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Fig. 8.7
Corkes sequence. Each plot represents an element of the observed homography
velocity matrix
A
8.6
Conclusion
In this chapter, we proposed an observer for the homographies defined on
SL
(3)
and their velocities defined on
(3). We proved that the observer is almost globally
stable. We also proved that isolated critical points exist but that they are far from the
equilibrium point and unstable. We performed several simulations with ground truth
to validate the theoretical results. Experiments with real data show that the observer
performs well even when the constant velocity assumption does not hold.
sl
Acknowledgements.
The authors gratefully acknowledge the contribution of INRIA, CNRS
and ANU. This research was partly supported by the Australian Research Council through
discovery grant DP0987411 and the PEGASE EU project.
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