e exterior orientation of the images, with test field 
reference points coordinates and interior orientation 
parameters being frozen; 
e complete unknown parameters vector estimation in 
condition of knowing relative distances. 
Such a technique allows to obtain the resulting accuracy for 
spatial reference points coordinates at the level of 5.14 mm and 
the accuracy of angle exterior orientation parameters at the level 
of 0.35°. These results are at the required level for the given 
problem of road surface 3D reconstruction and obstacle 
parameters estimation. 
4. RELATIVE ORIENTATION 
The next stage of stereo system calibration needed for reliable 
estimation of road and obstacle geometry parameters is cameras 
relative orientation. The theoretical analysis and the results of 
manual relative orientation made using images of road scenes 
obtained during first technological laboratory vehicle mission 
have shown that the accuracy of simple relative orientation 
procedure (eliminating vertical parallaxes for corresponding 
points) results in unreliable estimation of relative orientation 
parameters. 
The relative orientation procedure is performed in on-line mode 
using 2D test field similar to calibration procedure. For relative 
orientation parameters estimation a set including from three to 
six stereo pairs is acquired at different vehicle distances from 
the test field. A diapason of distances from test field is 
determined by requirement of observing the most part of 
reference points by vision system in all parts of images. The 
diapason varies from 10 m to 40 m and depends on test field 
size. Then the set of 2D test field observations is processed 
under conditions of planar location of reference points and 
given reference distances, resulting in relative orientation 
parameters vector. The estimated relative orientation parameters 
are transmitted to obstacle detection software and are used for 
estimation of vehicle position in the road, obstacle position in 
the lane and obstacle height and width. 
For estimation of relative orientation parameters the co- 
planarity condition is used: 
F = xx'(c{b{ — bie) + xf (bet ~ bjes ) + xz'(bje$ — bef) + 
* z'f (bh — byes) + xf (brc? — bef) + ff'(bez-by)- AD) 
— x'zb[C5 — zz'bycs — zf bye, - 0 
In formula (11) next designations are used: 
b,'- -sinag; 
b,'=—cosag,; 
by'=0; 
CJ'=—COSŒg - SIN KB; (12) 
C5'— —Sin Og : Sin Kg; 
€4'— COSKp; 
b,"- —sina'g:cos op; 
b,"— cosa pg: cos op; 
b,"— —sin 9g; 
c"— cosa''p:sin k'g—sin a g:sin 9'g:cos Kp; 
C" sina'p-sink'g+cosa'g-sinw'p-cosk'p; 
C4" — COS ' g: COS K' p. 
where 
ap, Kg - elements of relative orientation for the left 
image; 
Q'p, Op, K'p - elements of relative orientation for the 
right image; 
x, z, f - coordinates of points and focal distance of left 
image; 
x^ z/ f! - coordinates of points and focal distance of 
right image. 
To determine the elements of relative orientation the model of 
least squares method was used. 
The developed system on-line relative orientation procedure 
takes few minutes and is to be performed whenever cameras 
position is changed. The outdoor test field includes a set of 
reference points located on plane surface. The number and 
location of reference points in the test field is taken from 
condition of equal density of markers in all parts of the left and 
right images acquired from distances of 10 - 30 m. Figure 6 
represents a set of stereo pairs acquired during relative 
orientation procedure. The test field used for relative orientation 
includes 12 reference points marked by coded targets. 
  
  
Figure 6. A set of test field images for relative orientation 
For relative orientation procedure performing laboratory vehicle 
is installed in initial position at distance approximately 30 m in 
front of the test field and first image stereo pair is taken. Then 
the vehicle moves forward to the test fields and next some 
images are taken (usually three-four stereo pairs) while vehicle 
_ 8% 
Joho ppd ped dk ya 
th 
re 
ot 
TI 
au 
im 
us 
lat 
ba 
cal 
ac 
ob.