Image Processing Reference
In-Depth Information
9.4.3
D
EFORMATION
M
ODELS
Hitherto, we have focused on representing either the endocardial (or epicardial)
surface or the volume of the myocardial muscle. Tissue deformation, however,
can be modeled without necessarily modeling the ventricular boundaries. To
this end, material point correspondences in different temporal frames are
required. These correspondences can be obtained by matching certain geometric
properties over time (general techniques). If images are acquired using MR
tagging technology, several other approaches can be applied that exploit the
explicit correspondences inferable from tag displacements (MR tagging-based
techniques).
9.4.3.1
General Techniques
Several techniques have been proposed in the literature for deformation recovery
based on shape properties only. These methods are attractive because of their
generality. On the other hand, one must be sure of the validity of the underlying
assumptions or motion models before they are applied to analyze image sequences
corresponding to normal and pathological myocardial motion patterns.
9.4.3.1.1 Continuous Models
Amini and Duncan [95] have developed a surface model based on the assumption
of conformal motion, in which the angles between curves are preserved but not the
distances between points. The LV surface is divided into locally quadric patches
from which differential properties can be computed. Interframe patch correspon-
dences are obtained using a metric that is minimal for conformal motion. An
assumption made in this model is that the subdivision into surface patches and the
number of neighboring patches visited during the matching process are sufficient
to accommodate the largest stretching that can occur between frames. Bartels et al.
[176,229] model material deformations with multidimensional splines. The method
shares the properties of optical flow techniques to estimate motion fields. However,
these approaches do not return an explicit model of the deformations (only dis-
placements at discrete positions are provided). The main assumption of this tech-
nique is that, for a given material point, luminance is a conserved quantity. As in
optic flow techniques, with only this assumption the solution remains undercon-
strained and, therefore, a regularization term must be added. Illustrations of the
method applied to 2-D cardiac x-ray sequences are provided and the formulation
is readily extended to 3-D sequences. However, it is questionable whether lumi-
nance conservation can provide a reliable cue for deformation recovery in regions
with homogeneous intensity or in the presence of imaging artifacts and noise. For
MR tagging, in particular, the approach must be adapted because luminance is not
conserved owing to the physics of the imaging process [84].
Rueckert et al. [230] originally proposed the statistical deformation models
(SDMs) with application to brain modeling, and they have since been applied to
3-D cardiac modeling as well. A model is constructed by registering several
training sets using multilevel free-form deformations. Because registration is
Search WWH ::
Custom Search