Map-aided Fusion Using Evidential Grids for
Mobile Perception in Urban Environment
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
Abstract Evidential grids have been recently used for mobile object perception.
The novelty of this article is to propose a perception scheme using prior map knowl-
edge. A geographic map is considered an additional source of information fused
with a grid representing sensor data. Yager’s rule is adapted to exploit the Dempster-
Shafer conflict information at large. In order to distinguish stationary and mobile ob-
jects, a counter is introduced and used as a factor for mass function specialisation.
Contextual discounting is used, since we assume that different pieces of information
become obsolete at different rates. Tests on real-world data are also presented.
1 Introduction
Autonomous driving has been an important challenge in recent years. Navigation
and precise localisation aside, environment perception is an important on-board sys-
tem of a self-driven vehicle. The level of difficulty in autonomous driving increases
in urban environments, where a good scene understanding makes the perception
subsystem crucial. There are several reasons that make cities a demanding environ-
ment. Poor satellite visibility deteriorates the precision of GPS positioning. Vehicle
trajectories are hard to predict due to high variation in speed and direction. Also, the
sheer number of mobile objects poses a problem, e.g. for tracking algorithms.
On the other hand, more and more detailed and precise geographic databases be-
come available. This source of information has not been well examined yet, hence
our approach of incorporating prior knowledge from digital maps in order to im-
prove perception scheme. A substantial amount of research has focused on the map-
ping problem for autonomous vehicles, e.g. Simultaneous Localisation and Mapping
(SLAM) approach, but the use of maps for perception is still understudied.
Marek Kurdej e-mail: marek.kurdej@hds.utc.fr · Véronique Cherfaoui · Julien Moras ·
Philippe Bonnifait
UMR CNRS 6599 Heudiasyc, University of Technology of Compiègne, France
1
arXiv:1207.1016v1  [cs.RO]  4 Jul 2012
2
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
In this article, we propose a data fusion method based on Dempster–Shafer the-
ory [8] taking into account meta-knowledge obtained from a digital map. We show
the advantage of including prior knowledge into an embedded perception system of
an autonomous car. The vehicle environment is modelled by 2D occupancy grids
proposed in [2]. This paper describes a robust and unified approach to a variety of
problems in spatial representation using the theory of probability. The theory of ev-
idence was not combined with occupancy grids until recently to build environment
maps for robot perception [7]. Only recent works take advantage of the theory of ev-
idence in the context of mobile perception [4]. Some works use 3D city model as a
source of prior knowledge for localisation and vision-based perception [1], whereas
our method uses maps for scene understanding.
This article is organised as follows. In section 2, we describe the details of the
method. Section 3 presents the results and section 4 concludes the paper.
2 Multi-grid fusion approach
This section presents the proposed perception schemes. The grid construction
method is described in section 2.2 and all data processing steps are detailed in sec-
tion 2.4. Figure 1 presents a general overview of our approach.
LIDAR
Applanix
maps
ScanGrid
(local)
ScanGrid
(global)
PriorGrid
(global)
incorporating
prior
knowledge
ScanGrid
with prior
knowledge
fusion
MapGrid
discounting
output
Fig. 1 Method overview (lidar: laser scanner, Applanix: inertial measurement unit).
2.1 Heterogeneous data sources
There are three sources in our perception system: vehicle pose, lidar range scanner
point cloud and vector maps. The vehicle pose comes from the Applanix system
based on a GPS, an odometer and an IMU. The system is supposed to provide pre-
cise and integral positioning. Our main source of information about the environment
is an IBEO Alaska XT lidar able to provide a cloud of about 800 points 10 times per
second. The digital maps that we use were provided by the French National Geo-
graphic Institute (IGN) and contain 3D building models as well as the road surface.
Map-aided Fusion Using Evidential Grids for Mobile Perception in Urban Environment
3
We also performed successful tests with freely available OpenStreetMap project 2D
maps [6], but here we limited the use to building data. We assume the maps to be
precise and accurate.
2.2 Occupancy grids
An occupancy grid models the world using a tessellated representation of spatial
information. In general, it is a multidimensional spatial lattice with cells storing
some stochastic information. In our case, each cell representing a box (a part of
environment) X ×Y where X = [x−, x+], Y = [y−, y+] stores a mass function.
• ScanGrid (SG) construction: In order to process the lidar data, an eviden-
tial occupancy grid is computed when a new scan arrives, this grid is called
ScanGrid. Each cell of this grid stores a mass function on the frame of dis-
cernment (FOD) ΩSG = {F,O}, where F refers to the free space and O – to the
occupied space. The basic belief assignment, which reflects the sensor model, is
described in [4].
• MapGrid (MG): To store the results of information fusion, an occupancy grid
MG has been introduced with a FOD ΩMG = {F, C, N, S, V}. Respective classes
represent: free space F, mapped infrastructure (buildings) C, non-mapped infras-
tructure N, temporarily stopped objects S and mobile (moving) V objects. ΩMG
is a common frame used for information fusion. By using MG as a cumulative
information storage, we are not obliged to aggregate preceding ScanGrids.
• PriorGrid (PG) context representation: PG allows us to perform a contextual
information fusion incorporating some meta-knowledge about the environment.
This grid uses the same frame of discernment ΩMG as MG. The grid is obtained
by projection of map data, buildings and roads, onto a 2D grid with global coor-
dinates.
We define two sets of polygons defining the 2D position of buildings and
road surface by, respectively, B =

bi =

x1x2 ...xmi
y1y2 ...ymi

,i ∈[0,nB]

and R =

ri =

x1x2 ...xmi
y1y2 ...ymi

,i ∈[0,nR]

, B∩R = /0. Then, we attribute the mass to each
cell {X,Y} of the PriorGrid in the following way:
We note that B = {C}, R = {F, S, V}, T = {F, N, S, V} for convenience and
readability only. A denotes all other strict subsets of Ω. These aliases charac-
terise the meta-information inferred from geographic maps. For instance, on the
road surface R, we encourage the existence of free space F as well as stopped S
and moving V objects. Analogically, building information B fosters mass trans-
fer to C. Lastly, T denotes the intermediate area, e.g. pavements, where mobile
and stationary objects as well as small urban infrastructure can be present. Note
that neither buildings nor roads are present, so we exclude existence of mapped
infrastructure C, but we cannot omit other classes. Also, we define a level of con-
4
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
fidence β for each map source, possibly different for each context. Let ˜x = x−+x+
2
,
˜y = y−+y+
2
.
mPG{X,Y}(B) =
(
βB
if (˜x, ˜y) ∈bi
0
otherwise
∀i ∈[0,nB]
mPG{X,Y}(R) =
(
βR
if (˜x, ˜y) ∈ri
0
otherwise
∀i ∈[0,nR]
mPG{X,Y}(T) =
(
0
if (˜x, ˜y) ∈bi ∨(˜x, ˜y) ∈r j
βT
otherwise
∀i ∈[0,nB],∀j ∈[0,nR]
mPG{X,Y}(Ω) =





1−βB
if (˜x, ˜y) ∈bi
1−βR
if (˜x, ˜y) ∈ri
1−βT
otherwise
∀i ∈[0,nB],∀j ∈[0,nR]
mPG{X,Y}(A) = 0
∀A ⊊Ωand A /∈{B,R,T}
(1)
2.3 Incorporating prior knowledge
The frame of discernment ΩSG used in SG is distinct from ΩMG, so in order to
enable the fusion of SG and MG we define a refining rSG : 2ΩSG →2ΩMG such
that rSG ({F}) = {F}, rSG ({O}) = {C,N,S,V}, rSG(A) = S
θ∈A rSG(θ). The re-
fined mass function can be expressed as mΩMG
SG
(rSG (A)) = mΩSG
SG (A), ∀A ⊆ΩSG.
Then, Dempster’s rule is applied in order to exploit the prior information included
in PriorGrid:
m′ΩMG
SG,t = mΩMG
SG,t ⊕mΩMG
PG
(2)
2.4 Temporal fusion
Computing conflict masses
We use the idea from [5] to distinguish between two types of conflict, which arise
from the fact that the environment is dynamic. We denote /0FO the conflict induced
when a free cell in MG is fused with an occupied cell in SG. Similarly, /0OF in-
dicates the conflicted caused by an occupied cell in MG fused with a free cell in
SG. In an error-free case, these conflicts represent, respectively, the disappearance
and the appearance of an object. Conflict masses are calculated using the formu-
Map-aided Fusion Using Evidential Grids for Mobile Perception in Urban Environment
5
las: mMG,t (/0OF) = mMG,t−1 (O)·mSG,t (F), mMG,t (/0FO) = mMG,t−1 (F)·mSG,t (O),
where m(O) = ∑
A
m(A), ∀A ⊆{C,N,S,V}.
MapGrid specialisation using a counter
Mobile object detection is an important issue in dynamic environments. We propose
the introduction of a counter ζ in each cell in order to include temporal information
on the cell occupancy. For this purpose, incrementation and decrementation steps
δinc ∈[0,1], δdec ∈[0,1], as well as threshold values γO, γ/0 have been defined.
ζ (t) = min

1, ζ (t−1) +δinc

if mMG(O) ≥γO and mMG (/0FO)+mMG (/0OF) ≤γ/0
ζ (t) = max

0, ζ (t−1) −δdec

if mMG (/0FO)+mMG (/0OF) > γ/0
Otherwise ζ(t) rests unchanged. Using ζ values, we impose a specialisation of
mass functions in MG using the equation:
m′MG,t (A) = S(A,B)·mMG,t(B)
(3)
where specialisation matrix S(·,·) is defined as:
S(A\{V}, A) = ζ
∀A ⊆ΩMG and {V} ∈A
S(A, A) = 1−ζ
∀A ⊆ΩMG and {V} ∈A
S(A, A) = 1
∀A ⊆ΩMG and {V} /∈A
S(·, ·) = 0
otherwise
(4)
Fusion rule
An important part of the method consists in fusing a discounted and specialized MG
(see section 2.5 and preceding paragraph) with a SG combined with prior knowledge
(see section 2.3).
mMG,t =α m′MG,t−1 ⊛m′SG,t
(5)
The fusion rule ⊛is a modified Yager’s rule [10] adapted to mobile object de-
tection. There are of course many different rules that could be used, but in order
to distinguish between moving and stationary objects some modifications had to be
included. These modifications consist in transferring the mass corresponding to a
newly appeared object /0FO to the class of moving objects V as described by the
equation 6. Symbol
∩⃝denotes the conjunctive fusion rule.
6
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
(m1 ⊛m2)(A) = (m1 ∩⃝m2)(A)
∀A ⊊Ω∧A ̸= V
(m1 ⊛m2)(V) = (m1 ∩⃝m2)(V)+(m1 ∩⃝m2)(/0FO)
(m1 ⊛m2)(Ω) = (m1 ∩⃝m2)(Ω)+(m1 ∩⃝m2)(/0OF)
(m1 ⊛m2)(/0FO) = 0
(m1 ⊛m2)(/0OF) = 0
(6)
All the above steps allow us to construct a MapGrid containing reach informa-
tion on the environment state, including the knowledge on mobile and static objects.
2.5 Contextual discounting
Information discounting allows to forget information which is no longer valid. Dis-
counting parameter α serves to model the speed with which information becomes
obsolete. Thanks to the contextual discounting [3], we make use of more detailed
information regarding the confidence we have in the source in various contexts. We
noticed that different pieces of information become obsolete with different speed.
Hence, the coarsening used is Θ =

θstatic, θdynamic, θ free
	
, with θstatic = {C,N},
θdynamic = {S,V}, θ free = {F}, and discount rates α =

αstatic, αdynamic, αfree
	
. We
assign higher discount rates (lower confidence) to rapidly changing contexts such as
free space, stopped and moving objects, and lower rates to the static context. The
discounted mass function is obtained by the disjunctive combination of the input
mass function mMG and mass functions for each element of the partition Θ.
αmMG,t = mMG,t ∪⃝mstatic ∪⃝mdynamic ∪⃝m free
(7)
where each mass function ml (l = static, dynamic, free) is defined by ml (θl) = αl,
ml (/0) = 1−αl, ml(A) = 0, ∀A ⊆Ω∧A /∈{/0,θl}.
3 Results
3.1 Setup
The data set used for our experiments was acquired in cooperation with IGN in
Paris. The overall length of the trajectory was about 3 km. The size of the grid cell
in the occupancy grids was set to 0.5 m, which is sufficient to model a complex
environment with mobile objects. The discount rates α describing the speed of in-
formation becoming obsolete were defined empirically, but they can be learnt from
data, as proposed in [3]. We have defined the map confidence factor β by ourselves,
but ideally, it should be given by the map provider. β describes data currentness
Map-aided Fusion Using Evidential Grids for Mobile Perception in Urban Environment
7
(b)
(a)
(c)
(d)
Fig. 2 (a) Scene. (b) PG. (c) MG without prior information. (d) MG with prior map knowledge.
(age), errors introduced by geometry simplification and spatial discretisation. β can
also be used to depict the localisation accuracy. Other parameters, such as counter
steps δinc, δdec and thresholds γO, γ/0 used for mobile object detection determine the
sensitiveness of mobile object detection and were set by manual tuning.
3.2 Impact of prior knowledge
The results for a particular instant of the approach tested on real-world data are
presented on figure 2. The visualisation of the MG has been obtained by calculating
the pignistic probability of each class [9]. The presented scene contains two cars
(only one is visible in the camera image) going in the direction opposite to the test
vehicle and a bus parked on the road edge. Bus and car positions are marked on the
grids by green and red boxes, respectively. The test vehicle position is shown as a
blue box. Different classes of ΩMG are represented by different colours: F – white,
C, N – blue, S – green and V – red. PG on figure 2(b) shows the position of the road
space (white) and buildings (blue).
The principal advantage gained by using map knowledge is richer information
on the detected objects. A clear difference between a moving object (red, car) and
a stopped one (green, bus) is visible. Also, stopped objects are distinct from in-
frastructure when prior map information is available (cf. figures 2(c) and 2(d). In
addition, thanks to the prior knowledge, stationary objects (cyan) such as infras-
8
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
tructure are distinguished from stopped objects on the road. Grids make noticeable
the effect of discounting, as information on the environment behind the vehicle is
being forgotten. On the other hand, the parked bus is still in evidence despite being
occluded by the passing car.
4 Conclusion and perspectives
A new mobile perception scheme based on prior map knowledge has been intro-
duced. Geographic information is exploited to reduce the number of possible hy-
potheses delivered by an exteroceptive source. A modified fusion rule taking into
account the existence of mobile objects has been defined. Furthermore, the vari-
ation in information lifetime has been modelled by the introduction of contextual
discounting. In the future, we anticipate removing the hypothesis that the map is
accurate. This approach will entail considerable work on creating appropriate er-
ror models for the data source. Moreover, we envision differentiating the free space
class into two complementary classes to distinguish navigable and non-navigable
space. This will be a step towards the use of our approach in autonomous naviga-
tion. Another perspective is the use of reference data to validate the results, choose
the most appropriate fusion rule and learn algorithm parameters. We envision using
map information to predict object movements. It rests also a future work to exploit
fully the 3D map information.
Acknowledgements This work has been supported by ANR (French National Agency) CityVIP
project under grant ANR-07_TSFA-013-01.
References
1. Cappelle C. et al.: Virtual 3D City Model for Navigation in Urban Areas. In: J. Intell. Robot.
Syst., Springer (2011)
2. Elfes, A.: Using Occupancy Grids for Mobile Robot Perception and Navigation. In: Computer,
22(6), pp. 46–57 (1989)
3. Mercier, D., Quost, B., Denoeux, T.: Refined modeling of sensor reliability in the belief function
framework using contextual discounting. J. Inf. Fusion, 9(2), pp. 246–258 (2008)
4. Moras, J., Cherfaoui, V., Bonnifait, P.: Credibilist Occupancy Grids for Vehicle Perception in
Dynamic Environments. IEEE Int. Conf. Robot. Autom., pp. 84–89 (2011)
5. Moras, J., Cherfaoui, V., Bonnifait, P.: Moving Objects Detection by Conflict Analysis in Evi-
dential Grids. Int. Veh. Symp., pp. 1120–1125, Baden-Baden, Germany (2011)
6. OpenStreetMap project. http://www.openstreetmap.org. (Cited 9 Nov 2011)
7. Pagac, D., Nebot, E. M., Durrant-Whyte, H.: An evidential approach to map-building for au-
tonomous vehicles. In: IEEE Trans. Robot. Autom., 14(4), pp. 623–629 (1998)
8. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)
9. Smets, P.: Decision making in the tbm : the necessity of the pignistic transformation. Int. J.
Approx. Reason., 38(2) pp. 133–147 (2005)
10. Yager, R.R.: On the Dempster-Shafer framework and new combination rules. Information
sciences, 4 pp. 93–138 (1987)
Map-aided Fusion Using Evidential Grids for
Mobile Perception in Urban Environment
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
Abstract Evidential grids have been recently used for mobile object perception.
The novelty of this article is to propose a perception scheme using prior map knowl-
edge. A geographic map is considered an additional source of information fused
with a grid representing sensor data. Yager’s rule is adapted to exploit the Dempster-
Shafer conflict information at large. In order to distinguish stationary and mobile ob-
jects, a counter is introduced and used as a factor for mass function specialisation.
Contextual discounting is used, since we assume that different pieces of information
become obsolete at different rates. Tests on real-world data are also presented.
1 Introduction
Autonomous driving has been an important challenge in recent years. Navigation
and precise localisation aside, environment perception is an important on-board sys-
tem of a self-driven vehicle. The level of difficulty in autonomous driving increases
in urban environments, where a good scene understanding makes the perception
subsystem crucial. There are several reasons that make cities a demanding environ-
ment. Poor satellite visibility deteriorates the precision of GPS positioning. Vehicle
trajectories are hard to predict due to high variation in speed and direction. Also, the
sheer number of mobile objects poses a problem, e.g. for tracking algorithms.
On the other hand, more and more detailed and precise geographic databases be-
come available. This source of information has not been well examined yet, hence
our approach of incorporating prior knowledge from digital maps in order to im-
prove perception scheme. A substantial amount of research has focused on the map-
ping problem for autonomous vehicles, e.g. Simultaneous Localisation and Mapping
(SLAM) approach, but the use of maps for perception is still understudied.
Marek Kurdej e-mail: marek.kurdej@hds.utc.fr · Véronique Cherfaoui · Julien Moras ·
Philippe Bonnifait
UMR CNRS 6599 Heudiasyc, University of Technology of Compiègne, France
1
arXiv:1207.1016v1  [cs.RO]  4 Jul 2012
2
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
In this article, we propose a data fusion method based on Dempster–Shafer the-
ory [8] taking into account meta-knowledge obtained from a digital map. We show
the advantage of including prior knowledge into an embedded perception system of
an autonomous car. The vehicle environment is modelled by 2D occupancy grids
proposed in [2]. This paper describes a robust and unified approach to a variety of
problems in spatial representation using the theory of probability. The theory of ev-
idence was not combined with occupancy grids until recently to build environment
maps for robot perception [7]. Only recent works take advantage of the theory of ev-
idence in the context of mobile perception [4]. Some works use 3D city model as a
source of prior knowledge for localisation and vision-based perception [1], whereas
our method uses maps for scene understanding.
This article is organised as follows. In section 2, we describe the details of the
method. Section 3 presents the results and section 4 concludes the paper.
2 Multi-grid fusion approach
This section presents the proposed perception schemes. The grid construction
method is described in section 2.2 and all data processing steps are detailed in sec-
tion 2.4. Figure 1 presents a general overview of our approach.
LIDAR
Applanix
maps
ScanGrid
(local)
ScanGrid
(global)
PriorGrid
(global)
incorporating
prior
knowledge
ScanGrid
with prior
knowledge
fusion
MapGrid
discounting
output
Fig. 1 Method overview (lidar: laser scanner, Applanix: inertial measurement unit).
2.1 Heterogeneous data sources
There are three sources in our perception system: vehicle pose, lidar range scanner
point cloud and vector maps. The vehicle pose comes from the Applanix system
based on a GPS, an odometer and an IMU. The system is supposed to provide pre-
cise and integral positioning. Our main source of information about the environment
is an IBEO Alaska XT lidar able to provide a cloud of about 800 points 10 times per
second. The digital maps that we use were provided by the French National Geo-
graphic Institute (IGN) and contain 3D building models as well as the road surface.
Map-aided Fusion Using Evidential Grids for Mobile Perception in Urban Environment
3
We also performed successful tests with freely available OpenStreetMap project 2D
maps [6], but here we limited the use to building data. We assume the maps to be
precise and accurate.
2.2 Occupancy grids
An occupancy grid models the world using a tessellated representation of spatial
information. In general, it is a multidimensional spatial lattice with cells storing
some stochastic information. In our case, each cell representing a box (a part of
environment) X ×Y where X = [x−, x+], Y = [y−, y+] stores a mass function.
• ScanGrid (SG) construction: In order to process the lidar data, an eviden-
tial occupancy grid is computed when a new scan arrives, this grid is called
ScanGrid. Each cell of this grid stores a mass function on the frame of dis-
cernment (FOD) ΩSG = {F,O}, where F refers to the free space and O – to the
occupied space. The basic belief assignment, which reflects the sensor model, is
described in [4].
• MapGrid (MG): To store the results of information fusion, an occupancy grid
MG has been introduced with a FOD ΩMG = {F, C, N, S, V}. Respective classes
represent: free space F, mapped infrastructure (buildings) C, non-mapped infras-
tructure N, temporarily stopped objects S and mobile (moving) V objects. ΩMG
is a common frame used for information fusion. By using MG as a cumulative
information storage, we are not obliged to aggregate preceding ScanGrids.
• PriorGrid (PG) context representation: PG allows us to perform a contextual
information fusion incorporating some meta-knowledge about the environment.
This grid uses the same frame of discernment ΩMG as MG. The grid is obtained
by projection of map data, buildings and roads, onto a 2D grid with global coor-
dinates.
We define two sets of polygons defining the 2D position of buildings and
road surface by, respectively, B =

bi =

x1x2 ...xmi
y1y2 ...ymi

,i ∈[0,nB]

and R =

ri =

x1x2 ...xmi
y1y2 ...ymi

,i ∈[0,nR]

, B∩R = /0. Then, we attribute the mass to each
cell {X,Y} of the PriorGrid in the following way:
We note that B = {C}, R = {F, S, V}, T = {F, N, S, V} for convenience and
readability only. A denotes all other strict subsets of Ω. These aliases charac-
terise the meta-information inferred from geographic maps. For instance, on the
road surface R, we encourage the existence of free space F as well as stopped S
and moving V objects. Analogically, building information B fosters mass trans-
fer to C. Lastly, T denotes the intermediate area, e.g. pavements, where mobile
and stationary objects as well as small urban infrastructure can be present. Note
that neither buildings nor roads are present, so we exclude existence of mapped
infrastructure C, but we cannot omit other classes. Also, we define a level of con-
4
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
fidence β for each map source, possibly different for each context. Let ˜x = x−+x+
2
,
˜y = y−+y+
2
.
mPG{X,Y}(B) =
(
βB
if (˜x, ˜y) ∈bi
0
otherwise
∀i ∈[0,nB]
mPG{X,Y}(R) =
(
βR
if (˜x, ˜y) ∈ri
0
otherwise
∀i ∈[0,nR]
mPG{X,Y}(T) =
(
0
if (˜x, ˜y) ∈bi ∨(˜x, ˜y) ∈r j
βT
otherwise
∀i ∈[0,nB],∀j ∈[0,nR]
mPG{X,Y}(Ω) =





1−βB
if (˜x, ˜y) ∈bi
1−βR
if (˜x, ˜y) ∈ri
1−βT
otherwise
∀i ∈[0,nB],∀j ∈[0,nR]
mPG{X,Y}(A) = 0
∀A ⊊Ωand A /∈{B,R,T}
(1)
2.3 Incorporating prior knowledge
The frame of discernment ΩSG used in SG is distinct from ΩMG, so in order to
enable the fusion of SG and MG we define a refining rSG : 2ΩSG →2ΩMG such
that rSG ({F}) = {F}, rSG ({O}) = {C,N,S,V}, rSG(A) = S
θ∈A rSG(θ). The re-
fined mass function can be expressed as mΩMG
SG
(rSG (A)) = mΩSG
SG (A), ∀A ⊆ΩSG.
Then, Dempster’s rule is applied in order to exploit the prior information included
in PriorGrid:
m′ΩMG
SG,t = mΩMG
SG,t ⊕mΩMG
PG
(2)
2.4 Temporal fusion
Computing conflict masses
We use the idea from [5] to distinguish between two types of conflict, which arise
from the fact that the environment is dynamic. We denote /0FO the conflict induced
when a free cell in MG is fused with an occupied cell in SG. Similarly, /0OF in-
dicates the conflicted caused by an occupied cell in MG fused with a free cell in
SG. In an error-free case, these conflicts represent, respectively, the disappearance
and the appearance of an object. Conflict masses are calculated using the formu-
Map-aided Fusion Using Evidential Grids for Mobile Perception in Urban Environment
5
las: mMG,t (/0OF) = mMG,t−1 (O)·mSG,t (F), mMG,t (/0FO) = mMG,t−1 (F)·mSG,t (O),
where m(O) = ∑
A
m(A), ∀A ⊆{C,N,S,V}.
MapGrid specialisation using a counter
Mobile object detection is an important issue in dynamic environments. We propose
the introduction of a counter ζ in each cell in order to include temporal information
on the cell occupancy. For this purpose, incrementation and decrementation steps
δinc ∈[0,1], δdec ∈[0,1], as well as threshold values γO, γ/0 have been defined.
ζ (t) = min

1, ζ (t−1) +δinc

if mMG(O) ≥γO and mMG (/0FO)+mMG (/0OF) ≤γ/0
ζ (t) = max

0, ζ (t−1) −δdec

if mMG (/0FO)+mMG (/0OF) > γ/0
Otherwise ζ(t) rests unchanged. Using ζ values, we impose a specialisation of
mass functions in MG using the equation:
m′MG,t (A) = S(A,B)·mMG,t(B)
(3)
where specialisation matrix S(·,·) is defined as:
S(A\{V}, A) = ζ
∀A ⊆ΩMG and {V} ∈A
S(A, A) = 1−ζ
∀A ⊆ΩMG and {V} ∈A
S(A, A) = 1
∀A ⊆ΩMG and {V} /∈A
S(·, ·) = 0
otherwise
(4)
Fusion rule
An important part of the method consists in fusing a discounted and specialized MG
(see section 2.5 and preceding paragraph) with a SG combined with prior knowledge
(see section 2.3).
mMG,t =α m′MG,t−1 ⊛m′SG,t
(5)
The fusion rule ⊛is a modified Yager’s rule [10] adapted to mobile object de-
tection. There are of course many different rules that could be used, but in order
to distinguish between moving and stationary objects some modifications had to be
included. These modifications consist in transferring the mass corresponding to a
newly appeared object /0FO to the class of moving objects V as described by the
equation 6. Symbol
∩⃝denotes the conjunctive fusion rule.
6
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
(m1 ⊛m2)(A) = (m1 ∩⃝m2)(A)
∀A ⊊Ω∧A ̸= V
(m1 ⊛m2)(V) = (m1 ∩⃝m2)(V)+(m1 ∩⃝m2)(/0FO)
(m1 ⊛m2)(Ω) = (m1 ∩⃝m2)(Ω)+(m1 ∩⃝m2)(/0OF)
(m1 ⊛m2)(/0FO) = 0
(m1 ⊛m2)(/0OF) = 0
(6)
All the above steps allow us to construct a MapGrid containing reach informa-
tion on the environment state, including the knowledge on mobile and static objects.
2.5 Contextual discounting
Information discounting allows to forget information which is no longer valid. Dis-
counting parameter α serves to model the speed with which information becomes
obsolete. Thanks to the contextual discounting [3], we make use of more detailed
information regarding the confidence we have in the source in various contexts. We
noticed that different pieces of information become obsolete with different speed.
Hence, the coarsening used is Θ =

θstatic, θdynamic, θ free
	
, with θstatic = {C,N},
θdynamic = {S,V}, θ free = {F}, and discount rates α =

αstatic, αdynamic, αfree
	
. We
assign higher discount rates (lower confidence) to rapidly changing contexts such as
free space, stopped and moving objects, and lower rates to the static context. The
discounted mass function is obtained by the disjunctive combination of the input
mass function mMG and mass functions for each element of the partition Θ.
αmMG,t = mMG,t ∪⃝mstatic ∪⃝mdynamic ∪⃝m free
(7)
where each mass function ml (l = static, dynamic, free) is defined by ml (θl) = αl,
ml (/0) = 1−αl, ml(A) = 0, ∀A ⊆Ω∧A /∈{/0,θl}.
3 Results
3.1 Setup
The data set used for our experiments was acquired in cooperation with IGN in
Paris. The overall length of the trajectory was about 3 km. The size of the grid cell
in the occupancy grids was set to 0.5 m, which is sufficient to model a complex
environment with mobile objects. The discount rates α describing the speed of in-
formation becoming obsolete were defined empirically, but they can be learnt from
data, as proposed in [3]. We have defined the map confidence factor β by ourselves,
but ideally, it should be given by the map provider. β describes data currentness
Map-aided Fusion Using Evidential Grids for Mobile Perception in Urban Environment
7
(b)
(a)
(c)
(d)
Fig. 2 (a) Scene. (b) PG. (c) MG without prior information. (d) MG with prior map knowledge.
(age), errors introduced by geometry simplification and spatial discretisation. β can
also be used to depict the localisation accuracy. Other parameters, such as counter
steps δinc, δdec and thresholds γO, γ/0 used for mobile object detection determine the
sensitiveness of mobile object detection and were set by manual tuning.
3.2 Impact of prior knowledge
The results for a particular instant of the approach tested on real-world data are
presented on figure 2. The visualisation of the MG has been obtained by calculating
the pignistic probability of each class [9]. The presented scene contains two cars
(only one is visible in the camera image) going in the direction opposite to the test
vehicle and a bus parked on the road edge. Bus and car positions are marked on the
grids by green and red boxes, respectively. The test vehicle position is shown as a
blue box. Different classes of ΩMG are represented by different colours: F – white,
C, N – blue, S – green and V – red. PG on figure 2(b) shows the position of the road
space (white) and buildings (blue).
The principal advantage gained by using map knowledge is richer information
on the detected objects. A clear difference between a moving object (red, car) and
a stopped one (green, bus) is visible. Also, stopped objects are distinct from in-
frastructure when prior map information is available (cf. figures 2(c) and 2(d). In
addition, thanks to the prior knowledge, stationary objects (cyan) such as infras-
8
Marek Kurdej, Julien Moras, Véronique Cherfaoui, Philippe Bonnifait
tructure are distinguished from stopped objects on the road. Grids make noticeable
the effect of discounting, as information on the environment behind the vehicle is
being forgotten. On the other hand, the parked bus is still in evidence despite being
occluded by the passing car.
4 Conclusion and perspectives
A new mobile perception scheme based on prior map knowledge has been intro-
duced. Geographic information is exploited to reduce the number of possible hy-
potheses delivered by an exteroceptive source. A modified fusion rule taking into
account the existence of mobile objects has been defined. Furthermore, the vari-
ation in information lifetime has been modelled by the introduction of contextual
discounting. In the future, we anticipate removing the hypothesis that the map is
accurate. This approach will entail considerable work on creating appropriate er-
ror models for the data source. Moreover, we envision differentiating the free space
class into two complementary classes to distinguish navigable and non-navigable
space. This will be a step towards the use of our approach in autonomous naviga-
tion. Another perspective is the use of reference data to validate the results, choose
the most appropriate fusion rule and learn algorithm parameters. We envision using
map information to predict object movements. It rests also a future work to exploit
fully the 3D map information.
Acknowledgements This work has been supported by ANR (French National Agency) CityVIP
project under grant ANR-07_TSFA-013-01.
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