The simulation can also be used for real world situations. Let us 
say that we have a target area we would like to measure. The 
distance to the closest relevant detail of the area is 350 meters 
away and the distance to the background of our target area is 400 
meters. This kind of situation can occur for example in a case of 
a cityscape where we would like to measure some specific area 
within a city. Now, if we only have a normal photographic 
camera stand and would still like to capture a panoramic image 
with a long focal length lens to achieve high resolution from such 
a long distance, we need to consider the error caused by the offset 
projection centre. If we mount the camera on the stand from the 
camera base, the projection centre is, usually, located inside the 
lens. In the case of a long focal length this distance can be many 
centimeters. 
For example in the case of a 600mm lens, it is safe to assume we 
could have approximately 200 to 300mm offset in the Z- 
direction. We can also assume 10 to 20mm offset in the X- 
direction if we do not calibrate our rig. Using a 35mm format 
camera the diagonal FoV is 4? 10' while the required FoV to 
cover our target is 8? 10'. If we use 50% overlap, we need to 
capture five photos. The resulting errors are presented in Table 1. 
The Z-direction offset is 250mm and 15mm in the X-direction. 
Offset in the Y-direction is set to zero and the camera is only 
rotated horizontally. 
  
Angle -4.085° -2.005? 0.075? 2.155? 4.235? 
Point 1 0.4mm 0.9 mm 2.2 mm 3.5 mm 4.8 mm 
Point? 4.8mm 6.1 mm 7.3mm 8.6 mm 9.8mm 
  
Table 1. Errors at the second target plane with different bearing 
angles. The distance to the first target plane is 350 meters and 
400 meters to the second target plane. Z-direction offset causes 
Points 1 and 2 to produce different errors with different angles. 
4. DISCUSSION 
According to simulation, perspective errors due the eccentric 
panoramic frame-image acquisition are relatively small if the 
distance between camera system and objects is long enough. 
Even if we have examined only errors in the object space, this 
error is proportional to errors at the image space. Therefore, after 
a threshold distance, the maximum error at the image space can 
be tolerable, for example less than one pixel. For example, Wei 
et al. (1998) found similar conclusions in their research. For 
seamless stitching of sub-images, such small errors at the image 
space are advantageous. However, with some limitations we are 
able to have relative small error also for targets that are closer 
than previously mentioned threshold distance. 
Overall, the perspective error caused by the projection centre 
offset obviously weakens the geometrical quality of the 
panoramic imaging system. However, if we only consider a 
shallow area of interest, the error caused by the perspective error 
is smaller than if we consider the whole image area as a whole as 
shown in Figure 10. This gives us various alternatives if we are 
only able to acquire images of sub-optimal quality regarding the 
panoramic geometry. 
The first possibility is to use the images as they are, in a 
photogrammetric image block. Unfortunately, in the case of a 
long focal length this might cause problems due to correlation in 
   
the exterior orientation of the camera station. If we stitch the 
photos into a panoramic image, the geometrical exterior 
orientation of the image is more stable provided that the internal 
geometrical quality of the panorama is robust enough. 
If we have a large projection centre offset between the sub. 
images, the perspective error of the resulting image can be too 
large to permit the use of such a photo in a metric 
photogrammetric application. In that case, one possible Way to 
use such an image material is to stitch the photos, as shown in 
the Figure 10, using only features located within a limited depth 
of range. Stitching becomes seamless only within that depth of 
range, but we can create more stitched images for different 
depths. Examples of such stitched photos can be seen in the 
middle and rightmost photos of the Figure 10. The closer 
stitching distances result in poorer accuracy or smaller target 
depth. On the contrary, a usable depth of range increases if the 
offset of a perspective center becomes smaller. The leftmost 
image in Figure 10 illustrates how a small offset allows seamless 
stitching to a large depth of range. 
Even if we have an eccentric sub-image acquisition, we can use 
images for photogrammetric scene reconstruction if we use only 
those parts of images that are within depth of range in focus 
(Figure 10, the middle and rightmost photos). On the other hand, 
similar constraints can be used also for finding recommended 
areas from the image planes for automatic feature matching and 
thus improve stitching of sub-images into full panoramic 
mosaics. 
  
Figure 10. Left image shows two photos stitched with nearly 
concentric panoramic camera rig showing negligible perspective 
error. Middle and rightmost images show two photos with offset 
projection centre stitched together using only the points in close 
vicinity to the red line shown in the photo. 
Our simulation program can be used to estimate the proper usage 
of the photos at hand to help to decide in which way to best use 
the image material. We use the simulation program in our own 
projects, mainly in cases where we have to measure a specific 
target located far away. Another application is oblique aerial 
imaging. Using the simulation, we can estimate the perspective 
  
    
   
    
   
   
   
   
    
   
    
    
   
  
    
   
   
     
    
    
   
     
  
   
        
    
    
   
   
   
  
  
  
  
  
  
  
   
   
   
     
  
  
  
  
   
     
   
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