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5 CONCLUSIONS
In this study, we proposed a non-rigid surface
registration method which computes the
correspondence between two surfaces accurately and
efficiently. The cover tree based hierarchical
clustering and NN search were utilized to reduce the
search space for correspondence points in ICP. This
reduced the computational complexity of the
correspondence computation. In addition,
registration accuracy of the proposed method is
better than the methods using conventional
clustering, especially in the noisy dataset. The
proposed negative Jacobian term of energy function
led to registration with less deformation folding.
Extending cover tree construction to consider
orientation of the surface points introduced a hybrid
similarity measure for ICP that allows capturing
more reliable correspondence points.
A cover tree-based hierarchical clustering
reduced the search space of the correspondence
candidates of each point on S from all points on T to
only (1-c
4d
)/(1-c
4
) of the points, where d is the depth
of the sub-tree that corresponds to a cluster.
Therefore, the complexity was reduced from O(n
2
)
to O(n(1-c
4d
)/(1-c
4
)). Proof of this reduction can be
found in appendix 1. In addition, a cover tree-based
NN search found the k correspondence candidates of
every point on S from the points on T. The search
space of the correspondence computation for a point
was limited to k and the complexity was reduced to
O(c
12
n log n). The proposed cover tree based NN
search was not compared with the other NN search
algorithms such as k-d tree or v-p tree. In the future,
we consider doing this comparison.
We proposed an optimization function for non-
rigid ICP algorithm, including fitting term, stiffness
term, and Jacobian term. The proposed optimization
function with Jacobian penalty term regularized the
deformation so that the resulted surface has smooth
deformation with less folding. The results showed
that the proposed method led to the smallest ratio of
the negative Jacobian compared to the other non-
rigid ICP methods. The results also showed that the
ratio of the negative Jacobian was reduced by
incorporating proposed negative Jacobian term.
One interesting result was that the proposed
method showed the best results in CT-Kinect
datasets in aspects of registration accuracy and
percentage of the negative Jacobian. The Microsoft
Kinect camera has relatively poor perception
accuracy for the depth and thus the reconstructed
surface from the depth map was very noisy and
bumpy. This result demonstrated that the cover tree
based hierarchical clustering was suitable for the
noisy datasets. We improved the registration
accuracy by taking into account the distribution and
orientation of the point for tree construction.
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