3) 
re 
re 
Sergey Zheltov 
  
right images by L(X, Y), R(X,Y) respectively. Subtraction of the orthophotos (Fig.3(c)) is performed by the following 
way: D(X, Y) 2 L(X,Y) - R(X,Y). 
  
(a) 
  
  
    
i M 
?Left Right v, 
Figure 4. Invisible surface areas for left and right 
images 
  
  
  
  
  
  
(b) (c) 
Figure 3. Example of orthophotos and their difference. (a) Orthophoto from left image. (b) Orthophoto from right 
image. (c) Difference: (a) minus (b) 
Pixel coordinates of (i,j)-th orthophoto point are calculated as follows: 
(X,Y) = (X, +i *S, Y; +7 * Sy), 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 gray value to the (i,j)-th orthophoto pixel the point (X, Y,Z) is 
projected to the image using collinearity equations. The gray value is 
obtained by bilinear interpolation of four image gray values in pixels with 
nearest to the projected point integer coordinates. 
The basic principle of the developed detection method is the significant 
difference in orthophoto due to different view positions of the cameras 
(Fig.4). In the left image the surface area A» behind the object P is 
invisible. The same is for the surface area A, in the right image. Thus the 
gray values in invisible areas are taking from objects gray values. This 
results in «projecting» the object to the invisible surface area. 
5. DETECTION BY THE MATCHED FILTER 
We assume that the object to be detected has rather contrast edges that are near to perpendicular to the surface. If the 
stereosystem with respect to the surface is under an angle of view close to zero, then edges of the object become 
elongated and enough rectilinear. 
Let the object be a rectangle of height / and width w. Let the left-bottom corner of rectangle be located in surface point 
(X, Y, Z) perpendicular to the surface and parallel to the image plane. Then the invisible area behind the rectangle is a 
trapeze (Fig.5(a)) with dimensions satisfying the following equations (assuming the flat surface near the object 
(Fig.5(b))): 
b h v L zr - 1s] (7) 
ben Bag 
In these formula L is a distance from the camera to the object. 
  
   
Im age Ms YZ) 
1 
Surface 
a D (Y. 23 (b) 
     
Figure 5. Object dimensions in orthophoto 
For the following model parameters: h = 10cm., IZ- Zi — 1 m., L 2 50 m the parameter b is equal to 12.5 m. This shows 
that Y-dimension of the invisible surface area dominates on other dimensions. So this fact actively used in the detection 
algorithm, because the orthophoto difference contains clear triangles formed by object edges. 
  
Intern 
ational Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
1045