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

Chapter 5 Quantitative shape analysis of hippocampus in AD 115
pathology
P(·; L) : R 3k ↦→ R 3k′
which consists of k ′ (< k) landmarks
X ↦→ (˜x s1 , ˜y s1 , ˜z s1 , ˜x s2 , ˜y s2 , ˜z s2 , · · · , ˜x s k ′ , ˜y s k ′ , ˜z s k ′ ) T ,
(˜x sl , ˜y sl , ˜z sl ) T ∈ {
(x s , y s , z s ) T ∈ X : p s (L) < α }
found to separate the NC from the disease group at significance level α.
(5.5)
(5.6)
Here the distribution of the surface landmarks depends on how the shapes in the
SSM are aligned, and the variation between the subgroups will differ as rigid-body
or similarity transformations can be chosen to align the shapes.
5.2.2 Shape modeling step
In the shape modeling step, instead of performing a PCA on the data consisting of
all k landmarks of the surface, only the subset of landmarks identified as different
between subpopulations in the localization step are used. We mask the Helmer-
tized landmarks in XC and re-align the masked landmarks {P(Xi; L) : Xi ∈ XC}
by Procrustes analysis to form the training set
M = { ˜ Xi : ˜ Xi is Procrustes aligned P(Xi; L), Xi ∈ XC} (5.7)
for the subregional SSM. A PCA is performed on M
˜Xi = ¯ XM + W bi
(5.8)
where ¯ XM is the mean of samples in M, W is the matrix of eigenvectors describing
the variation modes from significantly different landmarks, and bi is the vector of
coefficients of each mode.