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Pose estimates were computed either in a single stage or in two stages: the first stage
estimated the box rotation and translation in their joint 6D parameter space; an optional
second stage attempted to refine the translation estimate in its 3D parameter space while
keeping the estimated rotation fixed. Different resolutions of parameter space analysis
were investigated: the sizes of parameter buckets, histogram bins, and mean-shift radii
took identical rotational values {0.02, 0.03, 0.04, 0.05}
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with their translational value
fixed at 30 mm for the first stage of estimation, and with identical translational values
{5, 10, 15} mm for the second stage. Estimator variants with only the first stage and
with both stages were run on the test data, making a total of 16 tested variants. Run
times of the estimators were recorded for a C++ implementation on a single CPU at 3.0
GHz. The measured times included building of the model hash table.
For each of the 10 box views, 100 data sets were acquired, yielding a total of 1000
pose estimates. Plots of the two kinds of error statistics, each for rotation and translation
estimates, versus expected run time for the 16 estimator variants are presented in fig. 4.
There are five main observations to be noted.
– The two kinds of error statistics agree, suggesting they are both reasonable error
measures for the estimates.
– The accuracy of the estimator is sufficient for manipulation tasks across all tested
variants.
– There is a trade off between rotational and translational accuracy.
– The highest rotational accuracy was achieved by estimators with the highest rota-
tional resolution; the highest translational accuracy was achieved by the estimator
with the lowest rotational resolution and the medium translational resolution in the
second estimation stage.
– The run time increases for estimator variants with higher resolution of parameter
space analysis; rotational resolution is much more expensive than translational res-
olution.
The last observation can be explained by the fact that smaller buckets in parameter
space need more sampling in order to get significantly filled. Sampling of full pose
parameters is much more expensive than of just translations, as done in the second
stage of estimation, which is why the translational resolution has less effect on run time
than the rotational resolution in the present statistics.
A less intuitive result is the apparent trade off between rotational and translational
accuracy. This suggests that, for the range of estimator variants here investigated, the
allover estimation error does not greatly vary but is merely distributed to varying pro-
portions between the rotational and translational degrees of freedom. As a consequence,
one should use different variants of the estimator for rotational and translational param-
eters. This point, however, deserves further investigation.
It should be noted that the run times given are mainly a relative measure of the costs
of the estimator variants. The absolute timings can be greatly improved by i) distribut-
ing parameter sampling and clustering across several CPUs, ii) building the model hash
tables before execution of the estimators, and iii) some additional algorithmic optimiza-
tions.
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The full rotational parameter range is the unit sphere; cf. eq. (4).
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