Biomedical Engineering Reference
In-Depth Information
minimization of mean square errors of image pair intensities at control points.
Alternative popular techniques use robust estimators, optimization of correla-
tion ratios, optical flow, fluid-flow non-rigid deformation models and mutual
information methods to construct statistical deformation models. An extensive
review of registration methods applied to medical imaging can be found in [51].
Among recent work in this area we mention here the method of Vemuri
et al.
[52] who derived a novel curve evolution approach in a level set framework for
image intensity morphing and non-linear associated PDE for the correspond-
ing coordinate registration between an atlas and an image. Applications of the
method included a clinical study on segmentation of the corpus callosum via
morphing of a shape model defined in the atlas space, after registration of the
data with the proposed method.
In this chapter we focus on methods that explicitly combine segmentation
and registration in a variational framework. By combining registration and seg-
mentation, one can recover the image region that corresponds to the organ of
interest, given a model of this structure. Level set deformable models offer a
very flexible framework to propagate a moving front with segmentation-driven
constraints while registering the segmentation result (i.e., the level zero curve)
to a given model. Distance transforms have been successfully applied in the
past to registration problems [53-55]. In a level set framework, Paragios has
published several papers recently focusing on matching geometric shapes in a
variational framework for global as well as local registration [56-58]. The first
attempt at combining segmentation and registration in a single geometric de-
formable model framework might be attributed to Yezzi
et al.
in [59]. Their key
observation is that multiple images may be segmented by evolving a single con-
tour as well as the mappings of that contour into each image. In the context of
level set framework, multiple recent works can be referenced that incorporate
shape priors in the segmentation process as reviewed in [60]. The main trend
of the reported efforts uses a shape model and incorporates a constraint in the
energy of the geometric deformable model that forces the evolving contour to
fit to the shape model [56, 61, 62]. In an effort to derive a rigorous and complete
scheme, Paragios and Rousson [56] focused on the integration of a shape model,
defined directly in a level set space, to derive a shape prior in an energetic form
and integrate it with a data-driven variational segmentation framework. Appli-
cations of their combined registration and segmentation framework focused on
the segmentation of physically corrupted or incomplete natural images.
