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International Archives of the Photogrammetry, Remote Sensin 
  
g and Spatial Information Sciences, Volume XXXIX-B4, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
quasi-orthophoto. This quasi-orthophoto is created from an 
adjacent image by introducing artificial longitudinal parallax 
during orthorectification process in order to achieve fully 
metrical 3D model. Created pair of images not only inherit the 
artificial parallax but residual parallax as well. This residual 
parallax is generated for the objects protruding from the terrain 
in the classical orthorectification process of two neighbouring 
aerial images. 
Stereoscopic vision of the height differentiation of the terrain is 
possible because of the presence of the artificial parallax, while 
height of the objects protruding from the terrain — through the 
residual parallax. Objects protruding from the terrain and not 
being orthorectificated, such as buildings, chimneys, towers or 
trees are called vertical objects in the next parts of this article. 
There are some alternative versions of stereo orthophoto 
possible. One of them relies on stereopair creation based on 
only one photo however stereoscopic effects is achievable only 
for the terrain. Observation of two overlapping orthophotos 
without stereo mate component is another option, but 
stereoscopic effect in this case is limited to vertical objects 
visible on the flat terrain background. 
The principles of “full version" of stereo orthophoto generation, 
which provides stereoscopy effect for both the terrain and 
vertical objects are presented in the figure 1. Upper part of the 
figure. explains why, between orthophotos generated from left 
and right images residual parallax is formed for the vertical 
objects. The scheme of stereo mate generation is shown in the 
lower part of the figure. In the process of the right image 
orthorectification orthogonal projection is replaced by quasi- 
parallel projection of the terrain points. 
     
Left Photo Right Photo 
  
  
  
  
  
Left Ortho : => Right Ortho 
  
  
  
Residual Parallax 
  
  
Left Photo Right Photo 
/ j 
/ Jf y 
betronho me ~~ Stereo mate 
  
  
  
  
  
Artificial Parallax 
Figure 1. Principles of stereo orthophoto generation. 
The mathematical function that links artificial parallaxes with 
the terrain elevation model could be linear, which corresponds 
with the slope parallel projection. However better results could 
be achieved by introducing logarithmic function into projection 
(Collins, 1970) as shown in the equation 1: 
H 
P z B-In (1) 
  
where P - artificial parallax, 
B - base line of photograph, 
H - flight height above the reference level, 
h - terrain height/elevation above reference level. 
Parallax calculation from equation 1 not only improves 
accuracy of stereo orthophoto height measurement but 
positively influences balance between the artificial and residual 
parallax with parallel projection and variable angle method (Li 
et al 2002). 
Figure 1 presents situation, where area around the vertical 
object is relatively flat. In such case residual parallax calculated 
from the equation 2 is a good height indicator. However, if the 
object is located in mountainous terrain, especially at the top of 
the mountain or in the middle of the valley, then the residual 
parallax is distorted, what-introduces errors in vertical objects 
height determination. This explains worse accuracy of stereo 
orthophotos in mountainous terrains (Figure 2). 
  
AH 
CS 
Ah 
  
  
  
Flat terrain 
  
  
Mountainous 
terrain 
  
  
Residual Parallaxes 
Figure 2. Residual parallax distortion for vertical objects in 
mountainous arcas. 
AH - Ap 
Ah = @) 
C 
ÂAp + B : — 
p P A 
where Ah — height of object relative to its base, 
Ap — residual parallax, 
B — base line of photograph, 
c — focal length, 
AH - flight altitude above vertical object position.