3.2 MODEL DIGITIZING 
The measurements are made pointwise by measuring 
the left image point first, and then searching the 
corresponding homolog point from the right image 
along the current epipolar line. The left image is 
always measured by the user either by showing a 
suitable sized window, or just by showing a cursor 
position. The searching of the right homolog point is 
made automatically or by the operator, depending on 
the user’s choice. 
If automatic searching is selected, then a small 
window is shown on the left image, and the position 
of a point inside the window is computed using the 
method of gradient weighted center. The same window 
is then searched from the right image moving the 
window along the X-direction, and possibly some pixels 
in the Y-direction, depending on the rest Y-parallax of 
the rectification step. If this is less than 0.5 pixels no 
movement in the Y-direction is necessary. The quick 
search is based on a simplified cross-correlation, and 
as a result the location of the right image window is 
found with an accuracy of at least one pixel. Finally, 
the actual right image observation is computed using 
the gradient weighted center of that window. 
As the automatic search easily fails, the manual 
digitizing is kept as an alternative. This is made by 
pointing the object on the left image by cursor, then 
the current epipolar line is drawn on the right image, 
where it is now easy to show the same point with 
cursor. In this case, only the X-parallax is measured 
and Y-coordinate is kept the same on both images. 
The 3-D coordinates of the object model are directly 
obtained from the homolog observations using parallax 
equations (12), a freely chosen base length (B), and the 
previously chosen camera constant (H). 
3.3 DISCUSSION 
For the moment, the implementation of the measure- 
ment stage is based on the searching of the homolog 
points along epipolar lines. The measurement stage 
can be developed so that a stereoscopic view is possible 
to use, but this requires also a moving measuring 
mark on both images and a special display 
instrument. 
The measurement stage is mainly manual, but this is 
anyway the most reliable method to obtain observa- 
tions of the most important object points, especially 
when there is a wide convergency angle between the 
images, and an automatical object recognition is not 
guaranteed to work reliably enough. Making the 
observational step more automatic needs further 
investigations. E.g. least squares image matching can 
be implemented, but it requires certain conditions, 
which cannot always be valid when using images 
which have large convergency angle. Also the 
possibility of adding more images to the system will 
be investigated, as well as the implementation of 
additional parameters for compensating nonlinear 
image deformation. 
680 
4. EXPERIMENTS 
The object reconstruction program has been used in 
relative orientation of two digitized postcard images 
of the Cathedral of Helsinki. 
The postcards were digitized using a resolution of 200 
pixels/inch, and 256 grey values. Only an area of 512 
x 512 pixels were used out of the original postcards. 
The size of a pixel was approximately 10 cm in the 
object space. The extracted images are shown in 
figures la and 1b. 
The arbitrarily chosen camera constant was put to 
2000 pixels, and the left lower corner of the image was 
treated as an origin. The images after the final 
rectification are shown in figures 2a and 2b. 
Stereoscopic viewing of these images is possible if the 
direction of sights are crossed. 29 points were used in 
the computation of this final rectification, which had 
a standard deviation of 0.96 pixels. Measurements 
were made using both the cursor positioning and the 
gradient weighted center of a shown window. 
The 3-D model was then digitized from the rectified 
stereo images, but it was linearly deformed. This 
model was compared to a cartesian model that was 
digitized using an analytical stereoplotter and a pair 
of previously photographed metric images. The 
geometry of the metric model was quite good 
(base/distance-ratio was about 1/2), and the root mean 
square error (RMSE) of the digitized model 
coordinates was less than 2 centimeters. 
A 15-parameter transformation between the deformed 
model and the cartesian model using 14 points gave 
RMSE-values of 21 cm in X, 32 cm in Y and 22 cm in 
Z, where Y was the depth direction. Also the actual 
base of the postcard model proved out to be only 6.7 
m with an object distance of approximately 70 m, 
which gave a base/distance value of 0.09. 
It has to be noted here that the inner orientation was 
completely unknown and the possibly radial distortion 
was still affecting in the images, which may explain 
the high RMSE-values. 
The aim of this experiment was not to produce any 
precise 3-D model, but to show that the relative 
orientation method described in previous chapters 
works, and it really produces stereo images that can 
be used in measurements. 
  
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