Elastic Registration of 3D Deformable Objects

Delta errors (%)
Delta errors (%)
Delta errors (%)
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0
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Proposed
GMMREG 2.5
Proposed
GMMREG 2.5
Proposed
GMMREG 2.5
20 40 60 80 100
15%
20 40 60 80 100
22%
20 40 60 80 100
30%
Fig. 3. Robustness test comparison with the best GMMREG set (r = 2.5).
original 15% 22% 30%
Fig. 4.
Sample surface errors on a slice.
the obtained alignments may not be accurate enough for
measuring changes.
Our algorithm has been successfully applied to align 3D
lung CT scans. The polynomial model proved to be a good approximation
of the underlying physical deformation. Promising
results were obtained on the available 8 image pairs with
a median δ error of 8.41% (the mean and standard deviation
were 7.99% and 3.03%, respectively). Some of these results
are presented in Fig. 5, where we also show the achieved
alignment on grayscale slices of the original lung CT images.
For these slices, the original and transformed images were
combined as an 8 × 8 checkerboard pattern.
V. CONCLUSIONS
We have proposed a novel elastic registration method which
works without established correspondences. The basic idea
is to set-up a system of non-linear equations whose solution
directly provides the parameters of the aligning transformation.
Herein, we considered a polynomial deformation model, but
other diffeomorphism can also be used by approximating it
via a Taylor expansion. The computational complexity has
been analyzed for two alternative forms of the equations and
optimal choice between these computational schemes has also
been discussed. The efficiency and robustness of the proposed
approach have been demonstrated on a large synthetic dataset.
Our method compares favorably to two recent 3D matching
algorithms [1], [9]. Finally, the algorithm achieved promising
results in aligning lung CT images.
ACKNOWLEDGMENT
This research was partially supported by the grant
CNK80370 of the National Innovation Office (NIH) & the
Hungarian Scientific Research Fund (OTKA); the European
Union and co-financed by the European Regional Development
Fund within the project TÁMOP-4.2.1/B-09/1/KONV-
2010-0005. Lung images provided by Mediso Ltd., Budapest,
Hungary.
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