notion 
vehicle 
ra can 
ionary 
ses, as 
within 
f their 
ally to 
idding 
'd low 
if the 
ribed. 
ors in 
'otion 
object 
cking 
cenes 
roach 
ndent 
'S are 
pe of 
rectly 
ns of 
g the 
1 No 
a not 
stical 
d. In 
alled 
95 
209 
    
   
   
  
  
  
  
  
  
         
   
  
  
  
  
  
  
  
     
  
  
     
  
  
    
Object(k) 
zu 
Egotrajectory Z 
Vk) / t Ti 
# f 8 e p - 
P) V V 
S a Road stripe Moving object - basic model 
Object(k+1) e 
Y 
V(k+1) f 
| P(keD 
Z (k) X rb 
ego A 
; ego Z X 
Object trajectory : X Gro : 
, World coordinates Moving object - specialized shape 
(a) (b) 
Figure 1: The object and egocar trajectories on the ground plane (top view) (a) and the model shapes (b). 
2.2 The dynamic model for a single hypothesis 
A moving object is defined here by its parameter state vector: s = [s“, €], with 
. 8? 2 [Px , Pz, G, V, u]?; € = (Width, ly, hy, la, ho] (1) 
Thus the object state consists of the dynamic part s? and the shape parameters £. The dynamic part describes a 
curved trajectory on a planar road (Figure 1(a)). The dynamic state parameters are as follows: (Px, Pz) is the 
on-road position of the object's origin point, O is the object's direction angle, V and w are the translational and 
rotational velocities respectively. As the observed object projections in the image are relatively small a simple volume 
model that consists of two parallelopipes is applied (Figure 1 (b)) allowing a classification of vehicles into cars and 
trucks. The shape parameters are as follows: Width means the width of both paralleopipes, /4, [5 are the lengths and 
hi, ha are the heights of each parallelopipe respectively. A specialized object shape is not required in this application, 
but if necessary more vehicle classes can be handled by using more shape parameters. The specialized shape in 
Figure 1(b) is described by the width, 5 length and 5 height parameters. 
Let M(k) be the measurement vector, associated with the s(k) object's state vector at discrete time k. The vector 
Mk) containes the positions of object primitives, that can be observed in the k-th image. The time-dependent 
model of both vectors behaviour is given by a stochastically disturbed nonlinear dynamic system with discrete time: 
s(k +1) = fls(k)] + v(k); M(k) = h[s(k)] + w(k) (2) 
where f(.) is the state transition function, h(.) is the state projection function, v(k) is the system noise and w(k) 
is the measurement error. As both state observation and measurement detection are disturbed by errors only an 
estimation of the state can be provided. The estimation task at time k is to give a state estimation s*(k) on the 
basis of real available measurements (m(i) « M(i)|i — 0, ..., k). A consecutive solution is achieved due to recursive 
methods, where the old estimate s*(k) is updated after a new measurement m(k + 1) is available. Two matrices 
E(k), R(k) are provided also — the error covariance matrices of current state estimation and measurement vector. 
2.3 The object recognition procedure 
The procedure for adaptive object recognition in many object scenes consists of following steps, that are performed 
for image segments SEGMENTS(k): 
1. FOR each hypothesis s*(k) with E*(k) DO: OBJ.TRACK(s*(k),E"(k), SEGMENTS(k)) 
2. Eliminate those segments from SEGMENTS(k) that contribute to a successfully tracked hypothesis 
3. For remaining segments make new object initializations : 
4. Select consistent object hypotheses 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995