International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
  
  
  
  
  
  
  
  
  
  
Figure 5. Original and restituted object and the cameras. 
U; X; Xh. 
v, |2 Rj*| y; — yh e 
W, €, 
wher 
a 
u, v, w = vector from projection center to image point 
in the object coordinate system 
R = rotation matrix from the changed angles 
x, y = image coordinates of image points 
xh, yh = image coordinates of the principal point 
i = index of the image (1 or 2) 
For the calculation of the point of intersection the simplified 
approach, which is mostly used for single models in photogram- 
metry was used: intersection of the two straight lines only in 
2D-space (U,W). 
U=t,-a,+U, = u,+U,, 
W=t,-w, +W,, =t,w,+W,; (3) 
(U,,-U, Ww OF LOW, u, 
H, Ww, —H.w, 
(U cU, WW; (MW; MW.) u, 
0. 
  
t= 
tx 
U,"w,—u, w, 
V,=t,-v, +1, , E zi vtV, 
VzqV 0V.)/72 . p,-2V.-V, 
where |. U, V, W = object coordinates of the restituted points 
u, V, W = vector from projection center to image point 
in the object coordinate system 
Us.» Voi» Wei = coordinates of projection center (1) 
t = scale factor 
V; = V calculated from image i 
i = index of the image (1 or 2) 
This works fine as long as the joining lines of the two 
projection centers and the two camera axes do not deviate much 
from the (U,W)-plane. For horizontal camera axes or for a base 
in V-direction it is not suitable. Strict formulas were tried, but 
considered too cumbersome. 
Two different V-coordinates were calculated, one for each one 
of the straight lines. The mean of them is used - together with 
the U- and W-coordinate from the intersection calculation - to 
show the point in the graph. The difference of the two V-values 
is used as "Y-parallax". 
The sheet calculating the actual graph uses the calculated 
coordinates to show the restituted locations and allows also to 
show the y-parallax with a user selectable exaggeration factor. 
This can also be used to show the principle of analogue 
orientations. One can exaggerate the y-parallaxes so much, that 
even small ones are visible, and then one can vary the "changes 
to the parameters" to eliminate or reduce those parallaxes. One 
can also add a sheet showing only the values of the y-parallaxes 
of selected points (e.g. the 6 “standard” points) and show this in 
an additional window. 
  
    
LETTER =) 
13 image 1 
14 original |change 
15 0.000gr|_0.000gr 
16: __0.000gr{(-8 65576 
17 0.000gr] 0.000gr 
  
  
  
  
  
  
  
  
  
  
  
  
  
18 0 0 
19 50 a 
20 75 D 
21 -15 a 
22 0 0 
23 0 0 
24 15| 0.001 
25 image2 
  
26 original | change 
2f 0.000gr|_0.000gr 
28.  Q.000gr|-8.855gr 
  
  
  
  
  
  
  
  
/ 29 0.000gr| 0.000gr 
30 50 ü 
3 5n 0 
32 75 7 
33 -15 0 
34 0 D « 
  
  
  
« «x »Xpal«T Lol 
  
| A B 
| 0.00006 0.00006 
  
40 50 60 70 50 
to 
e 
1 
2 
3 
4 0.00000 0.00000 
5 
6 
7 
-ü.00006 -0.00006 
Mo» M \Chart1 / params nt: py £ 18 py £ Chart2 /chall« « » nYX6py/ 18py /« 
  
  
  
  
Figure 6. Analogue “Common Phi”. 
Push broom scanner(s) 
The functionality of the graphics for push broom scanner 
images is limited. One version shows cameras with parallel 
projection in one direction and central projection in the other. 
This limits the sensor to a straight flight path and does not allow 
variation of the angles within an image. The overview graph as 
well as view(s) of the image(s) are available, but restitution 
with changed parameters is not yet possible. 
132