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Chapter 2 Literature Review 35
2.2.3 Establishment of correspondence
In order to build a shape model for the landmark data, the correspondence across
the data set has to be established first. A detailed review of the issue of shape
correspondence in building the shape model has been discussed in the review by
Heimann and Meinzer (2009), under the categories of mesh-to-mesh registration,
mesh-to-volume registration, volume-to-volume registration, parameterization-to-
parameterization registration, and population-based optimization. The former
three are registration-based methods without explicitly parameterizing the shape
data, while the latter two are parameterization-based.
The determination of transformation in registration or alignment, and the cor-
respondence problem are closely interrelated. The reciprocity between them is
manifest in the development and the presentation of the ICP algorithm. The
search for correspondence is expressed or implied in most registration algorithms.
Pairwise point set registration methods, such as ICP-like closest points (Brett
and Taylor, 2000; Vos et al., 2004) and non-rigid registration (Subsol et al., 1998;
Fleute and Lavallée, 1998; Shelton, 2000; Paulsen and Hilger, 2003) are used to
generate the correspondence. The model construction method by Hufnagel et al.
(2009) is based on the EM algorithm, which views the probabilistic assignments
correspondence as hidden variables. Self-organizing network is used by Ferrarini
et al. (2007) to solve the point correspondence problem in the shape modeling and
analysis.
The deformation field produced by volumetric registration between images are
also used to define the landmark correspondences (Frangi et al., 2001, 2002). The
landmarks are defined by an atlas to which the training images are registered, and
the landmarks are propagated back to the image via the inverse of the deforma-
tion from each image to the atlas, resulting in a set of corresponding landmarks.
Instead of defining and propagating the landmarks, the Statistical Deformation
Model (SDM, Rueckert et al., 2003) performs the statistical analysis directly on
the deformation field from the volumetric registration.