Image Processing Reference
In-Depth Information
where
E
= [
E
ij
] is the
Green strain tensor
[106]
3
1
2
∂
∂
x
y
∂
∂
x
y
∑
k
k
E
=
−
δ
ij
ij
i
j
k
=
1
(9.10)
3
+
∂
∂
u
y
1
2
∂
∂
u
y
∂
∂
u
y
∂
∂
u
y
∑
1
j
=
i
−
k
k
j
i
i
j
k
=
where
δ
ij
is the Kronecker tensor. From the strain tensor it is possible to decom-
pose the strains into two groups: axial and shear strains. The former correspond
to the diagonal elements and represent changes in length aligned with the axes
of the reference frame and the latter correspond to off-diagonal terms or defor-
mations where the two axes are coupled.
9.4
OVERVIEW OF MODELING TECHNIQUES
Great effort has been devoted to the analysis and segmentation of cardiac images
by methods guided by prior geometric knowledge. When focusing on the way
models are geometrically represented, three main categories can be distinguished:
surface models, volumetric models, and deformation models. In all cases both
discrete and continuous models have been proposed, as well as implicitly defined
surface models (Figure 9.2).
Alternatively, one may classify model-based approaches by considering the
information that is used as input for model recovery. This categorization is highly
influenced by the imaging modality for which the method has been developed.
Continuous models
Discrete models
Surface models
Implicitly defined models
Volumetric models
Continuous models
Discrete models
Deformation models
Continuous models
Discrete models
FIGURE 9.2
Proposed taxonomy of cardiac modeling approaches.
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