Image Processing Reference
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based on normalized mutual information, no expert segmentations in the form of
labeled volumes, as in Frangi [217], are required. These free-form deformations
are parameterized using a control point grid, and statistical analysis using PCA
is performed on the control point sets, yielding an average deformation and
principal components. Lötjönen et al. [193,231] constructed a four-chamber
model of the heart using SDMs. To more accurately represent the basal and apical
level, they generated training samples by nonrigidly registering a triangulated
surface template to short- and long-axis image volumes in an alternating manner.
Prior to training, the long- and short-axis data are corrected for patient motion
by sequentially shifting each slice while maximizing the normalized mutual
information between the data. Subsequently the models from the different subjects
are registered, and an SDM is computed from the registration control points. In
addition, an average intensity model is generated. This enables application to
segmentation by nonrigid registration of the intensity template to the image data,
while constraining the deformations to statistically trained limits. Model training
and segmentation tests were performed on MR data from 25 subjects in a leave-
one-out manner. In the same paper, two other types of models are compared on
segmentation performance: a landmark probability distribution model and a prob-
abilistic surface atlas. These models are applied to segmentation by adding a
model term to the normalized mutual information measure, and performing non-
rigid registration by maximizing the combined measure. This comparison indi-
cates that the probability-based models work better than the SDMs, mainly
because of overconstraining of the statistical models with a limited training set.
Lorenzo-Valdes et al. [151,232] present a probabilistic approach to cardiac
modeling. A probabilistic cardiac atlas of the left and right ventricle is con-
structed from a set of manual segmentations as follows: First, the cardiac cycle
is phase-normalized to a fixed number of frames. Subsequently, the manual
segmentations are rigidly registered to one reference subject. Probabilistic maps
are generated by blurring the segmented structure for each image and averaging
over all subjects. The model is applied to segmentation using expectation max-
imization. They evaluated the model on 14 normal subjects and 10 patients with
LV hypertrophy, and demonstrated that by blurring the normal-trained model, it
can be generalized to accommodate for the pathological shape variations in
patients with LV hypertrophy.
Perperidis et al. [188,189] proposed a registration-based approach to recover
cardiac deformation. They use a 4-D FFD, which couples space and time. In this
way, they are able to correct for differences in heart rate between a reference
subject and the subject under analysis, or for differences in acquisition parameters.
9.4.3.1.2 Discrete Models
Benayoun and Ayache [99] propose an adaptive mesh model to estimate nonrigid
motion in 3-D image sequences. The size of the mesh is locally adapted to the
magnitude of the gradient where the most relevant information is supposed to appear
(e.g., cardiac walls). Mesh adaptation is carried out at the first frame only; subse-
quent frames only deform the mesh to recover motion. The underlying hypothesis
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