Most model-based segmentation methods find a target object in a new image by constructing an objective function
and optimizing it using a standard minimization algorithm. In general, the objective function has two penalty
terms: 1) for deforming a template model and 2) for mismatch between the trained image intensities relative to
the template model and the observed image intensities relative to the deformed template model in the target
image. While it is difficult to establish an objective function with a global minimum at the desired segmentation
result, even such an objective function is typically non-convex due to the complexity of the intensity patterns
and the many structures surrounding the target object. Thus, it is critical that the optimization starts at a point
close to the global minimum of the objective function in deformable model-based segmentation framework.
For a segmentation method in maximum a posteriori framework a good objective function can be obtained by
learning the probability distributions of the population shape deformations and their associated image intensities
because each penalty term can be simplified to a squared function of some distance metric defined in the shape
space. The mean shape and intensities of the learned probability distributions also provide a good initialization
for segmentation. However, a major concern in estimating the shape prior is the stability of the estimated
shape distributions from given training samples because the feature space of a shape model is usually very high
dimensional while the number of training samples is limited. A lot of effort in that regard have been made to
attain a stable estimation of shape probability distribution.
In this paper, we describe our approach to stably estimate a shape probability distribution when good
segmentations of objects adjacent to the target object are available. Our approach is to use a conditional shape
probability distribution (CSPD) to take into account in the shape distribution the relation of the target object
to neighboring objects. In particular, we propose a new method based on principal component regression (PCR)
in reflecting in the conditional term of the CSPD the effect of neighboring objects on the target object. The
resulting approach is able to give a better and robust initialization with training samples of a few cases. To
demonstrate the potential of our approach, we apply it first to training of a simulated data of known deformations
and second to male pelvic organs, using the CSPD in m-rep segmentations of the prostate in CT images. Our
results show a clear improvement in initializing the prostate by its conditional mean given the bladder and the
rectum as neighboring objects, as measured both by volume overlap and average surface distance.
A main focus of statistical shape analysis is the description of variability of a population of geometric objects. In this paper,
we present work towards modeling the shape and pose variability of sets of multiple objects. Principal geodesic analysis
(PGA) is the extension of the standard technique of principal component analysis (PCA) into the nonlinear Riemannian
symmetric space of pose and our medial m-rep shape description, a space in which use of PCA would be incorrect.
In this paper, we discuss the decoupling of pose and shape in multi-object sets using different normalization settings.
Further, we introduce methods of describing the statistics of object pose and object shape, both separately and simultaneously
using a novel extension of PGA. We demonstrate our methods in an application to a longitudinal pediatric autism
study with object sets of 10 subcortical structures in a population of 47 subjects. The results show that global scale accounts
for most of the major mode of variation across time. Furthermore, the PGA components and the corresponding distribution
of different subject groups vary significantly depending on the choice of normalization, which illustrates the importance
of global and local pose alignment in multi-object shape analysis. Finally, we present results of using distance weighted
discrimination analysis (DWD) in an attempt to use pose and shape features to separate subjects according to diagnosis, as
well as visualize discriminating differences.