Z(X,Y) in some neighborhood of the object. The exterior 
coordinate system is defined with use of three marking points 
(pi.po,p3), where p; sets the start (approximately 30m from the 
car), p>-p; sets Y axis, p;,p2,p3 set XY plane (Figure 2-a). 
The exterior orientation parameters are found as follows. The 
rotation matrix U of exterior coordinate system in coordinate 
system of relative orientation is calculated by using Gramme- 
Schmidt method. Matrixes of directional cosines are converted 
by 3D rotation assigned by matrix U. New centres of cameras 
projection are set by displacement to point p;. 
Such coordinate system allows to simplify the road model. For 
example in case of flat surface (1) it reduces to Z(X, Y)-0 in 
exterior coordinate system. 
Z(X,Y) = aX + bY + c (1) 
In general case the road is represented by four-parametric 
model (2). Parameters a; are found by the least square method 
with use of 3D-marking points. 
Z(X,Y) = ao + a,X + aoŸ + a3Y”, (2) 
The model (2) was accepted after the extensive experiments 
with real data. It is proved to be the ideal compromise between 
small number of reliably estimated parameters and flexibility in 
representation of lengthwise and lateral character of the road 
particularly for highways. Example of road model obtaining 
from the marking points is shown on Figure 2-b. 
Left image Right image 
  
  
  
  
  
  
  
  
Figure 2. (a) marking points p;,p».ps set the road-based exterior 
coordinate system; (b) road model obtaining from 
the marking points 
3. ORTHOPHOTO TRANSFORMATION 
Orthophoto is orthogonal projection of 3D-scene, which 
eliminates all distortions caused by camera orientation and 3D- 
shape of the scene objects. 
Orthophoto transformation is performed by projecting the 
surface of known analytical model to some convenient plane 
with use of left and right images given by a stereoscopic 
system. Pixel coordinates of (ij)-th orthophoto point for 3D 
point (X, Y,Z) are calculated as (3): 
Xei*S.Y-j*S,. (3) 
where S,, S, - grid sample distances along X and Y axes 
respectively. 
The height Z(X,Y) is reconstructed from the surface using the 
bilinear interpolation of four nearest surface values. To assign a 
grey value to (ij)-th orthophoto pixel the point (X,Y,Z) is 
projected to the image using collinearity equations. 
As a result the grey values in invisible road areas are taken from 
3D-object's grey values. This leads to «projecting» the object to 
the invisible road area (Figure 3). 
  
Orthophoto 
  
  
  
  
Figure 3. Orthophoto generation. A; — invisible road area 
In the previous work (Zheltov, Sybiryakov, 2000) it has been 
shown that due to this property of orthophoto the calculation of 
difference of orthogonal projections results in appearance of 
characteristic geometric structures in neighbourhoods of 3D- 
objects not belonging to the given surface. As orthogonal 
projections eliminate the distortions caused by the surface 
irregularity the significant brightness variance is appeared on 
difference image only in 3D-object neighbourhood. 
Thus the problem of 3D—object detection is reduced to detection 
of 2D-structures with the predicted properties on the 
transformed image. The simple objects with straight-line edges 
correspond to the precise 2D-corner shaped structures. Angle 
value and shape of corner are known functions of object 
position but they do not depend on the object form. 
Unfortunately most of the image processing hardware generally 
supports only such single-pass operations like convolutions and 
projections computations. This restriction makes it quite 
difficult to create real-time algorithms for detection of corner 
shaped structures on the image. 
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