Image Processing Reference
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a model is obtained as the zero level set of a higher-dimensional embedding
function. This technique, sometimes referred as
geodesic deformable models
, has
been introduced independently by Caselles et al. [221] and Malladi et al. [222]
based on the work by Osher and Sethian [223]. Geodesic deformable models
have been applied by Yezzi et al. [156,157] to the segmentation of MR cardiac
images. Later, Niessen et al. [159] extended the method to treat multiple objects
and applied it to the segmentation of 3-D cardiac CT and MR images. Although
geodesic models have the ability to handle changes in topology, unwanted and
uncontrollable topological changes can occur in images with low-contrast edges
or with boundary gaps because this is a purely data-driven approach.
There are other types of implicit models not related to level sets. Tseng, Hwang,
and Sheehan [224], for instance, use an NN to define a continuous distance trans-
form (CDT) to the LV boundary. A feedforward NN is trained to learn the distance
function to the endocardial and epicardial contours using a few hand-segmented
image slices. The surface of the LV is then represented as the zeroes of the distance
function. The NN can generalize the boundaries of the LV in the slices not included
in the training set, thus serving as an aid to segment a 3-D image for which the
user has to provide the segmentation of a few slices only. Under an affine defor-
mation model, the distance transform is used to match different temporal frames
and to derive motion parameters. Wall thickness is computed by the centerline
method [102] using two CDT NNs for describing the endo- and epicardial surfaces.
A third approach to implicit modeling is the use of surface primitives that
are defined in implicit form. Lelieveldt et al. [160] segment thoracic 3-D MR
images using hierarchical blending of hyperquadrics [225] and concepts of con-
structive solid geometry (CSG)[226]. The method provides an automatic, coarse
segmentation of a multiple-object scene with little sensitivity to its initial place-
ment. The most representative organs in the torso (lungs, heart, liver, spleen,
and
cardiac ventricles) are incorporated in the model, which can be hierarchically
registered to the scanner coordinate system using only a few coronal, sagittal,
and transversal survey slices. Owing to the contextual information present in the
model, this sparse information has successfully been used to estimate the orien-
tation of the long axis of the LV. This allows observer-independent planning of
3-D, long-axis acquisitions in patients [227]. This technique was not designed to
estimate accurate cardiac functional parameters but can be used to generate a first
initialization for more accurate algorithms.
9.4.2
V
OLUMETRIC
M
ODELS
As opposed to the plethora of surface representations, the use of volumetric
models in the analysis and segmentation of cardiac images received little attention
in the early years. However, several techniques have appeared in the literature in
the last few years that specifically model the myocardium.
O'Donnell et al. [7,8] were the first to suggest a volumetric model to recover
myocardial motion from MR tagging. The model, termed
hybrid volumetric ventric-
uloid
, can be decomposed into three parts: (a) a thick-walled superquadric, (b) a
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