Image Processing Reference
In-Depth Information
motion is recovered using preprocessed MR tagging data obtained by sampling
the LV midwall surface from the 3-D FE model of Young and Axel [77].
Staib and Duncan [121] use sinusoidal basis functions to decompose the
endocardial surface of the LV. The overall smoothness of the surface is controlled
by decreasing the number of harmonics in the Fourier expansion. Model recovery
is cast into a Bayesian framework in which prior statistics of the Fourier coeffi-
cients are used to further limit the flexibility of the model. Matheny and Goldgof
[120] compare different 3-D and 4-D surface harmonic descriptions for shape
recovery. Time can be incorporated in two ways in the model: (a) as hyperspher-
ical harmonics, where an event in space-time is converted from Cartesian coor-
dinates to hyperspherical coordinates, and (b) as “time-normal” coordinates,
which are formed by including a temporal dependency in each spatial coordinate.
Experiments carried out with a 3-D CT data set of a canine heart have indicated
that hyperspherical harmonics can represent the beating LV with higher accuracy
than direct normal extensions of spherical, prolate spheroidal, and oblate sphe-
roidal harmonics. Coppini et al. [29] reconstruct a 3-D model of the LV based
on apical views in US images. LV boundaries are obtained by grouping edges
with a feedforward neural network (NN) integrating information about several
edge features (position, orientation, strength, length, and acquisition angle). This
allows the discarding of many edge points that are not plausible LV boundary
points. The 3-D LV geometry is modeled as a spherical elastic surface under the
action of radial springs (attracting the model to the edge points); a Hopfield [198]
NN is used to solve the minimization problem involved in the reconstruction of
this surface. Declerck, Feldmar, and Ayache [123] have introduced a spatiotem-
poral model to segment the LV and to analyze motion from gated SPECT
sequences. The model relies on a planispheric transformation that maps endocar-
dial points in one time frame to the corresponding material points in any other
frame. First, endocardial edge points are detected in all frames using a
Canny-Deriche edge detector [199] in spherical coordinates [200]. Selected
points in subsequent frames are matched to the current frame using a modification
of the iterative closest point (ICP) algorithm [200-202]. Based on corresponding
point pairs, the parameters of a planispheric transformation are retrieved by least-
squares approximation. This transformation allows the description of motion with
just a few parameters that can be related to a canonical decomposition (radial
motion, twisting motion around the apicobasal axis, and long-axis shortening).
9.4.1.1.2 Hierarchical Approaches
Some authors have addressed the problem of building
hierarchical representations
in which a model described with few parameters is complemented with extra
deformations that capture finer details. Gustavsson et al. [114], for instance, employ
a truncated ellipsoid to obtain a coarse positioning of the left-ventricular cavity
from contours drawn in two short-axis and three apical echocardiographic views.
Further model refinement is achieved using cubic B-spline curves approximating
manually segmented contours in multiple views. Chen et al. [116], Bardinet et al.
[9], and Fan et al. [150] use superquadrics [196] to coarsely describe the LV. Their
Search WWH ::
Custom Search