Image Processing Reference
In-Depth Information
Global Motion Analysis Based On Departure from an Affine
Model
Friboulet et al. [132] modeled the LV using a polyhedral mesh at each frame of
the cardiac cycle. The state of the LV was characterized by the center of gravity
and the moments of inertia of the polyhedral mesh. The deformation between
two frames was hypothesized to follow an affine model. By defining a metric to
compare two different polyhedral representations, the authors were able to quan-
tify the difference between the actual interframe deformation and the correspond-
ing deformation derived from an affine motion model. Several parameters of
global motion are then derived: the temporal variation of the longitudinal and
transversal moments of inertia, and the proportion of total motion explained by
the affine model. By means of case studies, it was demonstrated that these global
indices are able to discriminate between normal (EF
=
0.71) and highly diseased
(EF
0.1) LVs. On the other hand, the global nature of these indices precludes
the quantification of localized, inhomogeneous dysfunction of the LV.
=
Motion Decomposition through Planispheric Transformation
Declerck et al. [123] have proposed a canonical decomposition of cardiac motion
into three components: radial motion, twisting motion around the apicobasal axis,
and long-axis shortening. This decomposition is achieved through a transforma-
tion of the Cartesian coordinates of the LV wall to a planispheric space. In this
space, a 4-D transformation is defined that regularly and smoothly parameterizes
the spatiotemporal variation of the LV wall. Because the canonical decomposition
of motion can be directly obtained in the planispheric space, these descriptors
also vary smoothly along the cardiac cycle. Finally, by tracking the position of
material points over time in the planispheric space and subsequently mapping to
Cartesian coordinates, it is possible to reconstruct their 3-D trajectories.
Modal Analysis: Deformation Spectrum
Nastar and Ayache have introduced the concept of the deformation spectrum
[140], which can be applied within the framework of modal analysis [194]. The
deformation spectrum is the graph representing the value of the modal amplitudes
as a function of mode index. The deformation spectrum corresponding to the
deformation between two image frames describes which modes are excited in
order to deform one object into another. It also gives an indication of the strain
energy [140] of the deformation. As a consequence, a pure rigid deformation has
zero strain energy. Two deformations are said to be similar when the correspond-
ing deformation fields are equivalent up to a rigid transformation. In order to
measure the dissimilarity of two deformation fields, the lower-order modes related
to rigid transformation are discarded. The difference of the deformation spectra
so computed can be used to define a metric between shapes (e.g., the LV in two
phases of the cardiac cycle) that can be applied to classify them into specific
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