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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
3.3 Horizontal epipolar images generation 
The essence of the horizontal epipolar line rearrangement is a 
digital correct process. Under the ideal baseline conditions (B Y 
= 0, B z = 0), the left and right epipolar line, intersected by the 
epipolar plane and the horizontal images, are parallel and 
coincide with the scan line. In this condition, the horizontal 
image coordinates (u, v) and the original image coordinates (x, 
y) meet the following relationship: 
V' 
= ÀR 7 
original 
-/ 
(6) 
horizontal 
The projective relationship between two image coordinates is: 
x= j.a x u + b x v-cj 
y= -f 
a 3 u + b 3 v-c 3 f 
a 2 u + b 2 v-c 2 f 
(7) 
a 3 u + b 3 v - c 3 f 
However, the actual stereopair baseline is not completely level. 
(D If the baseline component B z = 0, В у ф 0, then the epipolar 
lines itself in the horizontal images are completely parallel, but 
with the angle of scan lines exist. Under this condition, if the x- 
axis of geodetic coordinate system is rotated to the horizontal 
component of the baseline direction, the horizontal epipolar 
images are generated. 
® If B z ^ 0, B Y ^ 0, the epipolar lines itself is not parallel. It is 
impossible to eliminate the B z , but the geodetic coordinate 
system can be rotated the angle 0 to parallel with the baseline, 
which make the smallest angle between the epipolar lines and 
the scan lines. Then follow the method of non-horizontal 
epipolar lines rearrangement, rearrange the epipolar lines of the 
horizontal images. 
The angle 9 between the epipolar lines and the scan lines can be 
calculated with the baseline component, that is tg6 = B Y /B X . Let 
R B is the rotation matrix which rotates the x-axis of geodetic 
coordinate system to the horizontal component of the baseline, 
the rotated baseline component is: 
'В 
( В Л 
°x 
0 
By 
у 
у 
(8) 
where: 
Bv 
= yß : 
X +B Y 
B x ! В Ху 
BJB v 
-By / В угу 
В Х ! В XY 
о 
о 
In the horizontal images conditions, based on the Equation (1) 
and (8), the Equation (9) is deduced: 
Byy 0 B 7 
= 0 
(9) 
where: 
(u P , v P ) = horizontal image coordinates 
(u, v) = epipolar image coordinates 
So the epipolar line equation of horizontal images is deduced: 
v = vp + k(u-u p ) (10) 
where: 
к = 
(И) 
According to the above Inferential reasoning formula, the 
horizontal epipolar images can be generated by the following 
steps: 
(1) Rotate the geodetic coordinates system to the horizontal 
component direction of baseline, and rotate the rotation matrix 
of the left and right images, get the horizontal images which 
parallel with the horizontal component direction of baseline. 
(2) Determine the scope of the horizontal images and the 
epipolar images by the coplanarity equation. 
(3) To every line of scan lines in horizontal images: 
(DAccording to the points in first row of left images, calculating 
the epipolar line equation by the formula (10). 
(2) Calculating the longitudinal coordinates (v) of epipoalr lines 
based on the epipolar image abscissa (u). 
©Projecting (u, v) to the original image, then getting the 
corresponding coordinates (x, y). 
(D In the original images, get the gray value of images points (u, 
v) by bilinear interpolation method 
4. SYSTEM INTEGRATION 
By using the dynamic epipolar rearrangement method, the 
concrete process of stereoscopic observation is as follows: 
(1) The first step is to tile the original stereopair, and build the 
multi-layer image pyramid data structure from low resolution to 
high resolution. By utilizing the improved pyramid image 
generation strategy, high fidelity on different image layer can 
be achieved, and the better measurement result can be gained 
even using the low resolution image in pyramid. This strategy 
can resolve the problem on scheduling and displaying the large 
volume of stereopair. 
(2) In the first step, the stereopair pyramid has been built. Then 
the epipolar images should be generated from the pyramid 
image. Depending on different viewport, the image in 
corresponding layer in certain tile is selected from the pyramid 
image. The selection take advantage of both multi-threading 
technology and memory pool technology based on page 
replacement LRU algorithm. So the selected images can be 
scheduled dynamically. The epipolar lines on the selected 
images are re-arranged in order to get a pair of epipolar images. 
According to the difference of the baseline angle, the generation 
of horizontal or non-horizontal epipolar images is different. 
(3) Up to this step, the epipolar images have been produced. 
Then the epipolar images should be transferred to screen buffer 
to show. The transfer course will contain truncation error 
because the epipolar images must be performed scaling 
transformation before shown in the screen. In order to inhibit 
this truncation error, integration operation of integrating the 
generation of epipolar images, as described in step 2, with the 
scaling operation on epipolar images are executed. After the 
integration operation, the epipolar images will be scaled and 
directly transferred to the screen buffer for the stereoscopic 
observation. 
5. EXPERIMENTS 
An experiment is designed in response to above principles and 
formulas, which based on the platform VS2005 and OSG 
(OpenSceneGraph). 
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