P fi
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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