![](bg5.png)
4.2 Ill-Conditioned Motion
Empirical evidence suggests that the instances where
the tilt estimation fails are the ones where the transla-
tion t is close to either a pure x-translation or a pure y-
translation. Randomly generating homographies with
this pattern of motion provides further evidence for
this. It can further be seen that a pure x-translation
gives rise to a poor estimate of ψ, while a pure y-
translation results in a poor estimate of θ. Results for
this experiment are presented in Figures 6 and 7. The-
oretical understanding of this will be necessary if the
instability is to be addressed.
0 2 4 6 8 10
homography number
−50
0
50
θ (degrees)
estimated θ true θ
0 2 4 6 8 10
homography number
−10
−5
0
5
10
15
ψ (degrees)
estimated ψ true ψ
Figure 6: When t is a pure x-translation, ψ seems to be
unreliably estimated.
0 2 4 6 8 10
homography number
−15
−10
−5
0
5
10
θ (degrees)
estimated θ true θ
0 2 4 6 8 10
homography number
−30
−20
−10
0
10
20
30
40
50
ψ (degrees)
estimated ψ true ψ
Figure 7: When t is a pure y-translation, θ seems to be un-
reliably estimated.
5 CONCLUSIONS
Tilt estimation is a prerequisite for constructing con-
sistent floor maps using images from a tilted camera.
In this paper we have presented an iterative scheme
for determining the tilt from a single homography.
Experiments with a simple path reconstruction have
been conducted, which show that if the tilt is rectified
then the correct Euclidean motion can be found using
the QR decomposition. Experiments using synthetic
data show that the estimated tilt angles are close to
the true tilt angles in most instances, however some
especially troublesome motions have been found.
ACKNOWLEDGEMENTS
This work has been funded by the Swedish Founda-
tion for Strategic Research through the SSF project
ENGROSS, http://www.engross.lth.se.
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