Image segmentation algorithms derived from spectral clustering analysis rely on the eigenvectors of the Laplacian of a weighted graph obtained from the image. The NCut criterion was previously used for image segmentation in supervised manner. We derive a new strategy for unsupervised image segmentation. This article describes an initial investigation to determine the suitability of such segmentation techniques for ultrasound images. The extension of the NCut technique to the unsupervised clustering is first described. The novel segmentation algorithm is then performed on simulated ultrasound images. Tests are also performed on abdominal and fetal images with the segmentation results compared to manual segmentation. Comparisons with the classical NCut algorithm are also presented. Finally, segmentation results on other types of medical images are shown.

A hierarchical model based on the Multivariate Autoregessive (MAR) process is proposed to jointly model neurological time-series collected from multiple subjects, and to characterize the distribution of MAR coefficients across the population from which those subjects were drawn. Thus, inference about effective connectivity between brain regions may be generalized beyond those subjects studied. The posterior on population- and subject-level connectivity parameters are estimated in a Variational Bayesian (VB) framework, and structural model parameters are chosen by the corresponding evidence criteria. The significance of resulting connectivity statistics are evaluated by permutation-based approximations to the null distribution. The method is demonstrated on simulated data and on actual multi-subject neurological time-series.

This paper presents a new algorithm for non-rigid registration between two doubly-connected regions. Our algorithm is based on harmonic analysis and the theory of optimal mass transport. It assumes an underlining continuum model, in which the total amount of mass is exactly preserved during the transformation of tissues. We use a finite element approach to numerically implement the algorithm.

Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm that learns shape variations from data at multiple scales and locations using spherical wavelets and spectral graph partitioning. Our results show that when the training set is small, our algorithm significantly improves the approximation of shapes in a testing set over PCA, which tends to oversmooth data.

In this work we address the uncertainty associated with fiber paths obtained in white matter fiber tractography. This uncertainty, which arises for example from noise and partial volume effects, is quantified using a Bayesian modeling framework. The theory for estimating the probability of a connection between two areas in the brain is presented, and a new model of the local water diffusion profile is introduced. We also provide a theorem that facilitates the estimation of the parameters in this diffusion model, making the presented method simple to implement.