Image Processing Reference
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describe the main modes of variation in the training set and the eigenvalues the
amount of variance explained by each mode. A critical issue in such landmark-
based models is the requirement of point correspondence: each landmark should
correspond to the same anatomical location in all the training samples.
For 3-D cardiac modeling applied to MR image analysis, three classes of
landmark-based approaches have been described.
Point distribution models
(PDMs) represent the shape model described earlier,
without image matching. Frangi et al. [217] build a PDM using nonrigid registra-
tion, where both the LV and RV are included in the model. Point correspondences
are defined by nonrigidly registering the training samples (represented as labeled
volumes) to a shape average computed through rigid registration. By defining a
point sampling for the shape average, and inverting the nonrigid deformation,
this sampling can be propagated to each individual shape. Subsequent computa-
tion of an average shape and PCA eigenvariations is identical to 2-D PDMs.
Recently this technique has been applied by Ordas et al. [218] to a large database
of dynamic shapes using grid computing techniques. As yet, this model has not
been applied to segmentation. McLeish et al. [219] use a 3-D point distribution
model to study the motion and deformation of the heart as a result of breathing.
Models are constructed for a single subject, where different shape samples rep-
resent the heart shape in different inspiration levels for the same subject. Because
this method tracks the heart using nonrigid registration, point correspondence is
achieved by propagating a set of landmarks, similar to Frangi's approach. This
yields eigenmodes per subject that characterize the motion and deformation of
the heart during breathing.
Active Shape Models
(ASMs) consist of a PDM, extended with a matching
scheme driven by information from the target image data, enabling statistically
constrained image segmentation. ASMs use a gray-level model of scan lines
perpendicular to the model contour or surface to estimate new update positions
for each landmark point. Alternatively, update points can be generated by an edge
detector or a pixel classification approach. The differences between the cloud of
candidate sample points and the model points are used for model alignment and
deformation in each iteration. The model deformation is restricted to the modes
of variation of the PDM. Van Assen et al. [152,153] describe an ASM built using
an application-specific point correspondence based on resampling the contours
of the LV to a fixed number of slices and radially spaced in-plane landmarks.
The matching mechanism generates update positions using a dynamic, unsuper-
vised tissue classification based on fuzzy clustering. Intensities are sampled for
each scan line and pooled. Subsequently, the clustering distinguishes different
tissues as blood, myocardium, and air, and update points are inferred on the class
transitions. Model training was performed on 53 data sets, whereas the model
was tested on 9 data sets. Alternatively, Kaus et al. [220,154] describe an ASM-
based approach, in which the matching mechanism is embedded in the internal
energy term of an elastically deformable model. Training samples are manual
segmentations expressed as binary volumes, and point correspondence is achieved
by fitting a template mesh with a fixed-point topology to each binary training
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