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This family of methods is of great importance because it transforms the 3D
reconstruction of the spine from radiographs from a long process that had to be
performed by a specialist to a relatively fast procedure that can be performed by a
skilled user (who is not necessarily an expert in either spine anatomy or 3D
reconstruction). In [ 29 ], mild cases were reconstructed in 90 s, on average, and
severe cases in 110 s (these times include both user interactions and computations).
5 Future Directions and Conclusion
Articulated statistical models are powerful tools for the analysis of the three-
dimensional shape of the human spine. Their use for descriptive statistics of the
spine shape of large patient groups was demonstrated, and the interpretation of the
results proved to be intuitive thanks to an appealing visualization scheme. We also
provided overviews of the methods needed to build articulated statistical models
and use these as a valuable part of more complex systems that perform 3D shape
inference.
It cannot be denied that articulated models are more complex to comprehend and
handle than unstructured point clouds. However, this chapter provides the basis of a
framework to handle articulated models rigorously. Fortunately, this does not mean
overly complex methods. In most cases, it means computing the Fr
chet mean
instead of the traditional mean and using the rotation vector instead of other rep-
resentations in the computations. Once these operations are isolated in dedicated
computer methods, the additional complexity associated with articulated models
becomes remarkably easy to manage.
Articulated models, however, do necessitate more mathematical operations when
they need to be compared to absolute 3D points or reprojected on images. This can
be important when comparisons have to be performed multiple times as part of an
optimization scheme. These additional computations are, however, partly balanced
by the strong constraints that a statistical model based on an articulated model can
place on the solution space.
We most certainly have not yet explored all the scenarios in which these
articulated statistical models could be useful. For instance, in this chapter, we
discussed in length three-dimensional shape modeling of the spine, but we did not
tackle the fourth dimension. However, time is the key to numerous challenging new
applications. For instance, tracking and analyzing the effect of a disease or the effect
of a treatment on the geometry of the spine are important endeavors. Studying the
deformation of the spine under different types of strain may also reveal important
information about the spine
é
s biomechanics. Interpreting multiple images of the
spine taken at different times and in different postures using multiple modalities
would be needed to model the in
'
uence of time in a sensible way. It therefore
seems that incorporating temporal variations will offer numerous opportunities and
challenges for further developing statistical articulated models of the spine.
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