Image Processing Reference
In-Depth Information
Friboulet, Magnin, and Revel [132] have developed a polygonal model to analyze
the motion of the LV from 3-D MR image sequences. LV contours are manually
outlined using a trackball. After applying morphological and linear filtering to
diminish quantization noise, the contours are radially resampled with constant
angular step. Finally, the stack of resampled contours is fed into a triangulation
procedure [214] that generates a polygonal surface with approximately equal-
sized triangles. Faber et al. [134] use a combination of cylindrical and spherical
coordinate systems to build a discrete model of the LV in SPECT perfusion
images. A radius function defined in a discrete (orientation) space of longitudinal
and circumferential coordinates describes the LV. For each orientation, the radius
is determined by finding the position of maximal perfusion (which is said to occur
in the center of the myocardium). After low-pass filtering to remove outlier
radii,
the radius function is mapped back to Cartesian space where the surface is
represented using triangular or quadrilateral meshes. This approach shares some
features of the work described in Faber et al. [131], but is purely static. Legget
et al. [28,215] use piecewise smooth subdivision surfaces [216] to reconstruct
the LV geometry from manually traced contours in 3-D US images. Some ele-
ments of the mesh can be labeled so that they allow for sharp edges (e.g., at the
mitral annulus and apex) and to define regional surface descriptors. Also from 3-D
US images, Gopal et al. [27] apply triangulated surfaces to reconstruct the geom-
etry of latex balloon phantoms mimicking the LV. Three-dimensional reconstruc-
tion is directly obtained by triangulating the points of manually delineated con-
tours from a stack of quasi-parallel slices. Song et al. [147] use a triangular
surface model to represent the heart. In contrast to several other techniques, a
given heart is approximated by a convex combination of shapes from a model
catalog. The authors cast the surface model optimization problem in a Bayesian
framework, such that the inference made about a surface model is based on the
integration of both the low-level image evidence and the high-level prior shape
knowledge through a pixel class prediction mechanism.
9.4.1.2.4 Statistical Shape and Appearance Models
These models capture the mean shape and shape variations from a training
population. In 3-D cardiac modeling, these models have been developed for shape
analysis and for gaining insight into commonly occurring anatomical variations.
Apart from shape analysis, the learned eigenvariations can be applied to image
segmentation and motion tracking by restricting the search space of an image-
matching mechanism to statistically plausible directions.
In statistical shape models, a shape is expressed as a set of corresponding
landmarks, which are parameterized as a coordinate vector concatenating the
landmark components. These vectors are aligned using Procrustes' algorithm with
respect to position, scale, and orientation, thus minimizing the sum of squared
distances between the landmarks. The residual sample point distributions after
alignment represent the pure shape-related differences in the population, and are
modeled by computing the shape average and applying a principal component
analysis (PCA) on the coordinate covariance matrix. The principal components
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