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

90 Chapter 4 Statistical shape model of Hippocampus
where W is the matrix which consists of all eigenvectors of XX T , and b is the
vector describing the shape of X.
The SSM built upon the optimized correspondence is evaluated in terms of its
compactness, generalization ability and specificity (Davies et al., 2003).
4.1.4.1 Compactness
The compactness of the SSM is measured by the cumulative variance of the first
M variation modes modes of model
Compactness(M) =
∑Mm=1 λm
∑n−1 m=1 λm
, (4.52)
where λm, m = 1, · · · , n − 1 are the descendingly sorted eigenvalues of the covari-
ance matrix Σ, with λ1 the largest eigenvalue.
4.1.4.2 Generalization ability
The generalization ability of the SSM measures the ability of the model to represent
an unseen shape. It is measured by a leave-one-out scheme
Generalisability(M) = 1
n
n∑
X
i=1
′ i(M) − Xi 2 , (4.53)
where X ′ i(M) is the reconstruction of the shape Xi by the model based on the
training set excluding Xi with the first M modes, · is the L2-norm defined on
the vector space.
4.1.4.3 Specificity
The specificity is the expected distance between the shapes generated by model
and the shapes in the training set. It is evaluated by the generation shapes by the