Image Processing Reference
In-Depth Information
Gaussian curvature and a polynomial stretching model by means of the relation-
ship
(,, ,, , , , )
EFG
ττ τ τ τ
τ
K
K
=+
τ
uv u v
(9.14)
2
2
where
f
(
) is the polynomial stretching model (linear or quadratic) [96],
E
,
F
, and
G
are the coefficients of the first fundamental form [273], and (
u
,
v
) are coordi-
nates of a local parameterization of the surface patch. Mishra et al. [96] present
a method to solve for
⋅
in Equation 14 and show that the local epicardial stretching
factors computed over the cardiac cycle follow a similar evolution to the temporal
variation of the principal strains obtained by Young et al. [109] using strain
analysis techniques.
τ
M
ODEL
-S
PECIFIC
S
HAPE
D
ESCRIPTORS
Geometrical Cardiogram (GCG)
Azhari et al. [274] describe a method for classification of normal and abnormal
LV geometries by defining a geometrical cardiogram (GCG), a helical sampling
of the LV geometry from apex to base [275]. The GCG at end systole and at end
diastole are subsequently analyzed via a Karhunen-Loeve transform (KLT) to
compress their information. A truncated set of the KLT basis vectors is used to
project the GCG of individual patients into a lower-dimensional space, and the
mean-square error between the projected and the original GCG is used to dis-
criminate between a normal and an abnormal LV [276]. From this vectorial
representation, LVV, EF [275], and WT [100] can also be computed.
Deformable Superquadric and Related Models
One of the first 3-D primitives used to model the LV was the superquadric. It is
a natural extension of the simplified geometric models originally used in 2DE
[14] and angiocardiography [10-13]. Along with three main axes indicating
principal dimensions, the superquadric models can be provided with additional
parametric deformations such as linear tapering and bending [9,118], free-form
deformations [122], displacement fields [7,8], or parametric functions providing
information about radial and longitudinal contraction, twisting motion, and defor-
mation of the LV long axis [5,6] and wall thickness [6]. In particular, Park et al.
[5,6] suggest resolution of deformation and motion into a few parametric func-
tions that can be presented to the clinician in the form of simple plots. All these
functions are either independent of the total LV volume (e.g., twisting) or can be
normalized with respect to the dimensions of the LV (e.g., radial and longitudinal
contraction). This allows interpatient comparisons of contraction and shape
change.
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