![](bg4.png)
points in the dataset, starting with only a few points
and increase the number in every iteration step. The
computational complexity is reduced in average to
O((0.5*N
j
)*(0.5*N
i
)) assuming we do not stop the
iteration until we reach the end (M
n
mesh).
If the iteration process is stopped, because the
ICP reached the minimum, the performance of our
implementation is always better than
O((0.5*N
j
)*(0.5*N
i
)). Our Progressive Mesh ICP
experiments need in average 25% of the time of the
standard ICP implementation.
6 FURTHER EXTENSIONS
Many of known modifications of the ICP can be
combined with the PMICP without loss of
generalization. For example the performance in the
closest points search is often increased using Kd-
Trees implementations (Z. Zhang, 1994) to
O(N
j
*log(N
i
)). The Kd-Tree search could be used in
addition to our PMICP leading to a significant
improvement in speed especially in the higher level
of details. The ICP algorithm is known to be very
sensitive to wrong initial poses of the two datasets
because of the fact, that the ICP will always
converge to the local minimum (which is of course
commonly not identical to the global minimum). So
the determination of the optimal initial start value
for the number of points in the mesh is very
important. In the current implementation the level of
detail in the Progressive Mesh is connected to
number of iterations in the ICP. Finding the optimal
number of points for each iteration step in ICP
iterations is one of possible improvements in the
next steps of our research.
7 CONCLUSIONS
We described a system to align range data surfaces
in a context of industrial process automation. We
focused on the improvements in the refinement step
of our hierarchical object localization system. The
well known and proven ICP Algorithm is modified
with the use of Progressive Meshes. To be sure to
meet the requirements of different applications we
evaluated our system with test scenarios, which
cover many types of possible range data scenes.
The simulation of real scenes offers the
possibility to use our approach in many scenarios.
The described two-step object localization is
integrated in our system robotic bin picking covering
different application scenarios (Boehnke, 2007).
ACKNOWLEDGEMENTS
The author would like to thank S. Rusinkiewicz for
providing the datasets. This work was supported in
part by VMT (Pepperl+Fuchs Group) in Mannheim/
Germany. The author wants to thank P. Roebrock,
M. Kleinkes, W. Neddermeyer, W. Winkler, and K.
Lehmann for their support in this project.
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