International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
3.2 Parametrization of the RANSAC algorithm
Two parameters are involved in the RANSAC algorithm: the
number of iterations £ and the tolerance e for the detection of the
outliers. Experiments have been carried out in order to determine
the influence of these parameters.
The figure 6 indicates that a too small value of ¢ generates addi-
tional local minima. On the other hand, values larger than 50 do
not improve significantly the global convexity of the function.
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| t=50
| t=100
0.14 t=200 |
e 1-500
0.12% au = à z ie Ll à 1 1 1 =
-10 8 -6 -4 -2 0 2 4 6 8 10
X translation (m)
Figure 6: Evaluation function for a translation with different
numbers of iterations £ in the RANSAC procedure.
The figure 7 shows that a smaller value of € gives a more convex
curve, but discards a larger amount of laser points.
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e
w
Proportion of outliers
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v a
À À
0.15
10 cm
0.1 25 cm
50cm |
i 75cm |
0.05| E00 ema
ot i i i 1 1 1 L i
-10 -8 -6 -4 -2 0 2 4 6 8 10
X translation (m)
Figure 7: Evaluation function for a translation with different val-
ues of the tolerance e in the RANSAC procedure.
For the further experiments presented in this article, the values
t — 50 and e — 50 cm have been selected. Nevertheless we
should point out that the tests were limited to one set of data, and
that the stability of the procedure should be evaluated against a
larger range of input data characteristics: aerial image resolution,
3D points density, laser accuracy, ...
3.3 Models of deformation
The registration approach has been tested against different defor-
mations applied to a cloud of laser points, which was originally
"perfectly" registered with the aerial image. These are mostly
rigid deformation: translation and rotation, but also curvature
along one of the planimetric directions. The convexity of the
evaluation function is tested for each of these deformations.
Planimetric Translation: the figure 8 presents a very sharp
global minimum, which may be reach from distances larger than
10 m. This is more than sufficient for an automatic calibration.
Proportion of outliers
02-|
0.15 À...
4
Mr : me: — 2
Y axis translation A ;
X axis translation
Figure 8: Evaluation function for planimetric translations.
Vertical Translation: on the other hand, the figure 9 indicates
that a vertical translation produces also a global minimum, but
less sharp than for planimetric translations. We should expect in
that case a not so good precision in the registration of the data.
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| Y axis |
| Zaxis |
0.15 Lorn m vs eden eerte dee - ds 1 1 + *
-40 -30 -20 -10 0 10 20 30 40
Translation (m)
Figure 9: Evaluation function for vertical translations.
Rotation: rotations around the planimetric and the vertical axes
present also a different behaviour (see the figure 10). But in that
case, the rotations around the vertical axis generate the sharper
minimum, which is not of great interest for calibration purposes,
since they are less likely to occur than rotations around horizontal
axes.
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