deformation is so 
rotation axis are 
acing the rotation 
Point 2 
  
> camera geometry 
0° increments. 
  
camera geometry 
0° increments. 
  
  
   
  
       
  
  
  
   
    
      
  
  
  
Pring} offal 75 
mm Piin 2 offset 25 
pu Pointi offset Z19 
— Pint à offset Z10 
   
     
s Be fsct 215 
quem Paint? offset 215 
  
  
  
Figure 8. Errors at the object space with various offsets in the X- 
direction as a function of rotation in degrees. Distance to the first 
target plane is 70 units and 100 units to the second plane. The 
  
     
    
       
  
  
   
   
  
   
  
  
  
  
   
  
  
  
  
  
  
    
    
  
  
Figure 6. Eccentric sub-image panoramic frame camera geometry 
with five project unit offset in Z-direction and 20° increments. 40 - 
Eccentricity can also be visualized with graphs. The graph in 
Figure 7 shows the error caused by various offsets in X-direction, 30 
as specified by the legend, as the function of the rotation angle in 
degrees. The distance to the first target plane is 70 units and 100 
units to the second plane. The offset varies from 5 to 15 units. <0 
The graph in Figure 8 illustrates the effect of the Z-direction 
offset, respectively. Vertical axis shows the error at the object 4 0 
space. 
In Figure 1, we showed the image geometry using distance of 20 D 
units to the first target plane, five units offset in the X-direction 
and 30 units distance to the second target plane. Figure 9 present 
an addition of two cases with longer distances to the target 0 
planes. In the second case, the distance to the first target plane is 
40 units and 50 units to the second target plane. The third case 
shows 40 units distance to the first target plane but the distance 
to the second target plane is extended to 60 units. 
  
verwen BYE 1 offaet x 
vertical axis shows the error in project units. 
60 
50 I 
Error 1,25 
  
Case 3 second target plane 
Error 2,5 i 
Case 2 second target plane 
  
  
  
__— Cases 2&3 first target plane 
Error 2.5 | à 
|, Case 1 second target plane 
  
  
   
   
Case 1 first target plane 
  
  
  
  
  
Figure 9. Five unit offset of the projection centre in the X- 
direction causes different amounts of perspective error in various 
shooting distance to depth ratios. 
In the first case, the distance to the first target plane is 20 units 
and 30 units to the second target plane. Shooting distance to 
  
  
Figure 7. Errors at the object space with various offsets in the X- 
direction as a function of rotations in degrees. The distance to the 
first target plane is 70 units and 100 units to the second plane. 
The vertical axis shows the error in project units. 
  
s — Point2 ettet xà depth ratio is the distance to the first target plane divided by the 
à ss Pointl offut X10 difference between the distances of the two target planes. In the 
ri mete xi first case, the ratio is two and the resulting perspective error is 
ee esit] esffsot X15 
2.5 units. In the second case, the distance to the first target plane 
is 40 and 50 units to the second target plane. This translates to a 
shooting distance to depth ratio of four and the resulting error is 
1.25 units. Therefore, by doubling the shooting distance and 
keeping the target depth the same, the perspective error is halved. 
In the third case, we extended the target depth in a way that the 
shooting distance to depth ratio is the same than in first case. 
This should lead to the same amount of perspective error than in 
the first case while extending the target depth by 200%. The 
distance to the first target plane is 40 and 60 units to the second 
target plane, so the shooting distance to depth ratio is two. The 
resulting error is 2.5 units. 
v Point2 offat X15