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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
  
  
  
  
  
Figure 2. DTM-grid with two cameras above. 
To visualize the camera a square image frame was shown, and 
the corners of the square were connected with the projection 
center of the camera. Adding a second camera was simple, so 
this was done as well. Also the vertical projection of the DTM- 
grid onto a horizontal plane is shown. A typical graph obtained 
with this sheet is shown in figure 2. 
The resolution is better than shown here, but the shape of the 
"deformed" grid in the images did not show up well enough. To 
show this in a better way, separate graphics were created for 
each image to show the "image" itself with good resolution. 
Now however, the coordinates of the image points had also to 
be calculated in the image coordinate system. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Figure 3. “image” graphic of a DTM-grid. 
No attempt was made to limit the drawing of the image to the 
inside of the image frame or in any other way. 
This gives rather strange situations in extreme cases, as 
mathematically the image plane is unlimited and image points 
are calculated as the intersection of a straight line — defined by 
the object point and the projection center — with the image 
plane. There is a critical plane, which is parallel to the image 
plane and passes through the projection center. Object points in 
this plane are theoretically imaged infinitely far away, 
practically a “Division by zero” error happens and they will be 
imaged to position (0, 0). Points just a little in front of this 
plane will be imaged very far away to one side, while points 
just behind it will be far away to the other side. A perhaps short 
joining line of two such points (on either side of the critical 
plane) can thus result in a very long image line! 
  
  
  
  
  
Figure 4. landscape with image 2 partly “outside”. 
This only happens, if the critical plane passes through the object 
area. The effect was considered rather curious than nasty, as 
such extreme situations were not meant to be used. For more 
"normal" situations the fact that part of the drawing is outside 
the image frame can sometimes be considered illustrative for 
the danger of errors in the coverage by errors in the camera 
inclination. 
Restitution 
To demonstrate the effect of orientation errors on the geometry 
of the restituted object another set of cameras. (restitution 
cameras) was introduced. The differences between the 
parameters of the restitution cameras and those of the original 
cameras are kept as parameters in the parameter sheet, being the 
"changes to the original parameters". 
In a new calculation sheet the changed parameters were 
calculated, then for each image point its location in the object 
coordinate system was calculated using those changed 
parameters of the camera.