Image Processing Reference
In-Depth Information
sample. Contrary to van Assen et al. [152,153], they separately model the endo-
and epicardial shape. However, a coupling is realized by integrating connecting
vertices between both surfaces and adding a connection term to the internal
energy. In addition, they adopt a spatially varying feature model for each land-
mark. Training and testing were performed on end-diastolic (ED) and end-systolic
(ES) image data from 121 subjects in a leave-one-out manner, and they report
an average border-positioning error of the order of 1-2 voxels. This approach has
the advantage that statistical shape constraints are imposed on the allowed elastic
mesh deformation, while allowing for some flexibility to deviate from the trained
shapes to accommodate for untrained shape variability.
The third type of landmark-based model is the
Active Appearance Model
(AAM). AAMs are an extension of ASMs with a statistical intensity model of
a complete image volume, as opposed to merely scan lines in the ASM match-
ing. An AAM is constructed by warping the voxel volume inside the training
samples to the shape average. After intensity normalization to zero mean and
unit variance, the intensity average and principal components are computed. A
subsequent combined PCA on the shape and intensity model parameters yields
a set of components that simultaneously capture shape and texture variability.
AAM matching is based on minimizing a criterion expressing the difference
between model intensities and the target image. This enables a rapid search for
the correct model location during the matching stage of AAMs, while utilizing
precalculated derivative images for the optimizable parameters. The sum of the
squares of the difference between the model-generated patch and the underlying
image serves as a criterion for model convergence. Mitchell et al. [170] devel-
oped a 3-D endo- and epicardial AAM and applied it to segmentation of cardiac
MR studies. They applied an application-specific point correspondence identical
to Van Assen et al. [152,153]. The model was trained and tested on 55 subjects,
and border position errors from 2-3 mm were reported. Stegmann [172] further
expanded the AAM to three dimensions and time; an AAM is described, in
which 3-D LV models in ED and ES are coupled, enabling simultaneous
detection in both frames. He also reports additional improvements: the integra-
tion of “whiskers” — surface scan lines pointing outward, where the intensity
is included in the intensity model, greatly extending the lock-in range of the
AAM. In addition, they have developed an automated correction for respiration-
induced slice shifts, which corrupt the deformation statistics. This method is
also 2-D AAM based. Correction for these slice shifts during training and
matching yielded considerable improvements. Using a training and testing set
of 12 subjects, they report on highly accurate estimates of ventricular volume
and EF in a leave-one-out validation.
9.4.1.3
Implicitly Defined Deformable Models
Either in continuous or discrete form, the two preceding models were character-
ized by having an explicit surface parameterization. A surface model can also be
defined by means of an implicit function. For instance, in the level-set approach,
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