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Figure 3: Object hypotheses in three images 
In the 2-D measurement case there is a nontrivial predicted state projection transformation h(s*(k)) (Figure 2). 
On the basis of predicted state several 3-D model points (the Pi-s, i — 1,..., 8 and C) are selected and the visible 
points are projected onto the image plane defining two boundary boxes — of the front or back part K and of the 
whole object boundary box G — as well as the center point c. The projected points are matched with new measured 
2-D points, that are contained in the following measurement vector: 
m(k)" = nina, Kida Gee, GCy; Gminz) Gmazz: G miny: Gmnazy: K., KJ (4) 
Various alternative methods for 2-D measurements can be applied. Two of them have been tested — line segment 
based measurements or closed contour (or region) based measurements. 
It is evident that the predicted projection vector is not directly dependent on the motion parameters. Additionally, the 
measurements provide no way to estimate the direction © and the lengths I; and I, independently each other. This 
problem is common to both measurement cases. Thus, a two step modification of the state vector is performed. First 
of all the estimation of the reduced state sx (k) and the geometry—based measurement s,(k) are performed. From the 
vector 68% (k) = [8% (k) — sr *(k —1)] current motions V (k),w(k) are calculated and the motion based measurement 
8m(k) = [Om (k), lim (k), l2m(k)]T are performed. These syntheitic measurements together with the first step mea- 
surement 8, (k) are next used for the modification of the remaining state sg(k) — [V (k), O(k), (Kk), l (k), l5 (k)]T. 
Hence the modification process at time k for one hypothesis can be summarized as follows: 
1. Modification of the reduced state and its covariance matrix 
sh(k) = s* n(k) + K(k){m(k) — h(s*(k))}; and Eh(k) = E* n(k) — K(k) H(k)E* r(k) 
zi 
where K(k) — E* g(k) HT (k){ H(k)E* (E) HT + R(k)} is the Kalman gain matrix. 
and H(k) = #2 s+ n(k) I5 the Jacobi matrix of function h(.). 
2. Detection of motion and motion based synthetic measurements from s%(k) — s%(k — 1). 
3. Modification of remaining state sz (k) on the basis of predicted remaining state s* g(k) and synthetic mea- 
surements (motion parameters, 8,4(k), 8m (k)). 
4. RESULTS 
The approach has been tested on several monocular image sequences of road scenes (see for example Figure 3). 
For image aquisition a low cost camera (its focal length to pixel size ratio was 708) was located in the egocar at the 
height of 1.67 m over the road plane. Up to 6 moving cars have occured in one image. From them up to five cars 
have been properly detected and tracked nearly all the time (i.e. in 95-100% of images). The sizes of their image 
projections have ranged from 20x20 pizel? to 50x70 pizel?. Only small and partially hidden cars located very far 
from the camera have been detected with a rate below 50% (their image sizes were about 10x12 pizel?). 
Quantitative results of parameter measurement and estimation for two moving objects — the left car and the middle 
truck — are presented in Figures 4-10. These results can be summarized as follows: 
e the depth estimation error is « 10 96 and the direction estimation error is «0.2 rad 
e the estimation of translational velocity is of good performance for the near car (error up to +2.5 m/s), for the 
truck the error is much higher (up to £7.5 m/s). 
e a rotational velocity should not occur, as the objects are moving approximately straight ahead, but small 
velocities are estimated up to +0.5 rad/s. 
e the error of car width estimation is « 0.2 m for the car and « 0.5 m for the truck; as the © angle is nearly 7 
the length can be only weekly measured (in the range of 3 — 8m); 
The presented approach was simulated on a workstation with 25 MIPS. The processing time of a complete scene 
analysis was 4 — 5 s, but for the object recognition procedure the required cpu time was only 0.6 — 0.8 s. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995