Docteur de l'université Automatic Segmentation and Shape Analysis ...

Chapter 2 Literature Review 37
2.2.4 Dimension reduction
In statistical modeling using SSM, PCA is usually used to determine a lower
dimensional subspace that accounts for most of the variance observed in a training
set (Cootes et al., 1992). High dimensional representation of shape data eq. (2.9) is
projected to the subspace, and reconstructed as the approximation of the original
shape in the valid space of the shapes of interest. To use PCA for shape analysis
requires the corresponding point being aligned to remove the false variation. The
principal shape components can be computed by an eigenanalysis on the covariance
matrix or an SVD on the data matrix. In practice, the first principal components
explaining approximately 90–98% of the total variance span a subspace in which
every valid shape can be approximated (Heimann and Meinzer, 2009).
Apart from PCA, independent component analysis (ICA, for review, see Hyvärinen
et al., 2001) using joint approximated diagonalization of eigenmatrices (Cardoso,
1999) has been used in shape modeling, which permits more localized variations
(Üzümcü et al., 2003; Suinesiaputra et al., 2004). Nonlinear modeling using kernel
PCA (Schölkopf et al., 1998) has also been applied in the shape analysis (Twining
and Taylor, 2001).
2.3 Measuring the hippocampal atrophy
The MRI studies into AD are interested in the atrophy of hippocampus in partic-
ular. Assessment of hippocampal atrophy on the MR images can be carried out at
a single time point by comparing the hippocampal volume with the average of the
population, or longitudinally tracking the progression of the disease and its effect
on the hippocampus. The volume reduction and shape change associated with the
atrophy are observable and can be quantified on high-resolution MR images.