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

72 Chapter 4 Statistical shape model of Hippocampus
In this chapter, the construction of SSMs from hippocampal surfaces by the op-
timization of minimum description length (MDL) and the evaluation of the con-
structed SSMs are described. We also presented a symmetric consistent method
to extrapolate the SSM to the unseen data and estimate the shape parameters.
The results of the SSM building have been used in “Increasing power to predict
mild cognitive impairment conversion to Alzheimer’s disease using hippocampal
atrophy rate and statistical shape models,” in Medical Imaging Compution and
Computer-Aided Intervention – MICCAI 2010, LNCS, vol. 6362. The work of
consistent estimation of shape parameters in SSM has been submitted to SPIE
Medical Imaging 2012.
4.1 Building the shape model
The SSM is built on a training set of hippocampal surfaces {Xi : i = 1, · · · , n}
in which each surface Xi is represented as a triangulated mesh. The triangulated
meshes are usually produced from binary images of segmented label maps by
marching cube algorithm (Lorensen and Cline, 1987), and smoothed to remove
aliasing and terracing artifacts.
For each surface Xi, the first step is to find a parameterization
fi : U × V ↦→ Xi ⊂ R 3 , i = 1, · · · , n (4.1)
which gives the position of the point on the 2D surface of the shape given the
parameter (u, v) in the parameter space U ×V . In order to build the shape model,
we expect that the point fi(u0, v0) on the shape surface i, and the point fj(u0, v0)
on the shape surface j with the same parameter (u0, v0), would correspond to the
same landmark.
For instance, we have two parameterized surfaces of hippocampi fi and fj. For a
landmark on hippocampus, say the head of hippocampus, fi(uhi , vhi ) and fj(uhj , vhj )
their parameters (uhi , vhi ) = (uhj , vhj ) = (uh, vh) should be the same. This can be