evaluated against the classical vehicle count approach in terms of mean time-to-detect and false alarm rate (i.e., false alarms per hour).As the performance of the proposed AID system relies on its two critical components (i.e., flexible time window estimation and incident-detectionoriented VRI), different sizes of time window and thresholds for final matching are tested in this section.The dataset described in Section 2 are used to perform the simulated tests for the algorithm evaluation.Also, the real-world case studies are carried out in this section.
6.1.Simulated Tests.For calibrating and testing the proposed AID system, the 3,682 pairs of vehicle matching results from the collected dataset are divided into two parts.First, a dataset of 800 pairs of correctly matched vehicles are used for model calibration and training.The upper and lower bound factors for time window estimation (i.e.,  ub and  lb ) are calibrated by using the travel time data of the 800 vehicles and the historical averaging speed on Thursday, which is the same as the test day (i.e., 16/2/2012, 23/2/2012, 1/3/2012, and 8/3/2012).In addition, the parameters of the statistical model (i.e.,  1 and  2 ) are estimated by utilizing the feature data extracted from the captured images of these 800 pairs of vehicles.Second, the remaining 2,828 pairs of vehicles detected at both upstream and downstream detectors are fed into the calibrated AID system for model evaluation.In order to mimic an incident between the upstream and downstream detectors, the record of vehicle at downstream site is intentionally removed to simulate the situation that the vehicle has passed the upstream detector but not the downstream one.In the testing of the proposed AID system, the AID algorithm is run for 2,828 times, which for each run the record of one of the 2,828 vehicles at downstream detector is removed, for determining the mean detection time.Specifically, the incident detection time is defined as Since we do not know the exact time when the incident happened, the incident detection time is then defined as the difference between the time when an alarm is issued (i.e.,  incident ) and the arrival time of incident vehicle at upstream station (i.e.,   ).By setting the threshold value equals to 2 (i.e.,  = 2), the mean detection time of the proposed AID algorithm is 203.2 seconds, whereas the mean detection time of the classical vehicle count approach is 644.1 seconds.As it is expected, the mean detection time is reduced substantially by incorporating the modified VRI system.Figure 5 shows the performance of the VRI-based incident detection algorithm for different threshold values adopted in final matching decision.It could be observed that the false alarm rate reduces as the threshold value increases.When the threshold value equals one, the VRI system will always match the downstream vehicle to the upstream one with the largest matching probability.Therefore, it would lead to a large number of false alarms (see Section 5.3).With the increase in threshold value, the modified VRI system relies more on the traditional vehicle count approach and results in a decrease in the false alarm rate.On the other hand, as the proposed VRI system is more relied on the traditional vehicle count approach (e.g.,  → ∞), the mean detection time also increases (see Section 3.1).To sum up, for the proposed VRI system, the lowering of the false alarm rates is at the expense of incident detection time.Thus, a balance should be struck between the rapid incident detection and low false alarm rate.
The estimation of arrival time window also has a significant impact on the performance of the proposed AID algorithm.It is not difficult to understand that a small time window size would result in faster incident detection.To test the performance of the proposed AID algorithm under different time window sizes, a time window with fixed size is assigned for each individual vehicle.Figure 6 shows the mean detection of the algorithm for different time window sizes.The mean detection time of the vehicle count approach increases dramatically as the size of the time window grows.It is also observed that the vehicle count approach is not capable of detecting the missing vehicle as the size of time window is larger than 50 seconds.To sum up, for the simulation that a large arrival time window is applied, the proposed AID algorithm clearly outperforms the vehicle count approach.
6.2.Real-World Case Studies.Apart from the abovementioned simulation tests, two real-world case studies are also carried out.Based on the record from the freeway authority, the first incident is reported on June 13, 2012, at 16:03.The reported incident location is at 20 + 600 westbound, which is in the section between camera 7A/8A and 9A/10A (see Figure 1).Based on this information, the research team has screened through the captured videos for identifying the incident vehicle.It is found out that on June 13, 2012, the incident vehicle has passed the upstream detector (7A/8A) at 15:55 (Figure 7(a)) and has an incident before it reaches the downstream detector (9A/10A).Four minutes later, a tow truck, which is probably called by the driver of the incident vehicle, has passed the upstream detector (Figure 7(b)) and towed the incident vehicle to pass the downstream detector at 16:09 Figure 7(c)).According to the above information of the incident vehicle, a 35-minute video record data (from 15:33 to 16:08 on June 13, 2012) of locations 8A and 10A are extracted and input into the proposed AID system for free flow condition.In this case, apart from the incident vehicle, 739 vehicles are detected at both stations during the 35-minute video record.By setting the threshold value of the ratio of matching probabilities equals to 8.5, the time of incident detection and the false alarm rate for this case study are found to be 15:58:22, and 3.42 false alarms per hour, respectively.Compared with the classic vehicle count approach, which would trigger an incident alarm at 16:01:28, the proposed AID system performs better in terms of the incident detection time.
The incident vehicle of the second real-world case study is shown in Figure 8.This incident is reported on June 17,  2012 at 10:31 a.m. and its detailed location is at 19 + 300A westbound (between 7A/8A and 9A/10A).By setting the threshold value of the ratio of matching probabilities equal to 8.5, the time of incident detection and the false alarm rate for this case study are found to be 10:28:22 and 2 false alarms per hour, respectively.Compared with the classic vehicle count approach, which would trigger an incident alarm at 10:33:50, the proposed AID system still performs better in terms of the incident detection time.
On the basis of these two real-world case studies, we may observe that the time of incident detection of the proposed AID algorithm is largely dependent on the actual information associated with the incident vehicle (e.g., distinctiveness of the incident vehicle feature and the size of the vehicle platoon).In real-world case study #2, the incident vehicle has "distinctive" vehicle color distribution (see Figure 8(a)) and, consequently, the disappearance of this very vehicle can be identified earlier than the vehicle count approach.The size of vehicle platoon may also have significant impact on the performance of the AID algorithm.The larger the platoon size is, the more likely it is that the arrival time windows of these vehicles may overlap each other at the downstream site and, hence, leads to the significant increase in incident detection time.

Conclusion and Future Works
This paper investigates the feasibility of utilizing the vehicle reidentification system for incident detection on a freeway section under the free flow condition.A modified vision-based VRI system is proposed to partially track the individual vehicle for identifying the "missing" vehicle due to an incident.A flexible arrival time window is estimated for each of the individual vehicle at upstream station to improve the matching accuracy.To reduce the potential false alarms, a screening method, which is based on the ratios of the matching probabilities and arrival time windows, is introduced to rule out the potential mismatches.
The proposed AID algorithm is tested on a 3.6 km segment of a closed freeway in Bangkok, Thailand.Based on the test results, it is found out that the detection time of the proposed AID algorithm is substantially shorter than the traditional vehicle count approach.Also, there is a trade-off between the false alarms rate and detection time for the proposed AID algorithm.Therefore, a balance should be struck between the rapid incident detection and low false alarm rate by adjusting the thresholding value .As demonstrated in Procedure 2, the proposed AID algorithm is a hybrid of the vehicle feature comparison method and the classical vehicle count approach, and the threshold value  can be viewed as a switch between these two methods.Therefore, the selection of  may be of great importance to the proposed AID algorithm.In this study, we adjust the threshold value manually based on the reliability of VRI system (the performance of the VRI system in different time period may be slightly different due to the changes in outdoor environment, and the threshold value  should be adjusted accordingly).Some other automatic thresholding processes [29] will be investigated in our future works.
Note that the proposed AID algorithm is specifically devised to detection incident on freeway system under freeflow conditions.As a natural and necessary extension, the ability of detecting incidents under dynamic traffic condition is required for the further development of incident detection system.The key component would be to devise an additional VRI based detection algorithm for congested situation.Theoretically, this purpose can be achieved by analyzing the temporal changes in travel time information obtained from VRI system under dynamic traffic conditions [25].
Based on the video record collected at the test site, 3,628 vehicles are detected at both stations (10B and 08B) during the two-hour video record.For the purpose of the algorithm development and evaluation, these 3,628 pairs of vehicles are manually matched (i.e., reidentified) by the human operators viewing the video record frame by frame.In other words, the ground-truth matching results of the 3,628 pairs of vehicles are obtained in advance.The mean travel time is 170.9 seconds.The first 800 pairs of vehicle data are used for the model training and calibration (which are discussed in the following sections), while the rest of the vehicle dataset are used for the simulation test of the proposed automatic incident detection algorithm.

Figure 3 :
Figure 3: Overall framework of AID system.

Figure 5 :
Figure 5: Mean detection time and false alarm rate.

Figure 6 :
Figure 6: Comparison between the proposed AID algorithm and vehicle count approach.

Figure 7 :
Figure 7: Real-world case study #1: (a) incident vehicle passes the upstream detector; (b) tow truck passes the upstream detector; (c) incident vehicle and truck passes through the downstream detector.

Figure 8 :
Figure 8: Real-world case study #2: (a) incident vehicle passes the upstream detector; (b) incident vehicle and truck passes through the downstream detector.
Approach.The basic operation of the vehicle count approach is illustrated in Figure2.When a vehicle   arrives at upstream station at time    , the expected arrival time window [   +   ,    +   ] of this vehicle at downstream station is estimated, where   and   , respectively, represent the lower and upper bounds of the vehicle's travel time.If another vehicle   is detected at upstream station, the corresponding arrival time window [   +   ,    +   ] can also be obtained.Unsurprisingly, there may be overlap between these two time windows, and both of these two vehicles are likely to arrive at downstream during time interval [   +   ,    +   ].The incident would then be detected by comparing the collected vehicle count data to the expected number of vehicles in the time interval.In the case that vehicle   is missing, if vehicle   arrives at downstream during time interval [   +   ,    +   ], then the incident alarm will not be triggered until time +   , which is clearly later than the upper bound of the arrival time of vehicle   (i.e.,    +   ).Because of the overlapping between the time windows, the vehicle count approach, which is solely based on comparing the vehicle