In this article, we propose a unified statistical framework for image segmentation with shape prior information.
The approach combines an explicitely parameterized point-based probabilistic statistical shape model (SSM)
with a segmentation contour which is implicitly represented by the zero level set of a higher dimensional surface.
These two aspects are unified in a Maximum a Posteriori (MAP) estimation where the level set is evolved to
converge towards the boundary of the organ to be segmented based on the image information while taking into
account the prior given by the SSM information. The optimization of the energy functional obtained by the MAP
formulation leads to an alternate update of the level set and an update of the fitting of the SSM. We then adapt
the probabilistic SSM for multi-shape modeling and extend the approach to multiple-structure segmentation by
introducing a level set function for each structure. During segmentation, the evolution of the different level set
functions is coupled by the multi-shape SSM. First experimental evaluations indicate that our method is well
suited for the segmentation of topologically complex, non spheric and multiple-structure shapes. We demonstrate
the effectiveness of the method by experiments on kidney segmentation as well as on hip joint segmentation in
CT images.
In this paper, we present a method to compute a statistical shape model based on shapes which are represented
by unstructured point sets with arbitrary point numbers. A fundamental problem when computing statistical
shape models is the determination of correspondences between the observations of the associated data set. Often,
homologies between points that represent the surfaces are assumed. When working merely with point clouds, this
might lead to imprecise mean shape and variability results. To overcome this problem, we propose an approach
where exact correspondences are replaced by evolving correspondence probabilities. These are the basis for
a novel algorithm that computes a generative statistical shape model. We developed a unified Maximum A
Posteriori (MAP) framework to compute the model parameters ('mean shape' and 'modes of variation') and the
nuisance parameters which leads to an optimal adaption of the model to the set of observations. The registration
of the model on the observations is solved using the Expectation Maximization - Iterative Closest Point algorithm
which is based on probabilistic correspondences and proved to be robust and fast. The alternated optimization of
the MAP explanation with respect to the observation and the generative model parameters leads to very efficient
and closed-form solutions for nearly all parameters. A comparison with a statistical shape model which is built
using the Iterative Closest Point (ICP) registration algorithm and a Principal Component Analysis (PCA) shows
that our approach leads to better SSM quality measures.
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