Image Processing Reference
In-Depth Information
is that the deformation is small. Meshes at two time instants are registered through
an energy-minimizing approach matching differential image properties (curvature
and gradient). Papademetris et al. [190,191] have proposed a deformation model
inspired by continuum mechanics. The method recovers a dense deformation field
using point correspondences obtained with the point-tracking algorithm of Shi et
al. [142]. Regularization is accomplished by measuring the internal energy of the
myocardial tissue assuming a linear elastic body model. This is equivalent to a
regularization term on the strain tensor space and not on the displacement
field. * Anisotropy of the fibrous structure of the LV is accounted for in the internal
energy by making the model stiffer in the fiber direction [233].
Recently, Sermesant et al. [171] presented a technique for the integration of
information from multiple modalities into a biomechanical model of the heart.
Their representation is based on a tetrahedral mesh for the myocardium of both
left and RVs. The method registers the model to multimodal image data by using
a hierarchical registration technique based on a modification of the ICP algorithm
to intensity and gradient features. The model incorporates both anatomical and
functional information that is inherited from the imaging sources: fiber orienta-
tion from diffusion tensor imaging and anatomical labels from the visible human
project. This model has been applied for the segmentation of SPECT and MR
image sequences. More recently the authors incorporated electrical information
into the template to generate an electromechanically coupled model [234].
Finally, Klein and Huesman [183] developed a 4-D deformable model for
motion compensation in dynamic cardiac PET images. The technique uses
temporal continuity and a consistency constraint to ensure that the motion
between two distant frames is consistent with that of two consecutive frames.
The method also uses a nonuniform elastic material model to obtain better
motion estimates.
9.4.3.2
MR Tagging-Based Techniques
The introduction of MR tagging has stimulated researchers to develop models of
cardiac tissue deformation. Compared to motion recovery based on point corre-
spondences or optic flow, MR tagging has the advantage that, in principle, material
point correspondences can be estimated from tag information. In this subsection,
different approaches for modeling the deformation fields are reviewed. Accurate
tag localization is a prerequisite for subsequent deformation recovery and, there-
fore, it is closely related to deformation models. A brief overview of tag-tracking
techniques is given in Appendix B .
9.4.3.2.1 Continuous Models
Several approaches have been proposed in which the parameterization of the
deformation field is a continuous function. The availability of continuous defor-
mation maps allows computation of local strains. Young et al., for instance,
For a survey of optic flow methods in computer vision, see Beauchemin and Barron [ 90 ].
*
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