132
A» ; Be
—_—y
1] 2 BER 101 11 19 20 21
4| 5 Nm 13114 22 23 24
7 8-9 25 26 27
X : X
ratio: x:y:z ratio: X:y:z
model: 10:7:5 Success model: 10:10:10
test: 10:7:5 test: B:5:5
Ji failure
Fig. 7: Results for a asymmetric corner and a subpart of a corner
Rotation. We analyse now the effect of rotation. The test will thus be rotated around the z-axis. Because we know the
matching to be influenced by principal moments (Besl, 1992), the same experiment is also performed with an asymmetric
corner. The final error for a symmetric and an asymmetric corner object is plotted in figure 8.
error
6
3 ratio: x:y:z
4] = r | 10:10:10
— —À 10:7:5
X angle
0 50. 100 150 200 250 300 350
Fig. 8: Matching results for rotated corners
The plot reveals a zone of convergence (final error below one) that is about +/- 40 degrees for the symmetric corner and
slightly larger for the asymmetric one. Comparing these results with the ones obtained for the translated corners we see that
the rotation angle is the major constraint for the closest point matching algorithm.
5. CONCLUSIONS
We presented a number of recognition experiments conducted in order to assess the capability of the closest point matching
algorithm to recognise objects measured by range images.
The presented results show that the translation between test and model is of minor influence to the success. On the contrary,
the rotation limits the convergence to a zone of about 80 degrees. Asymmetric objects show a slightly better performance,
whereas subparts can only be matched for some starting points.
The limited performance of subpart matching will be important for designing recognition system, where the closest point
matching algorithm is used to recognise an object measured from a single point of view. To overcome the large dependence
of the convergence on the starting points, one has to place the test object at different positions and orientations. The distance
between these heuristic positions should be smaller than the convergence zone of the algorithm.
At a first glance the necessity of multiple starting points seems to introduce much overhead. But since the convergence zone
is relatively large, the number of starting points is quite low. Furthermore the algorithm converges quickly and allows
subsampling of the point set representing the objects, which significantly reduces the computing time. These facts lead to a
feasible method for the recognition of arbitrary shapes.
6. ACKNOWLEDGEMENT
This research has been funded by the Swiss national Priority Program in Informatics, Knowledge-based systems, under
project number 5003-344336.
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995
