Image Processing Reference
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and (4) flexible hierarchical models encompassing a reduced set of DOFs coarsely
describing shape, plus an extended set of DOFs giving extra flexibility to the
model. Representative of this family are superquadrics with free-form deforma-
tions. Complexity is, to some extent, related to the computational demands of an
algorithm. Highly flexible algorithms are usually related to higher computation
time for deforming them to a given image data set.
*
On the other hand, it is also
a measure of the ability of a modeling technique to accommodate for fine shape
details.
Although idealized models of ventricular geometry (mainly ellipsoids or
ellipsoidal shells) are appealing for their parsimony and for historical reasons,
Table 9.1
shows that no study has quantitatively demonstrated their accuracy
in computing simple measurements such as LVV and EF. Compact models have
developed in two different directions. On the one hand, in particular for the
RV, some researchers have evaluated combinations of simple models that
roughly derive RVV from a small number of linear measurements [113,117].
The models, however, remain highly constrained and have been tested on
ex
vivo
casts experiments only. A second direction has been to trade off the
compactness of the superquadric models and their flexibility without the need
of hierarchical decompositions [5,6]. In this manner, flexibility is added in an
elegant way by which each parameter function has an interpretation in terms
of local and global shape changes. Park et al. [163] have demonstrated the
application of this technique with a cascade of SPAMM sequences that allow
for motion analysis in the whole cardiac sequence, overcoming some of the
limitations of tag fading in MR.
Most approaches that reached the stage of quantitative evaluation are based
on flexible or hierarchical representations. Both present challenges and advan-
tages. Flexible representations (e.g., polyhedral meshes or harmonic decomposi-
tions) are highly versatile and can accommodate detailed shape variations. Most
of the quantitative evaluation studies have been reported on local flexible models,
most of which are able to cope even with complex topologies. On the other hand,
restricting the space of possible shapes is usually difficult or requires substantial
manual intervention or guidance [107,108,110,169]. Hierarchical or top-down
approaches aim at a reduction in computational time and at improving robustness
by incrementally unconstraining the space of allowed shape variation [7-9,35,
114,116]. One weak point of hierarchical approaches is the need for
ad hoc
scheduling mechanisms to determine when one level in the representation hier-
archy should be fixed and a new level added, and up to which level the model
should be refined. Furthermore, optimization procedures involved in the recovery
of hierarchical models have to be designed with particular care. It is unclear how
it can be ensured that a succession of optimizations at different modeling levels
actually leads to optimum global deformation. Also, the questions arise regarding
how to link different levels of model detail with the resolution of the underlying
*
Here we disregard the obvious rigid transformation parameters to instantiate the model in world
coordinates.
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