Modeling diffusion directions of Corpus Callosum

Diffusion Tensor Imaging (DTI) has been used to study the characteristics of Multiple Sclerosis (MS) in the brain. The von Mises- Fisher distribution (vmf) is a probability distribution for modeling directional data on the unit hypersphere. In this paper we modeled the diffusion directions of the Corpus Callosum (CC) as a mixture of vmf distributions for both MS subjects and healthy controls. Higher diffusion concentration around the mean directions and smaller sum of angles between the mean directions are observed on the normal-appearing CC of the MS subjects as compared to the healthy controls

Modeling Diffusion Directions of Corpus Callosum

Diffusion Tensor Imaging (DTI) has been used to study the characteristics of Multiple Sclerosis (MS) in the brain. The von Mises- Fisher distribution (vmf) is a probability distribution for modeling directional data on the unit hypersphere. In this paper we modeled the diffusion directions of the Corpus Callosum (CC) as a mixture of vmf distributions for both MS subjects and healthy controls. Higher diffusion concentration around the mean directions and smaller sum of angles between the mean directions are observed on the normal-appearing CC of the MS subjects as compared to the healthy controls

A Riemannian Framework for Orientation Distribution Function Computing

International audienceCompared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy H_{1/2} of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation

k-Nearest Neighbor Based Consistent Entropy Estimation for Hyperspherical Distributions

A consistent entropy estimator for hyperspherical data is proposed based on the k-nearest neighbor (knn) approach. The asymptotic unbiasedness and consistency of the estimator are proved. Moreover, cross entropy and Kullback-Leibler (KL) divergence estimators are also discussed. Simulation studies are conducted to assess the performance of the estimators for models including uniform and von Mises-Fisher distributions. The proposed knn entropy estimator is compared with the moment based counterpart via simulations. The results show that these two methods are comparable

Segmentation of corpus callosum using diffusion tensor imaging: validation in patients with glioblastoma

Abstract Background This paper presents a three-dimensional (3D) method for segmenting corpus callosum in normal subjects and brain cancer patients with glioblastoma. Methods Nineteen patients with histologically confirmed treatment naïve glioblastoma and eleven normal control subjects underwent DTI on a 3T scanner. Based on the information inherent in diffusion tensors, a similarity measure was proposed and used in the proposed algorithm. In this algorithm, diffusion pattern of corpus callosum was used as prior information. Subsequently, corpus callosum was automatically divided into Witelson subdivisions. We simulated the potential rotation of corpus callosum under tumor pressure and studied the reproducibility of the proposed segmentation method in such cases. Results Dice coefficients, estimated to compare automatic and manual segmentation results for Witelson subdivisions, ranged from 94% to 98% for control subjects and from 81% to 95% for tumor patients, illustrating closeness of automatic and manual segmentations. Studying the effect of corpus callosum rotation by different Euler angles showed that although segmentation results were more sensitive to azimuth and elevation than skew, rotations caused by brain tumors do not have major effects on the segmentation results. Conclusions The proposed method and similarity measure segment corpus callosum by propagating a hyper-surface inside the structure (resulting in high sensitivity), without penetrating into neighboring fiber bundles (resulting in high specificity)

Multimodal Image Fusion and Its Applications.

Image fusion integrates different modality images to provide comprehensive information of the image content, increasing interpretation capabilities and producing more reliable results. There are several advantages of combining multi-modal images, including improving geometric corrections, complementing data for improved classification, and enhancing features for analysis...etc. This thesis develops the image fusion idea in the context of two domains: material microscopy and biomedical imaging. The proposed methods include image modeling, image indexing, image segmentation, and image registration. The common theme behind all proposed methods is the use of complementary information from multi-modal images to achieve better registration, feature extraction, and detection performances. In material microscopy, we propose an anomaly-driven image fusion framework to perform the task of material microscopy image analysis and anomaly detection. This framework is based on a probabilistic model that enables us to index, process and characterize the data with systematic and well-developed statistical tools. In biomedical imaging, we focus on the multi-modal registration problem for functional MRI (fMRI) brain images which improves the performance of brain activation detection.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120701/1/yuhuic_1.pd

Directional functions for orientation distribution estimation

Computing the Orientation Distribution Function (ODF) from High Angular Resolution Diffusion Imaging (HARDI) signals makes it possible to determine the orientation of fiber bundles of the brain. The HARDI signals are samples measured from a spherical shell and thus require processing on the sphere. Past work on ODF estimation involved using the spherical harmonics or spherical radial basis functions. In this work, we propose three novel directional functions able to represent the measured signals in a very compact manner, i.e., they require very few parameters to completely describe the measured signal. Analytical expressions are derived for computing the corresponding ODF. The directional functions can represent diffusion in a particular direction and mixture models can be used to represent multi-fiber orientations. We show how to estimate the parameters of this mixture model and elaborate on the differences between these functions. We also compare this general framework with estimation of ODF using spherical harmonics on some real and synthetic data. The proposed method could be particularly useful in applications such as tractography and segmentation. Details are also given on different ways in which interpolation can be performed using directional functions. In particular, we discuss a complete Euclidean as well as a “hybrid” framework, comprising of the Riemannian as well as Euclidean spaces, to perform interpolation and compute geodesic distances between 2 ODF’s

movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions

Finite mixtures of von Mises-Fisher distributions allow to apply model-based clustering methods to data which is of standardized length, i.e., all data points lie on the unit sphere. The R package movMF contains functionality to draw samples from finite mixtures of von Mises-Fisher distributions and to fit these models using the expectation-maximization algorithm for maximum likelihood estimation. Special features are the possibility to use sparse matrix representations for the input data, different variants of the expectation-maximization algorithm, different methods for determining the concentration parameters in the M-step and to impose constraints on the concentration parameters over the components. In this paper we describe the main fitting function of the package and illustrate its application. In addition we compare the clustering performance of finite mixtures of von Mises-Fisher distributions to spherical k-means. We also discuss the resolution of several numerical issues which occur for estimating the concentration parameters and for determining the normalizing constant of the von Mises-Fisher distribution

Near-tubular fiber bundle segmentation for diffusion weighted imaging: Segmentation through frame reorientation

This paper proposes a methodology to segment near-tubular fiber bundles from diffusion weighted magnetic resonance images (DW-MRI). Segmentation is simplified by locally reorienting diffusion information based on large-scale fiber bundle geometry. Segmentation is achieved through simple global statistical modeling of diffusion orientation. Utilizing a modification of a recent segmentation approach by Bresson et al. allows for a convex optimization formulation of the segmentation problem, combining orientation statistics and spatial regularization. The approach compares favorably with segmentation by full-brain streamline tractography