Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods.

# Publications

## 2014

Introducing BrainPrint, a compact and discriminative representation of anatomical structures in the brain. BrainPrint captures shape information of an ensemble of cortical and subcortical structures by solving the 2D and 3D Laplace-Beltrami operator on triangular (boundary) and tetrahedral (volumetric) meshes. We derive a robust classifier for this representation that identifies the subject in a new scan, based on a database of brain scans. In an example dataset containing over 3000 MRI scans, we show that BrainPrint captures unique information about the subject’s anatomy and permits to correctly classify a scan with an accuracy of over 99.8%. All processing steps for obtaining the compact representation are fully automated making this processing framework particularly attractive for handling large datasets.

In this paper, we use Spherical Topic Models to discover the latent structure of lung disease. This method can be widely employed when a measurement for each subject is provided as a normalized histogram of relevant features. In this paper, the resulting descriptors are used as phenotypes to identify genetic markers associated with the Chronic Obstructive Pulmonary Disease (COPD). Features extracted from images capture the heterogeneity of the disease and therefore promise to improve detection of relevant genetic variants in Genome Wide Association Studies (GWAS). Our generative model is based on normalized histograms of image intensity of each subject and it can be readily extended to other forms of features as long as they are provided as normalized histograms. The resulting algorithm represents the intensity distribution as a combination of meaningful latent factors and mixing co-efficients that can be used for genetic association analysis. This approach is motivated by a clinical hypothesis that COPD symptoms are caused by multiple coexisting disease processes. Our experiments show that the new features enhance the previously detected signal on chromosome 15 with respect to standard respiratory and imaging measurements.

We study the widespread, but rarely discussed, tendency of atlas-based segmentation to under-segment the organs of interest. Commonly used error measures do not distinguish between under- and over-segmentation, contributing to the problem. We explicitly quantify over- and under-segmentation in several typical examples and present a new hypothesis for the cause. We provide evidence that segmenting only one organ of interest and merging all surrounding structures into one label creates bias towards background in the label estimates suggested by the atlas. We propose a generative model that corrects for this effect by learning the background structures from the data. Inference in the model separates the background into distinct structures and consequently improves the segmentation accuracy. Our experiments demonstrate a clear improvement in several applications.

Magnetic resonance spectroscopic imaging (MRSI) is often used to estimate the concentration of several brain metabolites. Abnormalities in these concentrations can indicate specific pathology, which can be quite useful in understanding the disease mechanism underlying those changes. Due to higher concentration, metabolites such as N-acetylaspartate (NAA), Creatine (Cr) and Choline (Cho) can be readily estimated using standard Fourier transform techniques. However, metabolites such as Glutamate (Glu) and Glutamine (Gln) occur in significantly lower concentrations and their resonance peaks are very close to each other making it difficult to accurately estimate their concentrations (separately). In this work, we propose to use the theory of ’Spectral Zooming’ or high-resolution spectral analysis to separate the Glutamate and Glutamine peaks and accurately estimate their concentrations. The method works by estimating a unique power spectral density, which corresponds to the maximum entropy solution of a zero-mean stationary Gaussian process. We demonstrate our estimation technique on several physical phantom data sets as well as on in-vivo brain spectroscopic imaging data. The proposed technique is quite general and can be used to estimate the concentration of any other metabolite of interest.

**See also:**Multidimensional MRI Core Publications

We propose and demonstrate an inference algorithm for the automatic segmentation of cerebrovascular pathologies in clinical MR images of the brain. Identifying and differentiating pathologies is important for understanding the underlying mechanisms and clinical outcomes of cerebral ischemia. Manual delineation of separate pathologies is infeasible in large studies of stroke that include thousands of patients. Unlike normal brain tissues and structures, the location and shape of the lesions vary across patients, presenting serious challenges for prior-driven segmentation. Our generative model captures spatial patterns and intensity properties associated with different cerebrovascular pathologies in stroke patients. We demonstrate the resulting segmentation algorithm on clinical images of a stroke patient cohort.

We present a novel approach to determine a local q-space metric that is optimal from an information theoreticperspective with respect to the expected signal statistics. It should be noted that the approach does not attempt to optimize the quality of a pre-defined mathematical representation, the estimator. In contrast, our suggestion aims at obtaining the maximum amount of information without enforcing a particular feature representation. Results for three significantly different average propagator distributions are presented. The results show that the optimal q-space metric has a strong dependence on the assumed distribution in the targeted tissue. In many practical cases educated guesses can be made regarding the average propagator distribution present. In such cases the presented analysis can produce a metric that is optimal with respect to this distribution. The metric will be different at different q-space locations and is defined by the amount of additional information that is obtained when adding a second sample at a given offset from a first sample. The intention is to use the obtained metric as a guide for the generation of specific efficient q-space sample distributions for the targeted tissue.

**See also:**Multidimensional MRI Core Publications

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

**See also:**Multidimensional MRI Core Publications

Current neuroimaging investigation of the white matter typically focuses on measurements derived from diffusion tensor imaging, such as fractional anisotropy (FA). In contrast, imaging studies of the gray matter oftentimes focus on morphological features such as cortical thickness, folding and surface curvature. As a result, it is not clear how to combine findings from these two types of approaches in order to obtain a consistent picture of morphological changes in both gray and white matter. In this paper, we propose a joint investigation of gray and white matter morphology by combining geometrical information from white and the gray matter. To achieve this, we first introduce a novel method for computing multi-scale white matter tract geometry. Its formulation is based on the differential geometry of curve sets and is easily incorporated into a continuous scale-space framework. We then incorporate this method into a novel framework for "fusing" white and gray matter geometrical information. Given a set of fiber tracts originating in a particular cortical region, the key idea is to compute two scalar fields that represent geometrical characteristics of the white matter and of the surface of the cortical region. A quantitative marker is created by combining the distributions of these scalar values using Mutual Information. This marker can be then used in the study of normal and pathological brain structure and development. We apply this framework to a study on autism spectrum disorder in children. Our preliminary results support the view that autism may be characterized by early brain overgrowth, followed by reduced or arrested growth (Courchesne, 2004).

**See also:**Multidimensional MRI Core Publications

In this paper we construct an atlas that summarizes functional connectivity characteristics of a cognitive process from a population of individuals. The atlas encodes functional connectivity structure in a low-dimensional embedding space that is derived from a diffusion process on a graph that represents correlations of fMRI time courses. The functional atlas is decoupled from the anatomical space, and thus can represent functional networks with variable spatial distribution in a population. In practice the atlas is represented by a common prior distribution for the embedded fMRI signals of all subjects. We derive an algorithm for fitting this generative model to the observed data in a population. Our results in a language fMRI study demonstrate that the method identifies coherent and functionally equivalent regions across subjects. The method also successfully maps functional networks from a healthy population used as a training set to individuals whose language networks are affected by tumors.