210 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
predicted state 5 (k) — — —— h(s{k)) - state projection 
PS P6 ( C, Pi (i 2 1,..,8) ) : 3-D points 
pe Beet nM { c, pi (i = 1,..,8) ) : 2-D projections 
1 LT) 
PT, b p8.y om Le CIS pr 
7 Ga zm PRY aaa i 
P1 P P2 pl_x p2_x p8_x p4_x p 1 ; 
matching p2 
(B) edge based m(k) es 
Gray —————>— = y 
| | h(s*(k)) = pls ot n 
: GC Pig OT Dez 
P ° e | p2, or pl, 
; maz(p3,, p9,) or maz(p4,, p6,) 
EO x mach 27. or 98, 
pTy or p8, 
  
2-D measurements 
Figure 2: Alternative 2-D measurements are matched with the projected state vector 
3. THE RECOGNITION STEPS 
3.1 Initialization of an object hypothesis 
A model-based initialization can be divided into two main steps — segment grouping and state initialization. The first 
step means a segment classification into vanishing point, road, surrounding area or horizon, followed by a backpro- 
jection of the segments onto the 3-D space over the road plane and by grouping the hypothesized 3-D segments 
into road stripes, car objects and obstacles in the road area. 
The second step means the initialization of 3-D state parameters from the hypothesized group. Position coordinates 
Px, Pz are given from backprojection under the assumption Py = 0. Translational velocity V is set to a default 
value: V = Vego or V = —Vego The direction © is estimated from the relation between the widths of two boundary 
boxes in the image — the boundary box K of the assumed front or back part of the car and the boundary box G of the 
whole object projection — by assuming a default length. Other shape parameters are also given from backprojection 
of the two boundary boxes. The rotational velocity is set by default to current egomotion by considering the current 
road curvature: Ww ^ —Wego + Wroad OF W = Wego — Wroad 
3.2 Object tracking with recursive state estimation 
An extended Kalman filter (EKF) (Wiinsche, 88) with sequential modification is applied for the recursive estimation 
of the hypothesis parameters. For each object hypothesis estimation s*(k) with its error covariance matrix E"(k) 
and system error covariance Q(k) following steps are perfomed at the time k : 
1. The prediction equations: s*(k) — f[s*(k — 1); and E*(k) 2 F(k — 1)E*(k — 1)FT(k — 1) + Q(k — 1); 
where F(k) = lates is the Jacobi matrix of function f(.). . 
2. Detect the measurement m(k) with covariance matrix R(k). 
3. The modification of object state s*(k) and its covariance matrix E"(k) 
The measurement mode can be either based on object to object correspondence, due to repeated 3-D object initial- 
ization step in every image or it can be a 2-D measurement, that consists of 2-D image segment groups (like edge 
or contour groups). 
In the first case the measurement m(k) vector is equivalent to a state vector of reduced size. It consists of two parts: 
m(k) = sr(k) U 89(k) = [Px (k), Pz(k), Width(k), ha (k), ha (k))] U (85(k), li (Kk), l5 (k)]7 (3) 
In relation to a full state vector no translational and rotational velocities are given, as they can be measured only 
indirectly from the differences in position and orientation of estimated hypotheses in images k and k — 1. Additionally 
the orientation and length parameters are here indexed by g to indicate their geometry based nature. Measurements 
for these parameters of second type exist also, on the basis of the new measured object motion. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995