Recent studies have found correlation between the risk of rupture of saccular aneurysms and their morphological
characteristics, such as volume, surface area, neck length, among others. For reliably exploiting these parameters
in endovascular treatment planning, it is crucial that they are accurately quantified. In this paper, we present
a novel framework to assist physicians in accurately assessing saccular aneurysms and efficiently planning for
endovascular intervention. The approach consists of automatically segmenting the pathological vessel, followed
by the construction of its surface representation. The aneurysm is then separated from the vessel surface
through a graph-cut based algorithm that is driven by local geometry as well as strong prior information. The
corresponding healthy vessel is subsequently reconstructed and measurements representing the patient-specific
geometric parameters of pathological vessel are computed. To better support clinical decisions on stenting and
device type selection, the placement of virtual stent is eventually carried out in conformity with the shape of the
diseased vessel using the patient-specific measurements. We have implemented the proposed methodology as a
fully functional system, and extensively tested it with phantom and real datasets.
Groupwise registration and statistical analysis of medical images are of fundamental importance in computational
anatomy, where healthy and pathologic anatomies are compared relative to their differences with a common
template. Accuracy of such approaches is primarily determined by the ability of finding perfectly conforming
shape transformations, which is rarely achieved in practice due to algorithmic limitations arising from biological
variability. Amount of the residual information not reflected by the transformation is, in fact, dictated by
template selection and is lost permanently from subsequent analysis. In general, an attempt to aggressively
minimize residual results in biologically incorrect correspondences, necessitating a certain level of regularity in
the transformation at the cost of accuracy.
In this paper, we introduce a framework for groupwise registration and statistical analysis of biomedical images
that optimally fuses the information contained in a diffeomorphism and the residual to achieve completeness of
representation. Since the degree of information retained in the residual depends on transformation parameters
such as the level of regularization, and template selection, our approach consists of forming an equivalence class
for each individual, thereby representing them via nonlinear manifolds embedded in high dimensional space. By
employing a minimum variance criterion and constraining the optimization to respective anatomical manifolds,
we proceed to determine their optimal morphological representation. A practical ancillary benefit of this approach
is that it yields optimal choice of transformation parameters, and eliminates respective confounding variation in
the data. Resultantly, the optimal signatures depend solely on anatomical variations across subjects, and may
ultimately lead to more accurate diagnosis through pattern classification.
In this paper, we propose a novel method for the classification of 3D shapes, based on topo-geometric shape descriptors. Topo-geometric models have an advantage over existing shape descriptors that they capture complete shape information - capturing topology through skeletal graphs, and geometry via edge weights. The resulting weighted graph representation allows shape classification by establishing error correcting subgraph isomorphisms between the test graph and model graphs, where the best match is the one that corresponds to largest subgraph isomorphism. We propose various cost assignments for graph edit operations for error correction, which in turn takes into account any shape variations arising due to noise and measurement errors.