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

Chapter 2 Literature Review 33
The triangulation of these landmarks forms a surface mesh of the anatomical object
of interest. In general, the shape modeling by SSMs is based on this representation.
In the context where the topology of the mesh is less relevant, shape information
is adequately described by the landmark representation, giving rise to the name
‘Point Distribution Model’ (PDM, Cootes et al., 1992), which covers the majority
of current shape models (for survey, see Heimann and Meinzer, 2009).
Apart from the representation by a set of landmarks, other approaches have been
proposed in the literature of image registration, segmentation, and shape analysis.
By taking advantage of the fact that most biological objects are homeomorphic
to a sphere, one popular method for shape representation is the decomposition of
the landmark coordinates into spherical harmonics (SPHARM, Brechbühler et al.,
1995; Matheny and Goldgof, 1995), which are the eigen-functions for the angular
part of the Laplacian operator. Wavelet technique on contour (Davatzikos et al.,
2003) and sphere (Laga et al., 2006; Nain et al., 2007) has also been suggested
for shape description. Medial representation (M-rep, Pizer et al., 1999, 2003;
Yushkevich et al., 2003b) models geometry of the object by the skeleton of its
medial locus with spokes normal to surface representing the boundary. Other
representations include spline based methods (Tsagaan et al., 2001, 2002), level
set (Tsai et al., 2003; Pohl et al., 2006).
2.2.2 Alignment of point sets
For a given configuration of landmarks, its shape, or the size-and-shape, forms an
equivalence class associated with a Euclidean similarity, or rigid transformation
group respectively. Without loss of generality, the shape or size-and-shape of the
landmarks can be represented by one representative from its respective equivalence
class. It may be translated to the origin and aligned to a specified orientation
to preserve its size-and-shape, and scaled to a particular size for the analysis of
its shape. Procrustes analysis and iterative closest point (ICP) are two major
approaches to align the configuration point sets in shape analysis.