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been used and each pair of rotated image coordinates x^, y, 
is transformed to this common plane, using the following 
equations (Chen & Scarpace 1990): 
x! 
Vx = (-e<az) — 
z 
r 
r 
(3) 
/ 
Ww, - (-c-az) 
z 
r 
Both images are now free from tilt, but because of the Y 
displacement of the right image, the epipolar lines are not 
parallel to the row direction of the scanning coordinate system. 
Since the dY translation parameter of the right image is 
known, a new coordinate system is generated, where the 
effect due to Y translation is eliminated,. This is done by 
rotating the left fixed coordinate system by an angle 6, equal 
to the angle between the X axis and the line connecting the 
principal points of the two images. The angle 6 is given by the 
following equation: 
dY 
  
The coordinates on the left image in this coordinate system 
become: 
Fx, » x,cos0 * y,sin8 
(5) 
Fy, = -x,sin6 + y,cos6 
Similarly the coordinates on the right image become: 
Fx. = Vx',cos6 + Vy",sin6 
(6) 
Fy. =-Vx’ sin + Vy’ cos@ 
All the above equations describe a direct transformation, which 
performs the production of epipolar images, i.e. the 
rectification of a stereo pair to the normal case. In practice an 
inverse transformation is actually used according to the 
following methodology (Jain et al. 1995). First of all, the 
locations of the four corners of each image on the common 
plane are determined. Then, new left and right image grids are 
created with grid cell dimension equal to the scanned pixel 
size. Finally, each grid point of the new image is transformed 
back to the original image. Bilinear interpolation is used to 
interpolate pixel values to determine the grey tone values for 
the new left and right images in the common plane. Before 
interpolation, the computed image coordinates must be 
"corrected" by reintroducing radial lens distortion and other 
systematic errors known from camera calibration. This is 
necessary because the calculation of the rectified image 
coordinates considers only "pure" undistorted values, while the 
actual location of a point on the image is affected by the 
systematic errors introduced by the interior orientation of the 
video camera. 
2.3 3-D Animation of Stereoscopic Images 
When the rectification to the normal case is completed for all 
captured image frames, a 3-D virtual representation of the 
recordered event may be realized on the computer screen. 
The key to display stereoscopic images on a single flat screen 
is rapid alternation between left and right images, while 
ensuring, at the same time, that each image reaches only the 
intended corresponding eye. Specialised hardware available 
from Sterographics Corp. was used in this study in order to 
display 3-D image sequences on the computer screen. 
The system, called CrystalEyes, consists of an eyewear with 
shuttering lenses and an infrared emitter. The emitter, which 
sits on the top of the monitor, is connected to the display 
hardware and broadcasts a synchronization signal to the 
eyewear. The eyewear receives the signal and rapidly directs 
the appropriate image to the corresponding eye. When the left 
image is on the video screen, the left lens opens while the 
right lens closes. As a result, the viewer perceives a true 
stereoscopic view. Research has shown that for a 
stereoscopic view without any annoying flicker, the computer 
monitor and shutter lenses should be able to alternate the 
display of each image 60 times per second. This, however, is 
not the case in most SuperVGA boards, which do not support 
refresh rates greater than 60-72 Hz in high resolution graphics 
modes. This means that, at best, the monitor and shutter 
system will be able to deliver 30 images per second. To solve 
this problem, a separate GDC3 video converter is provided by 
Sterographics which takes the 60 Hz signal from the video 
board and converts it to 120 Hz. 
Although the CrystalEyes system is simple and does not 
require any hardware modification to the computer, specialised 
software has to be developed in order to map stereoscopic 
views on the screen in the desired format. According to the 
CrystalEyes standards, the left eye views must be placed to 
the top half of the screen and the right eye views to the 
bottom half. The two images, called subfields, are vertically 
compressed by a factor of two (Lipton 1991). This is 
necessary, because when the system passes in stereo mode, 
both left and right subfields are vertically interlaced and 
alternatively displayed on the screen. Another important point 
to add, is that when the two images are interlaced, there are 
some horizontal lines which become invisible in both images. 
These lines are between 10-20 and are placed at the end of 
the left and the top of the right image. To overcome this 
problem, a blank horizontal area must be inserted between the 
two subfields (Figure 2). The height of this area depends on 
the monitor type and on the graphics resolution. A calibration 
procedure is necessary in order to determine the height of the 
blank interval before any image is mapped to the screen in 
use. 
  
  
  
  
  
  
  
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Figure 2 
The representation of a dynamic scene in 3-D mode deepens 
on the display of a series of images, which consists of two 
parallel perspective projections. According to the CrystalEyes 
standard, the screen is divided in two rectangular viewports. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996