Image Processing Reference
In-Depth Information
A rather different approach is the one by Pentland and Horowitz [111], who
applied modal analysis and FE to reconstruct a 3-D model of the LV from x-ray
transmission data. Modal analysis offers a principled physically based strategy
for reducing the number of degrees of freedom (DOF) of the model and to obtain
an overconstrained problem for shape recovery. Optic flow is used to derive the
deformation of the 3-D model from the 2-D views, and a Kalman filter is used
for tracking the structures over time.
Instead of working with multiple cross sections or projection images, Gosh-
tasby and Turner [119] segment left- and right-ventricular endocardial surfaces
from 3-D flow-enhanced MR images. In this case, the endocardial surface is
modeled as a deformable cylinder using rational Gaussian surfaces [205]. The
model is deformed to fit the zero-crossings of the image Laplacian. To avoid
attraction by spurious edges, prior to fitting, the feature map is masked by a rough
LV region of interest obtained by intensity thresholding.
Some efforts have also been directed toward
geometric modeling of the RV
.
This chamber has a more complex shape than the LV. Spinale et al. [110] fit
semiellipses to model the crescentic shape of the RV from biplane ventriculo-
grams. Czegledy and Katz [113] model the RV using a crescentic cross-sectional
model composed of two intersecting circles of different radii. This 3-D model is
parameterized by only a few linear dimensions that can be measured directly
from CT, MR, or US images. From these dimensions, the RV volume is approx-
imated using analytical expressions. Denslow [117] models the RV as the differ-
ence of two ellipsoids (an ellipsoidal shell model). The parameters from this shell
are estimated from MR images (a long-axis and a four-chamber view) and from
those, volume estimates can be derived. Sacks et al. [115] model the endocardial
and epicardial walls of the RV by biquadric surface patches (contours were
manually traced from MR images), and have studied surface curvature and wall
thickness changes during the cardiac cycle using this representation.
9.4.1.2
Discrete Models
An alternative to continuous surface representations is the use of discrete surface
models. Several methods have been reported in the literature, and they can be
grouped as shown in the following subsection.
9.4.1.2.1 Physics-Based Models
Physics-based modeling has attracted the attention of many computer vision
researchers. In this framework, surface recovery is cast into the deformation of
a virtual body (the geometric model together with its material properties) under
virtual external forces derived from image or point features, or user-defined
constraints. In the final (deformed) state, this virtual body reaches an equilibrium
between the external forces and internal (regularization) constraints. A good
overview of the theory of physics-based deformable models and its applications
can be found in the topic by Metaxas [206] and in the survey by McInerney and
Terzopoulos [3].
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