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

Chapter 4 Statistical shape model of Hippocampus 107
4.4 Summary
In this chapter, we described the building of SSMs from the training shape data.
The shape surfaces are first parameterized on a unit sphere by area-preserving
mapping. The spherical parameterization of surfaces are then flattend to the
shape image representation, which are re-parameterized to eliminate the spurious
correspondences by groupwise optimization. The re-parameterization on the shape
image is analogous to the non-rigid deformation in image registration, which is
computed with fluid regularization. A fast algorithm solving fluid velocity using
discrete sine transform is applied to regularize the shape reparameterization. The
result SSM based on the correspondence in the parameter space is evaluated in
terms of its compactness, generalization ability and specificity.
Once the SSM is built, it is used to estimate the shape parameters of unseen
surfaces or point sets. An EM algorithm is used to estimate the transformation
and the deformation of the model to fit the data with correspondence as the hidden
variable. The data term to be optimized is symmetric between the model and the
surface data in order to impose the consistency of the estimation. The SSM also
provide the shape prior for the MAP estimator which includes a regularization
term. The consistent symmetric estimation is shown to improve the details and
the precision of the reconstruction of the shape surface from the model, and the
shape prior regularization is necessary to avoid the problem of overfitting. With
the presence of noises, mismatches, and disappearance of the correspondence, the
regularized MAP gives more accurate estimation of shape parameters.