Diapositive 1

1
Object association in the TBM framework, applicati
on to vehicle driving aid D. Mercier, E. Lefèvre,
D. Jolly Univ. Lille Nord de France, F-59000
Lille, France UArtois, LGI2A, F-62400 Béthune,
France
Association problem description
Input
Uncertain and imprecise information regarding the
association of each object Xi and with each
object Yj.
Example Object X1 cor-responds to object Y2 with
some degree of belief
Y1
X3
Y3
X2
Y4
X4
Y5
X1
Y2
Objects (vehicles) detected at time step t
Objects (vehicles) detected at time step t 1
Xi a perceived object
Yj a known object
Object means an object not present in the
scene.
Objective

• Find the best possible association between
  perceived objects X1, X2, , XN , and known
  objects Y1, Y2, , YM , under the following
  constraints
• each perceived object Xi is associated with at
  most one known object
• each known object Yj is associated with at most
  one perceived object
• object can be associated with any objects.

Questions to be solved
Contribution
Modeling in the belief function framework
(Transferable Belief Model TBM -)
Object association algorithm
TBM in a nutshell

• Frames of discernment involved
• ?i,j yi,j , ni,j the two possible answers
  (yes or no) to the question Is the perceived
  object Xi associated with the known object Yj?
• ?Xi Y1, Y2, , YM, 1, , M, answers
  to the question Which known object is associated
  with the perceived object Xi?
• ?Yj X1, X2, , XN, 1, , N, answers
  to the question Which perceived object is
  associated with the known object Yj?

Vacuous extension

• ? ?1, , ?K finite set of the possible
  answers to a given question Q of interest (frame
  of discernment)
• Information held by a rational agent regarding
  the answer to question Q can be quantified by a
  mass function or BBA m? such that m? 2? ?
  0,1 and
• m(A) represents the part of the unit mass
  allocated to the hypothesis The answer to
  question Q is in the subset A of ? .

Input
NM belief mass functions m?i,j mi,j regarding
each association (Xi, Yj)
Pignistic transformation

• Algorithm
• Express each piece of information m?i,j on a
  common frame ?Xi (or ?Yj) m?i,j??Xi (vacuous
  extension operation)
• Combine conjunctively BBAs m?i,j??Xi mj?Xi.
  Let us denote m?Xi this result.
• Chosen decision the association maximizing the
  probability BetP ?X1 ?X2 ?XN and
  verifying the constraints expressed in the
  objective section.

Example
Prospects
Conclusion from X1 point of view 1.The singleton
maximizing BetP?X1 is 2, so X1 is associated
with Y2. 2. Y1 is not associated, Y1 has
disappeared (or is hidden). On the other hand,
it is also possible to express the available
information on ?Y1 and ?Y2

• Investigation on conflicting decisions between
  perceived and known objects points of view.
• Decomposition of the BBAs (cf Denœuxs works).
• Introducing information from the tracking of the
  vehicles.

1 perceived object X1 and 2 known objects Y1 , Y2
By expressing this information on ?X1 (X1 point
of view with which known object Yj, the
perceived object X1 is associated?)
As there is only one perceived object X1, no
combination is necessary
These works have been financed by the French
region Nord-Pas de Calais.
The conjunctive combination m?X1 of m1?X1 and m2?
X1, and the pignistic probability BetP?X1 are
given by
Conclusion from Y1 and Y2 points of view
CISIT project (Campus International pour la
Sécurité et l'Intermodalité des Transports).
(Y1, Y2) is then associated with (,1) Y1 has
disappeared and Y2 is associated with X1. The
decision coming from X1and the decision coming
from Y1 and Y2 are the same. Unfortunately this
not always the case (in practice a reduce number
of cases)