[IEEE 2009 IEEE International Conference on Vehicular Electronics and Safety (ICVES) - Pune, India...
Transcript of [IEEE 2009 IEEE International Conference on Vehicular Electronics and Safety (ICVES) - Pune, India...
A Fixed Size Assumption Based Data Association Method for
Coalescing Objects Tracking using a Laser Scanner Sensor.
Pawel Kmioteka,b and Yassine Ruicheka
(a) Systems and Transportation Laboratory
University of Technology of Belfort-Montbeliard - France
pawel.kmiotek,[email protected]
(b) Department of Computer Science
AGH University of Science and Technology - Krakow, Poland
Abstract—Data association is one of the crucial parts in thereliable objects’ tracking system. In this paper, a methodology fordata association using an Oriented Bounding Box based objectrepresentation is presented. A laser scanner sensor is used forobjects perception. A data association algorithm for coalescingobjects is described. The algorithm is based on the NearestNeighbours principle enriched by an Inter-Rays uncertaintyparadigm and a Fixed Size assumption, which are introducedto improve the tracking process in terms of objects size andcenter position estimation. Experimental results are presented todemonstrate the effectiveness of the proposed technique.
I. INTRODUCTION
The work presented in this paper is a part of a project
launched in the Systems and Transportation Laboratory of the
University of Technology of Belfort-Montbeliard. The project
is focused on the study of the concept of intelligent vehicles
and their integration in the city of the future. The aim is to
develop a vehicle having the ability to navigate autonomously
in various urban environments. The research developments are
based on an experimental platform consisting of an electrical
vehicle with an automatic control, equipped with several
sensors and communication interfaces. To reach the objective,
the first primary task is to develop a perception system
for detecting, localising and tracking objects in this type of
environments. In this paper, the emphasis is put on tracking
of compact dynamic objects using a laser range finder (LRF).
Representation of dynamic objects is crucial for tracking
and trajectory planning. In the literature concerning tracking,
points with elliptical uncertainty are used for representing
objects position[1][2]. This representation is good enough
for obstacle detection, collision warning or driving assistance
systems in well structured environments like highways [2][3].
In the urban areas, however, the objects movements are less
predictable. Thus, for the task of autonomous navigation in
demanding urban areas, these representation methods are not
sufficient. Oriented Bounding Box (OBB) [4][5][6] provides
a good approximation of the size, shape and orientation angle
of dynamic objects, with a good data compression ratio.
In this paper, the OBB based model with an Inter-Rays
(IR) uncertainty paradigm and a Fixed Size (FS) assumption
is used to represent dynamic objects. The IR uncertainty and
FS assumption are introduced to increase the tracking system
reliability by better object’s size and centre position estimation.
Data association is an important part of multiple-objects
tracking. The raw data points clustering is the basic stage of
the objects separation. In the literature, fixed threshold [7][5],
or adaptive threshold [8][9], are used.
We use raw data points clustering with tract-to-cluster corre-
lation to achieve the preliminary data association and to detect
the three following possible situations: new object appearance,
separate object tracking, coalescing objects tracking. Each of
the detected situation is treated separately in terms of data
association. In this paper, emphasis is put on coalescing objects
data association and tracking. In the literature, there are many
variants of the Nearest-Neighbour (NN), Probabilistic Data
Association (PDA), Joint PDA (JPDA) [1] algorithms, used
to track coalescing objects. The drawback of these methods is
that they do not take into account the size of the objects and it’s
uncertainty, caused by the interaction context objects/sensor.
The proposed data association method uses NN principle
enriched by an association constraint, which is based on
track size. The track size is computed by a size estimation
methodology founded on the IR uncertainty paradigm and
objects’ FS assumption.
The Extended Kalman Filter (EKF) with Discrete White
Noise Acceleration Model (DWNA) [1] and ego odometry is
used for objects tracking.
The paper is organized as follows. Section II presents
the OBB representation for dynamic objects, with the IR
uncertainty paradigm and the FS assumption. The data asso-
ciation method is described in section III. The tracking model
is briefly explained in the section IV. Before concluding,
experimental results are presented in section V.
II. OBJECT REPRESENTATION
A. OBB based model for object representation
Urban environments are characterised by limited spaces
available for navigation and there are little objects movement
constraints. In these conditions, geometrical representation of
dynamic objects is necessary. Oriented bounding box (OBB)
is a way of representing objects geometry with sufficient
approximation for the means of navigation.
ICVES 2009
978-1-4244-5441-9/09/$26.00 ©2009 IEEE 62
Fig. 1. Inter-Rays uncertainty paradigm.
The OBB based representation is described by two vectors z
(1) and σ2z (2). The first one represents the OBB geometry and
includes the centre coordinations cx, cy, the orientation angle θ
and the size dx, dy. The second vector represents uncertainties
on the components of the vector z.
z = [cx, cy, θ, dx, dy]T (1)
σ2z = [σ2
cx, σ2cy, σ
2θ , σ2
dx, σ2dy]T (2)
To construct the OBB based measurement, a specific method
is used. The OBB construction method consists of the four
following main steps. The first step is to find a contour of
the tracked objects using a convex-hull technique [10]. In
the second step, a method based on Rotating Calipers (RC)
technique [11] is used to construct an OBB, which is best
aligned to the object’s contour. The third step consists of
the uncertainty computation. Finally, the forth step concerns
the application of the IR uncertainty paradigm and the FS
assumption. In this paper, we will focus on the forth step. The
previous steps are described in details in [4].
B. Inter-Rays uncertainty
An important aspect of OBB extraction is the fact that the
raw data points representing the extremities of the extracted
OBB do not coincide with the real object’s extremities (see
Figure 1).
In the Figure 1, minX , minY , maxX , maxY are respec-
tively the minimum x coordinate, the minimum y coordinate,
the maximum x coordinate and the maximum y coordinate
of the extracted OBB. The line Lr (respectively Lr + n)
is crossing the point maxY (respectively minX) and is
perpendicular to the OBB side to which maxY (respectively
minX) belongs. The Inter-Rays (IR) real object’s extremities
position estimation and their variances are added to the OBB’s
size and OBB’s size uncertainty. The real object’s extremi-
ties are situated between the raw data points delimiting the
OBB (maxY , minX) and the points Pr and Pr + n. Pr
(respecitvely Pr+n) is the intersection point between the ray
r (respecitvely r + n) with the line Lr (respectively Lr + n).
Considering the OBB’s local X axis, the real object’s
extremity position is uniformly distributed with the mean
µIRx, which is equal to the half of the IR line segment length
dIRx. The IR line segment is defined by the point maxY and
Pr. To fulfil Kalman Filter assumption, the distribution of the
real object’s extremity position is approximated by a normal
distribution with the mean µIRx, and the variance σ2IRx, which
is set to dIRx
6 . The Inter-Rays values z[µIRx] and z[σ2IRx] are
used in each iteration of the tracking algorithm to correct the
size of the OBB measurement [4]. The correction equations
are expressed as follows:
z[dx] = zperc[dx] + z[µIRx] (3)
z[σ2dx] = zperc[σ
2dx] + z[σ2
IRx] (4)
where zperc is the percepred measurement, z is the corrected
measurement used for tracking.
The same process is applied for the OBB’s local Y axis.
C. Fixed Size assumption
The idea of the fixed size (FS) assumption is based on the
fact that, in general cases, objects’ size does not change during
the tracking. However, due to the LRF’s limited resolution and
change of the relative distance and orientation of the observed
object, measurements of the object’s size vary in time. The
principle of the FS assumption is that the track representing
the tracked object cannot reduce it’s size. The FS algorithm
takes place in each iteration of the tracking after the track
prediction and measurements extraction.
For the following algorithm description, we consider the
local OBB’s X axis. The same process is applied to the local
OBB’s Y axis.
Having the percepted OBB measurement with the IR line
segment length zperc[dIRx], we obtain the corrected IR line
segment length z[dIRx] associated with the OBB measure-
ment:
z[dIRx] = min(zperc[dIRx], xk−1[dIRx]) (5)
where xk−1[dIRx] is the IR line segment length associated
with the track at time k-1. The quantity z[dIRx] is then
memorised in the track xk:
xk[dIRx] = z[dIRx] (6)
After using the equation (3) and (4), the next step consists
of the measurement’s size correction by using the following
equation:
z[dx] = max(z[dx], xk[dx]) (7)
where xk[dx] is the track predicted size at the time k.
After correcting the percepted measurement’s size, the
measurement’s center must be appropriately translated. The
updating of the center position is achieved as follows.
Firstly, the visibility factor V Fx is computed for the OBB’s
local X axis:
V Fx =max(βf
minX , βfmaxX)
βfminX + β
fmaxX
(8)
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Fig. 2. Visibility factor associated to the OBB’s local X axis.
where βminX and βmaxX correspond respectively to the an-
gles between OBB’s sides minXside and maxXside normals
and their radius vectors (see Figure 2). f is a parameter, which
is set to 4.
In the second step, the direction factor DFx associated
to the OBB’s local X axis is computed using the following
equation:
DFx =
{
1, if βmaxX > βminX (9a)
−1, if βmaxX < βminX (9b)
In the last step, the difference between the percepted size
zperc[dx] and the corrected size z[dx] is calculated:
∆dx = z[dx] − zperc[dx] (10)
Finally, the measurement’s center translation is expressed
as follows:
z[cx] = z[cx] + 12V Fx · DFx · ∆dx
z[σ2cx] = 1
2z[σ2dx]
(11)
III. DATA ASSOCIATION
One of the most important tasks of autonomous navigation
in urban areas is tracking of dynamic objects. Data association,
which is closely related to the objects representation and
sensory data, is a crucial part of the tracking process. In
this section, a data association methodology suitable for the
OBB representation and laser scanner data is proposed. The
emphasis is put on association of raw data points of coalescing
objects. Since geometrical features are taken into account, only
objects being previously recognised as separated ones can be
tracked correctly.
The data association algorithm is composed of the following
stages : preliminary association (raw data points clustering),
tracks to clusters correlation and raw data points to track
association. The preliminary association is based on distance
thresholding. Points belong to the same cluster if the Euclidean
distance between them is below a certain threshold. Each
cluster is represented by an Axis Aligned Bounding Box
(AABB). The raw data points clustering uses two thresholds:
Track prediction
Raw data points to tracks
prediction distances computation
0 gate 1 gate 2 or more gates
New track measurement
creation (clustering)
Intermediate
measurement
extraction
New Track
Points set
One Track
Points sets
Ambiguous
Points set
Intermediate
measurements
Ambiguous
points
association
Measurements creation
Track state
update
Data
Process
Measurements
Measurements
Decission
Raw data points classification
Fig. 3. Schema of NN+FS data association algorithm.
a general threshold and a neighbouring points one. Applied to
the points produced by neighbouring rays, the neighbouring
threshold is greater than the general one, which is used for all
non neighbour points.
After raw data points are clustered into an AABB, track to
cluster correlation takes place. The track is correlated with the
cluster if the track’s OBB intersects with the cluster’s AABB.
If the track do not intersect any cluster, the track is correlated
with the closest cluster. There are three possible outputs
of track to cluster correlation. A cluster can be correlated
with zero, one, two or more tracks. These cases represent
respectively the following situations: appearance of a new
object, tracking of separated object, and multi-object tracking.
Basing on the results of the previous step, raw data points
to track association follows. In this stage, raw data points,
positively associated with a track, create a measurement. Each
measurement is in the OBB format (see (1) and (2)).
In the first situation (appearance of a new object), all the
points are used to create the measurement. In the second one,
Mahalanobis distance based gating is used to associate raw
data points with a track. Not associated points are processed
to create new tracks. In the last case, a method based on the
Nearest-Neighbour principle is used. In this paper, two variants
of the method are proposed.
The first variant is a pure NN algorithm applied to raw data
points and tracks in interest. For each pair of raw data point
and a track correlated with the cluster, Mahalanobis distance
is calculated. The raw data point validated by tracks’ gates is
assigned to the closest track.
In the second variant (NN+FS), the Fixed Size assumption
is used to improve the NN association algorithm. Figure 3
shows the schema of the NN+FS variant. In the first stage
of the algorithm, raw data points are classified into three
classes: New Track Points (NTP), One Track Points (OTP),
Ambiguous Points (AP). The classification process is based on
the relation between raw data points and the gates of the tracks
in the cluster. The first class represents the points which are
outside all the gates. The second class consists of sets of points
which are inside only one track (one set per one track). The
last class consists of a set with points which are inside more
64
Fig. 4. Classification of raw data points using three classes.
than one gate (see Figure 4). The size of the gate is related
to the sum of the track prediction size and track prediction
position convariances by applying the following gate rule:
Td2 ≥ d2(ij) = νT
(ij)S−1ν(ij) (12)
where ν(ij) is the vector defined from the ith raw data point to
the jth track’s prediction OBB, S−1 is the inverse of the track
prediction covariance matrix. A value of the gate’s threshold
Td2 is taken from χ2 distribution with two degrees of freedom
and expresses the number of sigmas of the Normal distribution.
The points from the first class (NTP) are separated into
clusters (using the same clustering method as before in the
preliminary association). For each cluster, a new track is
created.
Each OTP class set associated with a track serves as a source
for obtaining intermediate measurement. In this process, the
basic OBB extraction method presented in [10] is used.
The aim of the last stage of the proposed NN+FS algorithm
is to tackle ambiguous points association using the AP class
set and intermediate measurements. Each ambiguous point
P(i) in this set has a list L(i) = {x(j)} of tracks to which
it may belong (point is inside the gate of each track of the
list), where i ∈ [1; N ] is a point number, N is the AP set
cardinality, x(j) is the jth track. For each pair composed by
a point P(i) and a track x(j) from the list L(i), the hypothesis
HP(i),x(j)that the ith point originate from the jth track
is tested. For this point-track pair (P(i), x(j)), we create a
temporary OBB z(ij)temp, constructed by including the point
in the track’s intermediate measurement. If the temporary OBB
size is not greater than the jth track prediction OBB size,
the point can be associated with the jth track. Otherwise,
the point is not associated with the track. It happens that
the point P(i) is associated with more that one track. In this
case, this point is associated with the jth track for which
the difference Diff(ij) = Diff(ij)[dx] · Diff(ij)[dy] is the
smallest, where Diff(ij)[dx] = |z(ij)temp[dx]−x(j)k[dx]| and
Diff(ij)[dy] = |z(ij)temp[dy] − x(j)k[dy]|.Tracks that have no raw data points associated stay valid
for the next iteration and its age is increased. The tracks that
exceed the maximum live span are deleted.
IV. TRACKING
The object’s state estimation is done by the means of
Extended Kalman Filter (EKF). All values of the track’s
state vector are expressed in the local ego-vehicle coordinate
system. Tracks are represented by the augmented OBB state
vector xk:
xk = [cx, cx, cy, cy, θ, θ, dx, dy]T (13)
Since tracking is done from dynamic platform, odometry
information is used to increase the tracking accuracy. State
change of the ego-vehicle is represented as differences of
position ∆x, ∆y and angle ∆γ between consecutive instants.
Thus, the input to the state transition equation is defined as:
uk = [∆x, ∆y, ∆γ] (14)
The Discrete White Noise Acceleration Model
(DWNA) [12] is used to describe objects kinematics
and process noise. Thus, taking into account the odometry
information, the track state transition is modelled as
follows [4]:
xk|k−1 = A(∆x, ∆y, ∆γ)F xk−1 + Buk + Gvk−1 (15)
where F is is the standard DWNA transition matrix, B
is the odometry-input model, G represents the noise gain
matrix, vk−1 is the process noise, defined with the Gaussian
distribution:
vk−1 = [cx, cy, θ, σdx, σdy], vk−1 ∼ N(0, Qk) (16)
where
Qk = Gvk−1GT (17)
with σdx and σdy are the process errors for OBB sizes dx and
dy respectively. The prediction covariance matrix is:
Pk|k−1 =∂A
∂x(xk−1)FPk−1
∂AT
∂x(xk−1)F
T + Qk (18)
where Pk−1 is the estimation covariance matrix.
The observation equation can be written as follows:
zk = Hxk|k−1 + wk (19)
where H is the observation model and wk , which represents
the measurement noise, is defined with a Gaussian distribution:
wk ∼ N(0, R)R = σ2zI5,5 (20)
where I5,5 is the identity matrix.
V. RESULTS
As a part of the ”intelligent vehicles and their integration
in the city of the future” project, a software platform is
developed to simulate the sensors and the multiple objects
tracking process. The simulator permits flexible changing of
all sensors parameters and mounting position. This allows to
test developed algorithms with different sensor configurations.
In the simulator laser range finder (LRF), LIDAR, stereovision
and odometry sensors are implemented.
For the test of the proposed algorithms, a Laser Range
Finder (LRF) is mounted in front of the vehicle. The step
65
Fig. 5. Objects configurations during the phase of ”multi-track dataassociation” (a) First scenario, (b) second scenario.
angle for the LRF is set to 1° with an angle range of 180°. In
the tests, the sensor range uncertainty σρ is set to 0.05m.
The proposed algorithm is evaluated using two scenarios,
with two tracked vehicles ( see Figure 5). The scenarios are
chosen to show the reliability of the proposed algorithm, which
stay stable even when two objects touch them selves.
In the first scenario, vehicles run towards each other by
travelling a symmetrical trajectory with respect to the Y axis of
the LRF reference. In the moment of vehicles frontal position,
the angles between the vehicles’ Y sides and the intersecting
LRF rays are close to the right angle. Thus, only the Y side
of the vehicles is seen by the LRF.
In the second scenario, the first vehicle runs towards the
second one, which does not move. When the two vehicles
become close to each other, the angles between the vehicles’
Y sides and the LRF rays are very small. Furthermore, the
X side of the second vehicle becomes occluded by the first
scenario.
In the second scenario, because of the vehicles orientation,
the LRF range uncertainty makes data association more diffi-
cult than in the first one.
We can see at the end of the two scenarios that the two
vehicles collide, and one vehicle pushes the other one (see
Figure 5). This part of the two scenario is considered to show
that NN+FS data association algorithm remains reliable even
in this extreme situation.
Three approaches are evaluated. The first is the pure NN
algorithm with the EKF based filtering. The second approach
is the pure NN algorithm with the EKF based filtering using
the IR uncertainty and the FS assumption. The third approach
is the NN+FS (NN enriched by track’s size information) with
the EKF based filtering using the IR uncertainty and the FS
assumption.
To evaluate the approaches, the vehicles’ size estimation
(Y side only - in the local tracks coordination system) is
compared. Size information gives the best insight into the
performance of the tested approaches, since badly associated
point directly influences track’s size. In the proposed scenarios
the Y side of the vehicles is visible during the phase of ”multi-
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
0 100 200 300 400 500 600 700 800 900
Object no.1 - Real Y side lenghtObject no.1 - Estimated Y side length
Object no.2 - Real Y side lenghtObject no.2 - Estimated Y side length
Fig. 6. First scenario - Evolution of the vehicles’ size (y side) using NNmethod without IR and FS.
3.6
3.8
4
4.2
4.4
4.6
4.8
5
0 100 200 300 400 500 600 700 800 900
Object no.1 - Real Y side lenghtObject no.1 - Estimated Y side length
Object no.2 - Real Y side lenghtObject no.2 - Estimated Y side length
Fig. 7. First scenario - Evolution of the vehicles’ size (y side) using NNmethod with IR and FS based tracking.
3.4
3.6
3.8
4
4.2
4.4
4.6
4.8
0 100 200 300 400 500 600 700 800 900
Object no.1 - Real Y side lenghtObject no.1 - Estimated Y side length
Object no.2 - Real Y side lenghtObject no.2 - Estimated Y side length
Fig. 8. First scenario - Evolution of the vehicles’ size (y side) using NN+FSmethod.
track data association” (see Figure 3), while the X side is
either not visible or occluded, and so cannot be used for
comparison.
In the figures, one can see the real object Y side size (the
two tracked objects are identical in terms of size) and it’s
estimation for each vehicle.
Considering the pure NN algorithm (see Figures 6, 9),
the absence of the IR uncertainty leads to underestimated
object size. Furthermore, the absence of the FS assumption
do not guarantee that the object size decreases in time (what
is different with reality). The integration of the IR uncertainty
allows a better estimation of the objects size. The correct size
estimation is assured by using the FS assumption, despite
unfavourable position and/or orientation of the objects (see
Figures 7, 8, 10 and 11.
Figures 6 - 8 show the evolution of the vehicles’ size
estimation (y side only - in the local tracks coordination
system) in the first scenario. The ”multi-track data association”
phase starts after about 500 iterations. One can see that the first
approach (pure NN) fails, the objects’ size estimates get worse
with time. The points originally belonging to the track number
1 are associated with the track number 2. The second approach
66
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
0 50 100 150 200 250 300 350 400
Object no.1 - Real Y side lenghtObject no.1 - Estimated Y side length
Object no.2 - Real Y side lenghtObject no.2 - Estimated Y side length
Fig. 9. Second scenario - Evolution of the vehicles’ size (y side) using NNmethod without IR and FS.
3.5
4
4.5
5
5.5
6
6.5
7
0 50 100 150 200 250 300 350 400
Object no.1 - Real Y side lenghtObject no.1 - Estimated Y side length
Object no.2 - Real Y side lenghtObject no.2 - Estimated Y side length
Fig. 10. Second scenario - Evolution of the vehicles’ size (y side) using NNmethod with IR and FS based tracking.
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
0 50 100 150 200 250 300 350 400 450 500
Object no.1 - Real Y side lenghtObject no.1 - Estimated Y side length
Object no.2 - Real Y side lenghtObject no.2 - Estimated Y side length
Fig. 11. Second scenario - Evolution of the vehicles’ size (y side) usingNN+FS method.
(pure NN with IR and FS based tracking) stays stable for a
certain period, but finally it also fails. The result is similar to
the first approach one. Indeed, the points originally belonging
to the track number 2 are associated with the track number 1,
with the difference that the second track size stays constant
due to the FS assumption. Only the third approach (NN+FS)
stays stable and manages to correctly associate points to tracks.
Figures 9 - 11 show the evolution of the vehicles’ size
estimation (y side only - in the local tracks coordination sys-
tem) in the second scenario. The ”multi-track data association”
phase starts after about 300 iterations. In this scenario, the
first approach (pure NN) manages to give the correct data
association, this is due to the favourable raw data points
configuration (see Figure 9). However, one can see that the
sizes are greatly underestimated due to the absence of the IR
uncertainty and the FS assumption in the tracking.
The second approach (pure NN with IR and FS based track-
ing) fails and the technique performs as in the first scenario
(see Figure 10). The third approach (NN+FS) performs well
and all points are correctly associated (see Figure 11).
VI. CONCLUSIONS
A method for tracking coalescing objects using LRF sensory
data is presented. Based on an oriented bounding box (OBB)
representation, the method introduces two new concepts: an
Inter-Rays (IR) uncertainty paradigm, which depends on the
interaction context objects/sensor, and a fixed size (FS) as-
sumption, which supposes that the real objects size does note
change during the tracking process. These two concepts are
used in the main stages of the algorithm: OBB represen-
tation, data association and tracking. Considering the NN
pure algorithm, three objects tracking approaches (NN, NN
with IR and FS based tracking, NN with IR and FS based
data association and tracking) are evaluated to analyse the
contribution of the IR and FS concepts. The analysis is done
with different scenarios to take into account different objects
spacial configurations. The experimental results show that the
method using NN with IR and FS based data association and
tracking presents a good reliability. Many investigations are
in progress and concern the improvement of the Fixed Size
algorithm, the integration of occlusion constraints and the
probability based data association for coalescing objects.
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