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locally linear embeddings (LLE) to map the high-dimensional observation data
from the spine model database, that are presumed to lie on a non-linear manifold,
onto a single global coordinate system of lower dimensionality. LLE preserves
neighbourhood relationships of similar spine geometries, thereby revealing the
underlying structure of the data such as spine classi
cation. Dimensionality
reduction by LLE succeeds in recovering the underlying manifold, whereas linear
embedding methods, such as Principal Component Analysis (PCA) or Multi-
Dimensional Scaling (MDS), would map various data points to nearby points in the
plane, creating distortions both in the local and global geometry.
Future work in the
field will look at extending these frameworks by enforcing
shape, texture, spatial and neighbourhood relations between the structures to
increase the reliability and repeatability of the segmentation approaches. Other
efforts are made to extend these techniques to post-operative cases. The methods
presented in this chapter can also be extended to other medical reconstruction
applications such as for the pelvis or femur, when a suf
cient amount of prior data
is available to adequately model various types pathologies.
Acknowledgments We would like to acknowledge the contributions of F. Cheriet and H. Labelle
in this research. Research funding was supported in part by the Fonds Quebecois de la Recherche
sur la Nature et les Technologies grants, the MENTOR program from the Canadian Institutes of
Health Research and the Canada Research Chairs.
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