Clustering Object Trajectories for Intersection Trafﬁc Analysis

Tania Banerjee, Xiaohui Huang, Ke Chen, Anand Rangarajan and Sanjay Ranka

CISE, University of Florida, Gainesville, Florida, U.S.A.

Keywords:

Intersection Trafﬁc Analysis, Trajectory Data Mining, Anomaly Detection.

Abstract:

Vehicle and pedestrian trafﬁc at a trafﬁc intersection provide crucial information about the performance of the

intersection for safety and throughput. It is possible to discover patterns and outliers on this data by applying

data analytics. In this paper, we present a novel clustering algorithm for trajectories that use a new distance

measure and a two-level hierarchical clustering approach based on geometric properties of the trajectories and

spectral clustering. Trajectory data is augmented with signal phasing and timing information, which gives new

insights to the trajectory data. We demonstrate the procedure on a real-life intersection where the prominent

patterns for trafﬁc movement are found, and the anomalous trajectories are extracted.

1 INTRODUCTION

Traditionally, most intersections have induction loop

detectors installed underneath the road. These detec-

tors detect vehicles passing over them and may be

used to monitor the vehicle throughput at an intersec-

tion. However, these detectors incur high costs for de-

ployment as well as maintenance and may not sense

pedestrians or scooters. Additionally, even for the ve-

hicles that can be detected, the loop detectors cannot

precisely tell the class of the vehicle passing over it.

To address these limitations, many intersections are

now being equipped with other types of sensors, such

as video cameras and radars. The use of videos has

tremendous potential as it provide rich information in

addition to counting the vehicles. Examples of this

include tracking the type of object passing through

an intersection, tracing the trajectories of objects, and

detecting anomalous trafﬁc behaviors. These addi-

tional information can be used to improve safety and

performance of an intersection.

An object moving through an intersection is cap-

tured by the video camera installed at the intersec-

tion, and it is possible to generate the coordinates us-

ing video processing algorithms such as (Huang et al.,

2018) and (Huang et al., 2020) where the coordinates

of the path are annotated with the timestamp, and the

height and width of a bounding box enclosing the ob-

ject. A trajectory is deﬁned as a path traced by a mov-

ing object and is represented by a time series of spa-

tial coordinates of the object. A triplet representation

of the object ((x

, y

, t

), (x

, y

, t

) ··· (x

, y

, t

))

provides the location of the object at different time

instants. We leverage the trajectories generated us-

ing video processing and fuse it with SPaT (Signal

Performance and Timing) data to determine vehicle

and pedestrians on the intersection for different sig-

nal phases.

Broadly, we develop a novel end-to-end workﬂow

for analyzing vehicular and pedestrian trafﬁc at an in-

tersection, beginning with ingesting video data and

controller logs, followed by data storage and process-

ing to generate dominant and anomalous behavior at

the intersection which helps in various applications

such as near-miss detection. The key contributions of

our paper are as follows:

1. We develop a new distance measure for comput-

ing distances between trajectories. Using this dis-

tance measure, we develop an ofﬂine, two-level

hierarchical clustering scheme. At the ﬁrst level,

the trajectories are clustered based on their direc-

tion of movement. At the second level, spectral

clustering is applied. Clustering helps us to detect

the outliers automatically.

2. We show how new insights and perspectives into

the trajectory data are possible by joining the tra-

jectory database with the SPaT data. For example,

the combined data can be used to detect signal vi-

olations, to count the number of vehicles enter-

ing the intersection on a yellow light, and several

other useful behavior patterns.

Extensive results are provided on video and SPaT data

collected at an intersection. These results demonstrate

that video and signal timing information is useful in

quantifying

Banerjee, T., Huang, X., Chen, K., Rangarajan, A. and Ranka, S.

Clustering Object Trajectories for Intersection Trafﬁc Analysis.

DOI: 10.5220/0009422500980105

In Proceedings of the 6th International Conference on Vehicle Technology and Intelligent Transport Systems (VEHITS 2020), pages 98-105

ISBN: 978-989-758-419-0

1. Safety of pedestrians and bicyclists by study-

ing the nature of the anomalous vehicle trajecto-

ries and also the statistics of occurrence of these

anomalies (counts of anomalies depending upon

the hour and day of the week)

2. Effective tuning of signal timing based on demand

proﬁles. It also helps us compare the new tech-

nologies such as video-based monitoring and ex-

isting technologies such as induction loops.

The approach presented in this paper can be used

to develop a system that uses edge-based video-

stream processing to convert video data into space-

time trajectories of individual vehicles and pedestri-

ans. These trajectories are transmitted and stored to a

centralized system for intersection level and city wide

processing.

The rest of the paper is organized as follows. We

present existing work on trajectory analysis in Sec-

tion 2. The background information for our applica-

tion may be found in Section 3, while the method-

ology developed as part of this paper is presented in

Section 4, which includes computing distance mea-

sures and clustering trajectories along with case-

studies for some intersections. The conclusions are

presented in Section 6.

2 RELATED WORK

The general advancement of location acquisition tech-

nologies has made it feasible to generate a massive

database of trajectories for different kinds of entities,

such as vehicles, hurricanes, migratory animals. It re-

quires data mining techniques to gain insight into this

massive dataset. Feng et al. (Feng and Zhu, 2016),

Mazimpaka et al. (Mazimpaka and Timpf, 2016),

and Banerjee et al. (Banerjee et al., 2019) describe

the fact that a complete trajectory data mining appli-

cation involves components for data collection, data

preprocessing, management and storage, query pro-

cessing, data mining, and privacy protection. Most of

the existing work on trajectory data mining focuses

on trajectories at a macro level, such as those through

cities, states, countries, or continents, where trajec-

tory data in collected using satellites or an appropri-

ate satellite-based radio navigation system. Examples

are vehicle positioning data, or data from hurricanes

or animal movement (Lee et al., 2008), activities in

and around a city (Loecher and Jebara, ). Unlike

this work, the focus of this paper is on the analysis

of object trajectories at signalized intersections us-

ing trajectory clustering to ﬁnd patterns and anoma-

lies of trafﬁc behavior with reference to the signaling

phase of the intersection as well as the spatial con-

straints. The trajectory data is collected from videos

installed at the intersections, and the trajectory data

is fused with SPaT data from the intersections. SPaT

data may be obtained either from high-resolution con-

troller data or from DSRC (Dedicated Short-Range

Communications) RSU (Roadside Unit). In the fol-

lowing we brieﬂy describe some of the related work

in this area.

Trajectory clustering algorithms may be di-

vided into three groups, namely, supervised, semi-

supervised, and unsupervised algorithms. This dis-

tinction arises if labeled data is used to aide in the

clustering where the labels uniquely identify the clus-

ters (Bian et al., 2018). We use unsupervised clus-

tering in this work, and the user can just invoke

the algorithm without having to input any labeled

data. Model-based unsupervised clustering strate-

gies use probabilistic models for clustering trajecto-

ries (Morris and Trivedi, 2011). Gaussian Mixture

models and hidden Markov models are used in (Mor-

ris and Trivedi, 2011), to model the trajectory coordi-

nates and the trajectory dynamics, respectively. An-

other existing unsupervised clustering strategy is it-

erative (Lloyd, 1982), where the cluster centers are

found and updated iteratively. In our work, we use a

hierarchical clustering scheme where the trajectories

are ﬁrst clustered based on their general direction of

movement using geometrical properties of the trajec-

tories. Then spectral clustering is applied on each tra-

jectory cluster to identify the typical pattern of move-

ment and associated anomalies.

Clustering a given set of objects involves comput-

ing the pairwise distance between them so that the

closest objects may be clustered together. Thus, the

concept of a distance measure is essential for clus-

tering trajectories. A trajectory is a time-series and

one of the existing distance measures used in litera-

ture for a time-series is the longest common subse-

quence (LCSS (Vlachos et al., 2002), edit distance

with real penalty (ERP) (Chen and Ng, 2004), dy-

namic time warping (DTW) (Kruskal and Liberman,

1983) and FastDTW (Salvador and Chan, 2004). Ap-

plying DTW or FastDTW directly to the trajectories at

an intersection collected in real-time using video pro-

cessing is not effective, because location coordinates

are often dropped due to artifacts of video process-

ing and occlusion. Partial trajectories results in a very

high distance value for two otherwise similar trajec-

tories ( Figure 2). We have developed a new distance

measure that is more effective for these type of tra-

jectories. The distance measure is based on the warp

path of two trajectories. The warp path is obtained by

applying FastDTW, and using the warp path, we de-

Clustering Object Trajectories for Intersection Trafﬁc Analysis

termine the area between the trajectories and divide

the area by the length of the two trajectories to get the

average perpendicular distance between the trajecto-

ries.

3 BACKGROUND

The background information required for analyzing

the trajectories is presented in this section. Section 3.1

describes the trajectory generation in brief while Sec-

tion 3.2 describes the recording of the current signal

state of an intersection. Finally, Section 3.3 presents

a detailed comparison of the candidate distance mea-

sures.

3.1 Trajectory Generation

A video processing software processes object loca-

tions frame by frame from a video and outputs the

location coordinates along with the corresponding

timestamp. The video is captured by a camera in-

stalled at an intersection. To accurately locate the co-

ordinates of an object, the video processing software

must account for the different types of distortions that

creep into the system. For example, for a ﬁsheye lens,

there would be a signiﬁcant amount of radial distor-

tion. After taking into account the intrinsic and ex-

trinsic properties of the camera, a mapping is created,

which is used by the video processing software to map

observed coordinates to modiﬁed coordinates that are

nearly free of any distortion. To represent the location

of a 3D object using a dimensionless point, one looks

to ﬁnd the center of mass of the object. A bounding

box is drawn enclosing the object. The center of the

box is approximated to be the center of mass of the

object. After generating timestamped coordinates of

a trajectory, the software computes other properties

such as speed, the direction of movement.

3.2 Signalling Status

An intersection almost always has trafﬁc lights to con-

trol the ﬂow of trafﬁc safely. The changes in signals

from green to yellow to red are events that are cap-

tured in controller logs by advanced controllers and

also sometimes broadcast by DSRC RSUs, and the

corresponding data are called Signal Phase and Tim-

ing (SPaT) data. To specify a particular signal and in

a more general sense the direction of movement, the

trafﬁc engineers deﬁne a standard that assigns phases

2 and 6 to the two opposite directions of the major

street and 4 and 8 to those of the minor street. Fig-

Figure 1: Phase Diagram showing vehicular and pedestrian

movement at four way intersections. The solid gray arrows

show vehicle movements while the blue dotted arrows show

pedestrian movements. (US Department of Transportation,

2008).

ure 1 shows these phase numbers as well as the phase

numbers for the turning vehicles and pedestrians.

In our application, we store the current signal

phase in a compact 6-digit hexadecimal encoding. To

explain the formatting, let us consider the correspond-

ing 24-bit binary equivalent. The bits 1-8 are pro-

grammed so that they are 1 if the corresponding phase

is green, and 0 otherwise. Similarly, the bits 9-16 and

bits 17-24 are reserved for programming the yellow

and red status for the eight-vehicle phases, respec-

tively. For example, green on phases 2 and 6 at an

intersection, would have a binary encoding of 0100

0100 for the ﬁrst 8 bits, the next eight bits would be

0000 0000 for yellow, and the last set of 8 bits for

red would be one where the second and sixth bits are

0 represented as 1011 1011. Thus, the overall 24-bit

binary representation of the current signalling state is

0100 0100 0000 0000 1011 1011, or 4400bb.

3.3 Comparing Trajectories

The ﬁrst step toward clustering a set of trajectories is

applying a good distance measure that will, for any

two trajectories, tell how close the trajectories are to

each other in space and time. There are two poten-

tial candidates for distance measures of the intersec-

tion trajectories: Euclidean Distance (ED), and Dy-

namic Time Warping (DTW). Among these, ED is the

square root of the sum of the squared length of verti-

cal or horizontal hatched lines. The disadvantage of

using ED is that for trajectories of different length, it

cannot calculate their distance reliably.

DTW can compute distances between trajectories

when they vary in time, or speed, or path length.

Although DTW utilizes a dynamic programming ap-

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100

Figure 2: An example where two similar trajectories as

highlighted in the top and the bottom images, have high dis-

tance value when DTW/FastDTW is directly used to com-

pute distance. This is potentially due to differential tracking

of vehicles due to potential occlusion.

proach for an optimal distance and has a time com-

plexity O(N

), where N is the number of coordi-

nates in the two trajectories, there are approximate

approaches such as FastDTW that realize a near-

optimal solution and has a space and time complexity

of O(N). FastDTW is based on a multilevel iterative

approach. FastDTW returns a distance and a list of

pairs of points, also known as the warp path. A pair of

points consists of coordinates on the ﬁrst and second

trajectories and represents the best match between the

points after the trajectories are warped. The distance

returned by FastDTW is the sum of the distances be-

tween each pair of points on the path. Quite natu-

rally, the distance is small if the trajectories occur in

the same geographical coordinates and are traversed

at similar speeds.

DTW and FastDTW work well for trajectories that

are entirely captured by the sensor system. In re-

ality, the sensor system and the processing software

may not capture the trajectory in its entirety. In that

case, distance returned by the dynamic time warp-

ing algorithm is not representative of the actual dis-

Figure 3: Two straight trajectories represented by ABCDE

and FGH. The dashed lines show the point correspondence

(warp path) obtained using FastDTW. The trajectory FGH

is shorter as the beginning part of the trajectory was not

captured.

tance. Figure 2 highlights two example trajectories

for which DTW returns a high value for distance sug-

gesting the tracks are dissimilar. For example, for two

tracks going straight, if the starting portion of one of

the tracks get truncated due to a processing error, as

shown in Figure 3, the distance between the tracks

will be

+ BF

+CF

+ DG

+ EH

. Thus, the

distance computed results in a high value, which of-

ten falls in the range of distance between two unre-

lated trajectories. Hence, we developed a new dis-

tance measure by utilizing the warp path returned by

the FastDTW.

4 CLUSTERING

We describe our trajectory clustering method in this

section. There are two main components to cluster-

ing, the ﬁrst is to use an efﬁcient distance measure

for the trajectories to be clustered and the second is to

use a clustering algorithm that uses the distance mea-

sure to create clusters of trajectories that behave in a

similar manner. We describe the novel distance mea-

sure developed as part of this work in Section 4.1 and

present our clustering algorithm in Section 4.2

4.1 Distance Measure

The new distance measure developed in this section,

applies to trajectories captured using real-time video

processing. The ﬁrst step in the computation of the

distance measure is to obtain the warp path using

a time warping algorithm, e.g. FastDTW. Triangles

are constructed using the warp path as shown in Fig-

ure 3, where the triangles are 4ABF, 4BCF, 4CDF,

4DFG, 4DEG, and 4EGH. Since the coordinates

of the vertices (A, B, C, D, E, F, G, and H) are known,

the area of each may be computed using the following

formula from coordinate geometry.

Area = |

− c

) + b

− a

) + c

− b

)

(1)

Clustering Object Trajectories for Intersection Trafﬁc Analysis

101

where the vertices of the triangle have coordinates:

),(b

), and (c

). The sum of area of all

triangles is computed and ﬁnally the distance, D

i j

, be-

tween two trajectories T

and T

, is computed as:

i j

= (

∑

k=1

Area

)/L

i j

(2)

where Area

is the area of the k

triangle and L

i j

is the

average length of the two trajectories, T

and T

, and n

is the total number of triangles. If there is no warping,

and the number of matched pairs is m, then n = 2m, by

construction. However, if there is warping, then n <

2m. D

i j

is the average perpendicular distance between

the trajectories, which intuitively is the average height

of the triangles.

To get a more accurate local distance measure, we

segment the trajectories and compute the distance of

the starting and the ﬁnishing segments. Let SD

i j

and

i j

be the distances of the starting and the ﬁnish-

ing segments, respectively. Then, SD

i j

is the dis-

tance between the ﬁrst pair of matching points that

are not warped (CF and DG in Figure 3) and corre-

spondingly, FD

i j

is the distance between the last pair

of matching points that are not warped (DG and EF

in Figure 3). SD

i j

may be computed as the average

height of triangles 4CFG and 4CDG, and FD

i j

that of triangles 4DGH and 4DEH. Thus, we use

triplets of (D

i j

, SD

i j

, FD

i j

) to represent the distance

between two trajectories. These three portions of the

distance measure can be suitably weighed for com-

puting a scalar distance if required.

Computation of Similarity Matrix. The similarity

matrix, S, is computed from the distance measures by

setting up empirical thresholds for the magnitude of

the distance between two trajectories. For example,

given two trajectories T

and T

, if their average dis-

tance D

i j

of Equation 2 is less than x and the start

section distance, SD

i j

is less than y and the last sec-

tion distance, FD

i j

is less than z, then T

and T

are

considered similar. The corresponding entry in the

similarity matrix, in that case, would be S

i j

= S

= 1.

If any distance value exceeds the thresholds - x, y, and

z, then the trajectories would be considered dissimilar

and in that case, S

i j

= S

= 0. In this manner, the

similarity matrix is computed and is ready to be used

in spectral clustering.

4.2 Hierarchical Clustering

Clustering a large set of N trajectories is a O(N

) op-

eration since pairwise distance needs to be computed

to prepare a distance matrix. A two-level hierarchi-

cal clustering scheme is proposed here to address the

phase2 WB

SN (562, 880), (560, 149)

NS (560, 149), (562, 880)

WE (84, 536), (962, 547)

EW (962, 547), (84, 536)

phase2stopbar (815, 153), (819, 707)

phase4stopbar (244, 739), (825, 750)

phase6stopbar (330, 155), (287, 726)

phase8stopbar (287, 240), (804, 231)

Figure 4: Snippet of a conﬁguration ﬁle that shows the user

inputs needed for an intersection. The coordinates may be

obtained using a visualization tool (Chen et al., 2020).

quadratic complexity. Clustering at the ﬁrst level par-

titions the set of trajectories into homogeneous clus-

ters based on their direction of the movement. Then

spectral clustering is applied to cluster the trajecto-

ries for each phase separately and to detect anoma-

lies. The clustering scheme is explained in detail in

this section.

4.2.1 Partitioning Trajectories based on

Movement Phase

Any object at an intersection must obey the traf-

ﬁc rules, and hence its trajectory is necessarily con-

strained both in time and space. One of the goals

of the software is to detect trafﬁc violations and the

underlying causes to make the intersection safer ulti-

mately. These violations may appear as spatial out-

liers or as timing violations. Figure 1 shows the

phases for pedestrian and vehicular movements. A

given set of trajectories is partitioned into eight bins

aligned respectively with the eight phases and to four

additional bins corresponding to the right turns for

phases 2, 4, 6, and 8.

Since the trajectories are essentially a series of co-

ordinates, it is possible to use basic vector algebra and

trigonometry to get their general direction. For exam-

ple, the spatial coordinates of a track T

is given as

, y

), (x

, y

), ···, (x

, y

). Let

A = [x

] and

B = [x

] be two vectors connecting the origin to

the start and end points respectively, of T

, with their

direction away from the origin. Let

AB be a vector

connecting the start and the end points, with its head

at the end point, (x

). Then, using the rules of vec-

tor addition,

A +

AB =

B , which implies

AB =

B −

A .

Thus,

AB = [x

− x

− y

Once constructed, a trajectory vector may be com-

pared with a reference vector to obtain the direction of

the trajectory. The start and endpoints of these refer-

ence vectors may be obtained using CAD tools sup-

ported by visualization software, and the coordinates

of the start and endpoints are speciﬁed in a conﬁgura-

tion ﬁle.

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102

Phase 2

stopbar

Phase 8 stopbar

Phase 4 stopbar

Phase 6

stopbar

Figure 5: Pictorial representation of information in conﬁg-

uration ﬁle.

The cosine of the acute angle between a trajectory

vector ~u , and a reference vector ~v is given by.

cos θ =

|~u .~v |

(3)

When the directions are nearly matching, the value of

the cosine is close to 1.0.

A snippet of a conﬁguration ﬁle used to spec-

ify the reference vectors is shown in Figure 4. The

user can specify the direction of the phase 2 move-

ment using the phase2 parameter of this ﬁle, which

has a value WB (West Bound) in this example. The

other phases, as described in Figure 1 may be derived

with reference to the phase 2 direction. The param-

eters SN, NS, WE, EW, are used to specify the start

and endpoints of reference vectors for through lanes

along South-North, North-South, West-East and East-

West directions respectively. Figure 5 shows the cor-

responding reference vectors. The start and endpoint

coordinates of the stop bars are also needed to differ-

entiate left and right turn movements that otherwise

align with each other. An example of this is given

later in this section.

Given a trajectory, the cosine value in Equation 3

may be computed for the trajectory vector and the ref-

erence vectors, and if the value computed is close to

1 for any of these vectors, the trajectory may be as-

signed the corresponding through phase (one of 2, 4,

6 or 8).

For any intersection, the coordinates of the ref-

erence vectors have to be determined once, and the

conﬁguration ﬁle may be reused over time until the

geometry of the intersection is changed.

4.2.2 Clustering Trajectories in a Partition

The next step in the hierarchical clustering scheme

is to cluster the trajectories that have the same direc-

tion of movement. The spectral clustering algorithm

is applied in this step. Prior experimentation with a

simple KMeans clustering approach for this problem

highlights the beneﬁts of using spectral clustering in-

stead. A pure KMeans algorithm requires user input

for the number of possible clusters, which is impossi-

ble for the user to know in advance. Spectral cluster-

ing, through its smart use of standard linear algebra

methods, gives the user objective feedback about the

number of possible clusters and further accentuates

the features of the trajectories to make the separation

of clusters easier.

The inputs to a spectral clustering algorithm are

a set of trajectories, say, tr

, tr

, ···, tr

, and a sim-

ilarity matrix S, where any element s

i j

of the matrix

S denotes the similarity between trajectories tr

and

. It is to be noted that we consider s

i j

= s

≥ 0,

where s

i j

= 0 if tr

and tr

are not similar. Given these

two inputs, spectral clustering creates clusters of tra-

jectories such that all trajectories in the same cluster

are similar to each other. In contrast, two trajecto-

ries belonging to different clusters are not so similar

to each other. For example, for the given set of tra-

jectories, spectral clustering creates separate clusters

for trajectories following different lanes or those that

change lane at the intersection. As a result, spectral

clustering also helps identify the outliers, which are

anomalous trajectories that are not similar to any of

the other trajectories in the set. The two inputs to a

spectral clustering algorithm may be represented as a

graph G = (V, E), where vertex v

in this graph rep-

resents a trajectory tr

. Two vertices are connected if

the similarity s

i j

between the corresponding trajecto-

ries tr

and tr

is greater than a certain threshold ε,

and the edge is weighted by s

i j

. Thus, the clustering

problem may be recast as ﬁnding connected compo-

nents in the graph such that the sum of the weights of

edges between different components is small. Hence,

by obtaining the number of connected components we

know the number of clusters and then get the clusters

by applying a KMeans algorithm.

We used the linalg library provided by NumPy

and to perform the linear algebra operations in spec-

tral clustering. Once the number k of connected com-

ponents is known, a KMeans algorithm is run on the

ﬁrst k eigenvectors to come up with the clustering re-

sults. The function KMeans is a standard KMeans

clustering algorithm from the Python sklearn.cluster

library.

The clusters generated by spectral clustering for

all the left turn trajectories are shown in Figure 6.

The clusters for straight and right turn trajectories are

omitted here due to space constraints.

Clustering Object Trajectories for Intersection Trafﬁc Analysis

103

Figure 6: Second level of the two-level hierarchical clustering scheme where spectral clustering is applied on trajectories with

the same direction of motion. The clusters of some left-turn trajectories are presented in this ﬁgure.

4.2.3 Finding Representative Trajectory

After the trajectories are clustered, we identify a tra-

jectory in each cluster that is representative of that

cluster. The representative for each cluster is com-

puted as the trajectory t belonging to the cluster that

has the least average distance from all the other tra-

jectories.

5 ANOMALOUS BEHAVIOR

Detecting anomalous trafﬁc behavior is one of the top

goals for clustering trajectories. An anomalous tra-

jectory may be one that violates the spatial or tem-

poral constraints at an intersection. The spatial con-

straints amount to the restrictions a vehicle must fol-

low at an intersection, such as never go in the wrong

way. Temporal constraints, on the other hand, are the

restrictions imposed by the signaling system at an in-

tersection. We consider these two types of anomalous

behavior in the rest of this section.

Signal Timing Violations. The fusion of video and

SPaT data allows us to detect the validity of the trajec-

tories with reference to the current signaling phase of

the intersection. The video clock and the SPaT clock

are sometimes off by a few seconds. The clocks may

be treated as synchronous by adding an offset to the

trajectories. This offset may be computed manually

by comparing the time a signal in the video transi-

tions to green and the time in the SPaT when there

Figure 7: Collection of tracks representing vehicles that en-

ter the intersection on a yellow light.

is a “Phase Begin Green” event for the correspond-

ing phase. It is also possible to compute the offset

automatically in software by checking the timestamp

of the ﬁrst trajectory that crosses, say, the phase2 stop

bar, (Figure 5) and the timestamp in SPaT when phase

2 signal becomes green and then adding a 2.5 seconds

of driver reaction time to the signal transition times-

tamp. Figure 7 shows the trajectories that happen dur-

ing a yellow light.

Trajectory Shape Violation. Figure 8 shows the

anomalous trajectories. In all the cases here, the tra-

jectories are turn movements. Sometimes these tra-

jectories take a very wide turn. At other times the

trajectories turn left from a through lane, and at still

other times, the trajectories start taking a turn much

before the actual stop bar, causing wrong-way access

to the adjacent lane.

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104

Figure 8: Collection of tracks that represent vehicles that

have anomalous behavior because of their shape.

6 CONCLUSIONS

We presented a novel method for analyzing vehicle

and pedestrian trajectories at intersections and ap-

plying data mining techniques to ﬁnd patterns and

anomalies. We developed a new distance measure

speciﬁcally for two trajectories at a trafﬁc intersec-

tion. We applied a hierarchical clustering algorithm

based on geometric properties of the trajectories and

spectral clustering. We demonstrated our workﬂow

on a real-life intersection. We augment trajectory data

with SPaT data and show an example of how this is

useful in detecting vehicles that crossed an intersec-

tion on a yellow light, and also potentially detecting

signal violations. This application may be leveraged

to implement useful applications to determine turn

movement counts, to monitor demand and through-

put of an intersection, to detect and manage incidents

at an intersection.

ACKNOWLEDGEMENTS

This work was supported in part by the Florida De-

partment of Transportation (FDOT) and NSF CNS

1922782. The opinions, ﬁndings, and conclusions ex-

pressed in this publication are those of the author(s)

and not necessarily those of FDOT, the U.S. Depart-

ment of Transportation, or the National Science Foun-

dation.

The authors are thankful to the City of Gainesville

for making available the video and controller logs for

various intersections.

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