International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
the area of rear triangle is Wev /(2W — 2e). 
Equations (1) and (2) define the movement boundary for 
operators during autostereoscopic measurement. Within this 
boundary, operators can move their heads forward, backward, 
upward, and downward and still perceive correct 3D images. 
The free space in which the operators can move depends on the 
monitor size, the viewing distance and eye base. It is also 
shown that the front range f, is slightly smaller than the rear 
range 7, In our DTI monitor, the front range and rear range are 
o n c 5 
respectively estimated as 10.8 and 14.2 cm from nominal 
viewing line, yielding totally 25 cm continuous range for a 
viewer to adjust his or her position in the direction 
perpendicular to the screen plane. This study also shows that 
the trapezoids of all viewing zones have the same volume. 
For the DTI monitor in our study, the number of viewing zone 
IS 7. A viewer can obtain stereo effect in seven locations by 
adjusting his or her position laterally. It should be noted that 
these are the locations that perfect stereo effect is ensured. In 
fact, a viewer can move his or her head outside the range 
defined by the monitor width. Therefore, there are practically 
more than 7 zones where viewers can receive stereo effect. 
However, since the viewing direction is not right perpendicular 
to the monitor in this situation, the magnitude of the light 
transmitted to the viewer's eyes is considerably reduced. As a 
result of this, the stereo view will become darker while the 
viewer positions are away from the screen center. 
3.2 Perceived Depth 
Human eyes are able to perceive depth to view 3D objects and 
distinguish the distance correctly (Jones et al, 2001). The 
perceived depth of an autostereoscopic mapping system 
determines the resolution for the object elevation to be 
measured. Hence the geometry of perceived depth should be 
discussed. The perceived depth is caused by horizontal parallax, 
which is the distance between corresponding points in two 
different images. When the correct stereo view is observed, the 
two optical axes intersect in front of the display plane. The 
image presented to the right eye of the observer appears to the 
left, and the left image presented to the left eye will appear to 
the right. The perceived depth appears in the front of display 
plane. The geometry is shown in Figure 4. 
  
v 
>< 
   
*: Image point 
  
+ e — 
Y 
Z 
Figure 4. Perceived depth in front of the display plane. 
In Figure 4, "' denotes the distance between display and 
viewer's eyes; p is represented the parallax of corresponding 
points on two images. The perceived depth ^? is the offset 
term ahead the display to the image point fused by viewer's 
d a ae plz, =elv'—z) 
eyes. The geometry relation is given as ; s 
Thus the relationship between the perceived depth ^^ and the 
viewing distance can be written as 
1 
Lir pv 
= > 
exp (3) 
If we treat e and p as constants, the perceived depth is linearly 
proportion to the viewing distance. From Eq. (3) when viewer's 
head moves toward to the display plane, the perceived depth 
becomes shorter; viewer's head moves away from the display 
plane, the perceived depth becomes longer from the display 
plane. The change of perceived depth inside the viewing zone 
is also linearly proportion to the change of viewing distance 
p 
Az = 
p e + p 
Av' 
. According to the geometry of viewing zone, 
the limitation of viewer's head moving boundary inside the 
Av' = 2ev(W + e)/[W(W +2e)] 
  
viewing zone is in xz-plane. 
Therefore, the maximum change of perceived depth inside the 
viewing zone is 
  
dey = Xo QevW vere gp 
: (4) 
If the e and viewing distance V' are treated as constants, the 
differentiation of Eq. (3) with respect to the desired variable p 
directly yields 
dz = Xe 4 
?^ (e py (5) 
Eq. (5) is the relationship between the perceived depth 
difference and the horizontal parallax difference. Assuming 
e=65em D = 1 to 25 cm, we can plot Eq. (5) to Figure 5 for 
different viewing distances. 
dz 
  
  
  
p (cm) 
Figure 5. Ratio of perceived depth difference and parallax 
difference. 
As is shown, the perceived depth difference is dependent on the 
parallax difference of the images. The relationship is not linear. 
In general, z, is inversely proportional to the horizontal parallax; 
the perceived depth is directly proportional to the viewing 
distance. The perceived depth difference dz, is amplified under 
autostereoscopic mode because the parallax p is small 
comparing to the view distance. This is a good property of 
autostereoscopic monitor. This means the horizontal parallax 
difference dp can be more apparently reflected in the change of 
perceived depth dz,. 
    
  
     
  
   
  
    
    
     
  
  
  
    
  
   
  
    
  
    
   
    
  
  
   
   
   
   
   
   
  
  
  
  
  
  
  
  
  
  
  
  
  
   
   
  
   
    
     
  
  
   
   
   
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