bad | 
Vjacheslav Listsyn 
  
where D,, is the projection of distance to the point on an axis X; F is the focal length of camera lenses; m; is the scale 
along the axis Z; A is virtual shift of the camera along the axis Z. 
If the plane where the landmarks are situated is parallel to the defined XOZ plane and H is the distance between planes 
then 
A-m 
Selm N 
H-m, (Mine ) 
where m, is the scale along the axys Y, ne is the line number from the bottom of the image, and N is the line number 
corresponding to the camera optical axis position. Thus, for a planar model the shift value is a linear function and such 
transformation is an affinity one. 
After these transformations, all lines and figures located on the underlying surface are reduced to a form identical on 
both left and right images of the stereo pair. At the same time, three-dimensional objects acquire a certain inclination: to 
the right - on the left image, and to the left - on the right image. 
After the considered transformations, the fragments of the stereoscopic picture are subtracted: the right image is 
subtracted from the left. On the difference image, the intensity of patterns corresponding to figures on the underlying 
surface are close to zero, while contrast points related to three-dimensional objects are marked as face-down triangles. 
The presence of such patterns becomes a sign that 3D-object is detected. The above considered transformations are 
analogous, to a certain extent, to methods considered in (Zheltov, 2000), but without modeling of the underlying 
surface. 
Suppose there is a vertical plane perpendicular to the camera optical axis and there is a straight line in this plane that 
form angle y with the vertical axis. Then after above considered transformation this line will be transformed into the 
straight line and angle y will be transformed into the angle y. Here 
A: m, 
tg( ets c 
Thus if two contours on a difference image were generate by the same contour of some 3D object, then the following is 
true: 
B-m, 
Ig T )- 18 os ) | = Hm, 
where B is the base of stereo pair, Ysa is the angle of the contour on difference image that was generated by the contour 
of 3D object on the right image, and Yen is the angle of the contour on difference image that was generated by the 
contour of 3D object on the left image. 
Thus if some 3D object has nonzero contrast with the background, then after above considered transformations patterns 
looking like face-down triangles will be present on difference image in positions defined by the position of the 3D 
object edges. The angle between the sides of such a triangular pattern is determined by (1). 
Different methods could be used to search for these patterns. Here we consider the method based on the matched 
filtration. This method allows us to search for contours with beforehand determined incline (in this case — vertical 
contours that are typical for artificial objects). 
For convenience we form two difference images: one from positive pixels and another from negative pixels. To search 
for characteristic patterns (i.e. face-down triangles) contour selection of difference images and matched filtration of 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 535