Biomedical Engineering Reference
In-Depth Information
Early approaches for morphometric analysis in the medical imaging literature
required a human rater to define a number of reliability identifiable landmark
points on a shape template and to manually locate their corresponding points on
each of the images subject to the analysis. The beginning of the modern phase
of this approach in medical imaging could perhaps be dated back to 1989 with
Bookstein's work on landmark-based morphometrics [23]. Shape transformations
are obtained by interpolating the mapping on the landmarks everywhere else in
the brain, using a thin plate spline model. This approach has been mainly used
in 2D neuroimaging studies, often restricted to the corpus callosum, since not
many anatomical structures lend themselves to 2D analysis. Moreover, defining
landmarks in 3D with high accuracy and reproducibility is often a very difficult
and impractical task, especially in large studies.
Finding shape transformations from 3D medical images requires the use of an
automated or semi-automated method for finding the deformation map
ϕ
. Algo-
rithms based on maximizing the similarity between an image treated as template
and other images in the study have been widely used for solving this deformable
registration problem[24, 33, 44-50]. Thesemethods assume that if a shape transfor-
mation renders two images similar, it implies anatomical correspondence between
the underlying anatomies. This is a reasonable assumption, but it can easily be
violated in practice, since two images can be made similar via shape transforma-
tions that do not respect the underlying anatomical correspondences. For example,
one can simply flow gray matter into gray matter, white matter into white mat-
ter, and CSF into CSF, thereby creating images that look alike, since these three
tissue types have similar intensity distributions throughout the brain, without the
underlying shape transformations reflecting true anatomical measures, since, for
example, it could morph the precentral gyrus to the postcentral gyrus.
An important issue with intensity-based transformations is that of inverse
consistency. In particular, if we attempt to match Image1 to Image2, then Image2
to Image1, we should get shape transformations that are the inverses of each other.
This condition is not necessarily met in practice, especially by image similarity
measures. Therefore, techniques that specifically impose inverse consistency have
also been examined in the literature [44, 51, 52].
Somewhat related to image intensity matching are methods optimizing in-
formation theoretic criteria, in order to find appropriate shape transformations.
The main advantage of these methods over image similarity methods is that they
can potentially be used across different imaging modalities, i.e., when tissue in-
tensities are different in two images to be matched. The most popular criterion
of optimality has been mutual information [46, 53, 54], which is maximized when
the “predictability” of the warped image based on the template is maximized,
and which tends to occur when the different tissue types in two images are well
registered.
A different class of algorithms is based on some form of feature matching
[26, 48, 55-60].
A number of features, such as edges or curves or surfaces, are
