A Fuzzy, Nonparametric Segmentation Framework for DTI and MRI Analysis

Multi-contrast multi-atlas parcellation of diffusion tensor imaging of the human brain

In this paper, we propose a novel method for parcellating the human brain into 193 anatomical structures based on diffusion tensor images (DTIs). This was accomplished in the setting of multi-contrast diffeomorphic likelihood fusion using multiple DTI atlases. DTI images are modeled as high dimensional fields, with each voxel exhibiting a vector valued feature comprising of mean diffusivity (MD), fractional anisotropy (FA), and fiber angle. For each structure, the probability distribution of each element in the feature vector is modeled as a mixture of Gaussians, the parameters of which are estimated from the labeled atlases. The structure-specific feature vector is then used to parcellate the test image. For each atlas, a likelihood is iteratively computed based on the structure-specific vector feature. The likelihoods from multiple atlases are then fused. The updating and fusing of the likelihoods is achieved based on the expectation-maximization (EM) algorithm for maximum a posteriori (MAP) estimation problems. We first demonstrate the performance of the algorithm by examining the parcellation accuracy of 18 structures from 25 subjects with a varying degree of structural abnormality. Dice values ranging 0.8-0.9 were obtained. In addition, strong correlation was found between the volume size of the automated and the manual parcellation. Then, we present scan-rescan reproducibility based on another dataset of 16 DTI images - an average of 3.73%, 1.91%, and 1.79% for volume, mean FA, and mean MD respectively. Finally, the range of anatomical variability in the normal population was quantified for each structure.

Bayesian Parameter Estimation and Segmentation in the Multi-Atlas Random Orbit Model

This paper examines the multiple atlas random diffeomorphic orbit model in Computational Anatomy (CA) for parameter estimation and segmentation of subcortical and ventricular neuroanatomy in magnetic resonance imagery. We assume that there exist multiple magnetic resonance image (MRI) atlases, each atlas containing a collection of locally-defined charts in the brain generated via manual delineation of the structures of interest. We focus on maximum a posteriori estimation of high dimensional segmentations of MR within the class of generative models representing the observed MRI as a conditionally Gaussian random field, conditioned on the atlas charts and the diffeomorphic change of coordinates of each chart that generates it. The charts and their diffeomorphic correspondences are unknown and viewed as latent or hidden variables. We demonstrate that the expectation-maximization (EM) algorithm arises naturally, yielding the likelihood-fusion equation which the a posteriori estimator of the segmentation labels maximizes. The likelihoods being fused are modeled as conditionally Gaussian random fields with mean fields a function of each atlas chart under its diffeomorphic change of coordinates onto the target. The conditional-mean in the EM algorithm specifies the convex weights with which the chart-specific likelihoods are fused. The multiple atlases with the associated convex weights imply that the posterior distribution is a multi-modal representation of the measured MRI. Segmentation results for subcortical and ventricular structures of subjects, within populations of demented subjects, are demonstrated, including the use of multiple atlases across multiple diseased groups.

System for integrated neuroimaging analysis and processing of structure

Mapping brain structure in relation to neurological development, function, plasticity, and disease is widely considered to be one of the most essential challenges for opening new lines of neuro-scientific inquiry. Recent developments with MRI analysis of structural connectivity, anatomical brain segmentation, cortical surface parcellation, and functional imaging have yielded fantastic advances in our ability to probe the neurological structure-function relationship in vivo. To date, the image analysis efforts in each of these areas have typically focused on a single modality. Here, we extend the cortical reconstruction using implicit surface evolution (CRUISE) methodology to perform efficient, consistent, and topologically correct analyses in a natively multi-parametric manner. This effort combines and extends state-of-the-art techniques to simultaneously consider and analyze structural and diffusion information alongside quantitative and functional imaging data. Robust and consistent estimates of the cortical surface extraction, cortical labeling, diffusion-inferred contrasts, diffusion tractography, and subcortical parcellation are demonstrated in a scan-rescan paradigm. Accompanying this demonstration, we present a fully automated software system complete with validation data.

Cerebral cortical folding analysis with multivariate modeling and testing: Studies on gender differences and neonatal development

This paper presents a novel statistical framework for human cortical folding pattern analysis that relies on a rich multivariate descriptor of folding patterns in a region of interest (ROI). The ROI-based approach avoids problems faced by spatial normalization-based approaches stemming from the deficiency of homologous features between typical human cerebral cortices. Unlike typical ROI-based methods that summarize folding by a single number, the proposed descriptor unifies multiple characteristics of surface geometry in a high-dimensional space (hundreds/thousands of dimensions). In this way, the proposed framework couples the reliability of ROI-based analysis with the richness of the novel cortical folding pattern descriptor. This paper presents new mathematical insights into the relationship of cortical complexity with intra-cranial volume (ICV). It shows that conventional complexity descriptors implicitly handle ICV differences in different ways, thereby lending different meanings to "complexity". The paper proposes a new application of a nonparametric permutation-based approach for rigorous statistical hypothesis testing with multivariate cortical descriptors. The paper presents two cross-sectional studies applying the proposed framework to study folding differences between genders and in neonates with complex congenital heart disease. Both studies lead to novel interesting results.

Gaussian mixtures on tensor fields for segmentation: applications to medical imaging

In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results.

Belief propagation based segmentation of white matter tracts in DTI

This paper presents a belief propagation approach to the segmentation of the major white matter tracts in diffusion tensor images of the human brain. Unlike tractography methods that sample multiple fibers to be bundled together, we define a Markov field directly on the diffusion tensors to separate the main fiber tracts at the voxel level. A prior model of shape and direction guides a full segmentation of the brain into known fiber tracts; additional, unspecified fibers; and isotropic regions. The method is evaluated on various data sets from an atlasing project, healthy subjects, and multiple sclerosis patients.

Clinical neonatal brain MRI segmentation using adaptive nonparametric data models and intensity-based Markov priors

This paper presents a Bayesian framework for neonatal brain-tissue segmentation in clinical magnetic resonance (MR) images. This is a challenging task because of the low contrast-to-noise ratio and large variance in both tissue intensities and brain structures, as well as imaging artifacts and partial-volume effects in clinical neonatal scanning. We propose to incorporate a spatially adaptive likelihood model using a data-driven nonparametric statistical technique. The method initially learns an intensity-based prior, relying on the empirical Markov statistics from training data, using fuzzy nonlinear support vector machines (SVM). In an iterative scheme, the models adapt to spatial variations of image intensities via nonparametric density estimation. The method is effective even in the absence of anatomical atlas priors. The implementation, however, can naturally incorporate probabilistic atlas priors and Markov-smoothness priors to impose additional regularity on segmentation. The maximum-a-posteriori (MAP) segmentation is obtained within a graph-cut framework. Cross validation on clinical neonatal brain-MR images demonstrates the efficacy of the proposed method, both qualitatively and quantitatively.

A fuzzy, nonparametric segmentation framework for DTI and MRI analysis: with applications to DTI-tract extraction

This paper presents a novel fuzzy-segmentation method for diffusion tensor (DT) and magnetic resonance (MR) images. Typical fuzzy-segmentation schemes, e.g., those based on fuzzy C means (FCM), incorporate Gaussian class models that are inherently biased towards ellipsoidal clusters characterized by a mean element and a covariance matrix. Tensors in fiber bundles, however, inherently lie on specific manifolds in Riemannian spaces. Unlike FCM-based schemes, the proposed method represents these manifolds using nonparametric data-driven statistical models. The paper describes a statistically-sound (consistent) technique for nonparametric modeling in Riemannian DT spaces. The proposed method produces an optimal fuzzy segmentation by maximizing a novel information-theoretic energy in a Markov-random-field framework. Results on synthetic and real, DT and MR images, show that the proposed method provides information about the uncertainties in the segmentation decisions, which stem from imaging artifacts including noise, partial voluming, and inhomogeneity. By enhancing the nonparametric model to capture the spatial continuity and structure of the fiber bundle, we exploit the framework to extract the cingulum fiber bundle. Typical tractography methods for tract delineation, incorporating thresholds on fractional anisotropy and fiber curvature to terminate tracking, can face serious problems arising from partial voluming and noise. For these reasons, tractography often fails to extract thin tracts with sharp changes in orientation, such as the cingulum. The results demonstrate that the proposed method extracts this structure significantly more accurately as compared to tractography.