carried out. Figure 3 shows the error (in pixels)
between lines through different angles.
There can be seen how the error is minimum at
the position where the transformation was
calculated, it means at its second motion or third
image. This error varies depending on the position of
the tool, it increases with higher angles, when the
position of the tool separates from the minimum
error position. Figure 4 compares the algorithm
performance for 5 and 20 degrees motion angles.
There the error varies differently. In the case of 5
degrees the error increases greatly with each motion
that separates the tool from the minimum error
position. While for 20 degrees this error also
increments, but remains stable.
This results validate the line-based algorithm and its
low computational cost demonstrate its real-time
performance. The error increasement with large
position separations is mainly product of the
deviation at the intersection point. It can be seen that
the calculation of vd has a great impact in the result
and future work should be focused in this issue.
4 CONCLUSIONS
A method to estimate the relative orientation of an
object with respect to a camera has been proposed.
The object assumed was represented by feature
lines. 2D correspondences of a line due to known 3D
transformations of the object were the information
used to calculate its orientation. We showed that
with only two rotations the angular variation
between lines provides sufficient information to
estimate the relative orientation. This motion
analysis led to address questions as the uniqueness
of solution for the minimum number of movements
and possible motion patterns to solve it directly. In
the case of controlled motions, one component
rotations through normal axes simplify calculations
to provide a robust technique to estimate the relative
orientation with no initial conditions defined.
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Orientation error
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Figure 3: Relative error in pixels using the rotational
motion analysis algorithm.
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Orientation error increment for 5 degrees motion angle
Angles α1+ α2 (degrees)
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Orientation error increment for 20 degrees motion angle
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Orientation error increment for 20 degrees motion angle
Relative error (pixels)
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Figure 4: Algorithm performance comparation between 5
and 20 degrees, with a first rotation α1 followed by