B5. Istanbul 2004 
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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
3.2 Tracking strategy 
To track the spheres along their trajectory and compute the 
coordinates at each frame, the following strategy has been 
implemented: 
a) target extraction by an interest operator, in each 
image; 
b) labelling of each target in each frame; 
c) computation of object coordinates by spatial 
intersection of the homologous rays. 
3.3 Target extraction 
In each image, the spheres are extracted in two stages: first the 
Foerstner operator is applied to extract (possibly only) all 
tracing points, then the interest points are filtered by template 
l.s.m. using a synthetic image of the sphere to reject false 
candidates. 
Indeed, it proved difficult to achieve to the above mentioned 
goal. Due to the high reflectance of the sand grains, the spot of 
grain were often as “interesting” as a nearby sphere. This make 
obviously more difficult to discriminate, when labelling the 
targets. On the other hand, the illumination level was kept high, 
to allow shorter shutter time. Some improvement was obtained 
spraying ink over the sand surface, so reducing the spot 
intensity. Trying to discriminate based on the roundness of the 
interest point didn’t yield the expected results, so we had to 
accept as potential targets many more candidates that the 
number of spheres, in the hope that filtering by l.s.m. would 
discard the false targets. This was partially successful, because 
we had to allow for scale and shape parameters in the matching, 
due to variations of image scale and reflection spots on the 
spheres. Overall, with some tuning of the options in feature 
extraction and l.s.m., we could find values all right in every 
test, with the same illumination, but still we ended up with more 
interest points than targets. Figure 8 shows two images of the 
sequence just after releasing the gate. Depending on the slope 
angle, it may happen that the last column of spheres remain 
still. 
  
DIEI 
    
1 L 
Figure 8: Left and right view of a test sequence. 
3.4 Labelling of the targets 
To consistently track the spheres along their trajectory, it was 
decided to estimate a polynomial function for each sphere, to 
predict its position in subsequent frame. The position in image 
space depends on the movement of each sphere and on the 
radial distortion, which reaches 400 micrometers and more at 
the image border and must therefore be accounted for. 
As a compromise between a too simple linear model and a more 
accurate model with linear changes of acceleration, we used a 
2" order polynomial, whose coefficients can be estimated from 
the position of the same target at three epochs. Sudden changes 
in speed and direction of the sand occur during the sliding of 
the specimen. This risks sometimes to render the prediction of 
the position inaccurate, because the frame rate is too low. An 
obvious solution to this problem would be increasing it, but we 
could not reduce image resolution to this aim, because we 
would have missed too many targets in such case. 
To start the prediction, the operator selects and labels 6 targets 
on the first image of the sequence. Since the specimen surface 
is planar, the approximate position of the other targets in the 
image is computed by a rectification from object to image 
plane, using the object point coordinates of the board drills. 
The labelling of the 2™ and 3™ image targets is performed by 
naming the candidate closest to the position in image 1% in 
positive x direction, i.e. along the channel: since the 
displacement in the first images applies only to the first 
columns and is still small compare to the column spacing, this 
works fine. 
In the subsequent images, the position of each target in the next 
image is predicted. Then the closest candidate to that position is 
found and assigned the label and the coefficient of the 
prediction model are updated with the new position. 
À series of checks was therefore set up to discriminate 
ambiguities and to deal with the spheres starting to roll faster 
than the sand because the pin, due to differential movements of 
the sand layers, came to the surface, becoming ineffective. 
3.5 Computation of object coordinates 
After each frame sequence for a single camera has been 
processed, yielding the pixel coordinates of each sphere in the 
sequence, coupling of the homologous spheres along the 
sequence is performed exploiting the epipolar geometry, after 
space resection of the camera stations and attitudes from the 
control point coordinates. The theoretical accuracy of the 
targets in object space is the same predicted by the simulation 
(RMS of 1.2 mm in X,Y and of 2.5 mm in Z). This means 
about 1 pixel accuracy in object space which is not really much 
for target and images of good contrast, although well within the 
specification of the experiment. Since the coordinates are 
computed with a direct formula for space intersection, the 
parallax in object space is available and can be used to check 
whether the labelling is correct. 
3.6 Results 
A series of 4 tests have been executed with different slope 
angles and different sand quality. Overall, the procedure is 
successful as far as the slope angle is not too high: in such 
cases, too many pins get out of the sand and also, because of 
higher dynamics, the prediction model fails more often. 
Apart from the initial labelling of 6 points in the first image, the 
procedure of selection, tracking, labelling and point coupling 
runs automatically. 
With medium and low slope angles, on average about 95% of 
the 176 targets were traced along the sequence in every test, 
despite a rather low frame rate. Parallaxes in object space are 
normally between 0.1 and 0.8 mm; suddendly, if the prediction 
fails, they increase by one or more order of magnitude, so the