We proposed a mathematically sound and uniﬁed framework for the computation
of model parameters and observation parameters and succeeded in determining
a closed form solution for optimizing the associated criterion alternately for all
parameters. Experiments showed that our algorithm works well and leads to
plausible results. It seems to be robust to diﬀerent initial mean shape choices
and is stable even for small numbers of observations. We showed the eﬃciency of
our approach compared with a SSM built by the traditional ICP and PCA for a
typical correspondence problem on synthetic data: The SSM based on the EM-
ICP models the whole data set, it is able to represent the ellipsoids featuring
a bump and those without as that deformation information is included in its
variability model. On the other hand, the results show that the SSM based on
the ICP is not able to model the bump. This is due to the fact that the ICP
only takes into account the closest point when searching for correspondence,
thus, the point on top of the bump is not involved in the registration process.
The EM-ICP, however, evaluates the correspondence probability of all points,
therefore, also the point on top of the bump is matched. We illustrated these
two concepts in ﬁgure 1d). Furthermore, in the test series on putamen data,
our SSM achieved superior results in both performance measures. Especially the
values of the maximal distance illustrate the beneﬁt of the new approach. From
a theoretical point of view, a very powerful feature of our method is that we are
optimizing a unique criterion. Thus, the convergence is ensured.
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This work is supported by a grant from the DFG, HA2355.