White matter (WM) consists of fibers that transmit information from one brain region to another, and functional fiber clustering that combines diffusion and functional MRI provides a novel perspective for exploring the functional architecture of axonal fibers. However, existing methods only concern functional signals in gray matter (GM), whereas the connecting fibers may not transmit relevant functional signals. There has been growing evidence that neural activity is encoded in WM BOLD signals as well, which provides rich multimodal information for fiber clustering. In this paper, we develop a comprehensive Riemannian framework for functional fiber clustering using WM BOLD signals along fibers. Specifically, we derive a novel metric that is highly discriminative of different functional classes while reducing the variability within classes and, in the meantime, enables low-dimensional coding of high-dimensional data. Our in vivo experiments show that the proposed framework is able to achieve clustering results with inter-subject consistency and functional homogeneity. In addition, we develop an atlas of WM functional architecture for standardizable yet flexible use and exemplify a machine-learning-based application for the classification of autism spectrum disorders, which further demonstrates the great potential of our approach in practical applications.

The analysis of connectivity between parcellated regions of cortex provides insights into the functional architecture of the brain at a systems level. However, the derivation of functional structures from voxel-wise analyses at finer scales remains a challenge. We propose a novel method, called localized topo-connectivity mapping with singular-value-decomposition-informed filtering (or filtered LTM), to identify and characterize voxel-wise functional structures in the human brain from resting-state fMRI data. Here we describe its mathematical formulation and provide a proof-of-concept using simulated data that allow an intuitive interpretation of the results of filtered LTM. The algorithm has also been applied to 7T fMRI data acquired as part of the Human Connectome Project to generate group-average LTM images. Generally, most of the functional structures revealed by LTM images agree in the boundaries with anatomical structures identified by T1-weighted images and fractional anisotropy maps derived from diffusion MRI. In addition, the LTM images also reveal subtle functional variations that are not apparent in the anatomical structures. To assess the performance of LTM images, the subcortical region and occipital white matter were separately parcellated. Statistical tests were performed to demonstrate that the synchronies of fMRI signals in LTM-derived functional parcels are significantly larger than those with geometric perturbations. Overall, the filtered LTM approach can serve as a tool to investigate the functional organization of the brain at the scale of individual voxels as measured in fMRI.

Alzheimer's disease (AD) is the most common form of dementia in the elderly. As early detection and diagnosis is imperative for the intervention and prevention of its progression into more detrimental stages, pioneering works have been proposed that use the resting-state functional MRI (rs-fMRI) to identify early mild cognitive impairment (EMCI) based on various convolutional neural networks (CNNs). However the accuracy is not satisfactory. In this paper, we propose a multi-view model based on the SlowFast network, a recently proposed model for video recognition. The rs-fMRI data are treated as videos from three perspectives (i.e. coronal, horizontal and sagittal, corresponding to three anatomical planes in human body) and the jointly learned hierarchical representations are fused in the fully connected layer. We examine our model on a publicly accessible Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our method significantly outperforms other competing methods and achieves state-of-the-art accuracy. Besides, we also provide a baseline on the classification task over all clinical phases of AD.

Functional MRI based on blood oxygenation level-dependent (BOLD) contrast is well established as a neuroimaging technique for detecting neural activity in the cortex of the human brain. Recent studies have shown that variations of BOLD signals in white matter are also related to neural activities both in resting state and under functional loading. We develop a comprehensive framework of detecting task-specific fiber pathways. We not only study fiber tracts as open curves with different physical features (shape, scale, orientation and position), but also incorporate the BOLD signals associated with them to find stimulus-relevant pathways. Specifically, we propose a novel Riemannian metric, which is a weighted sum of distances in product space of shapes and functions. This metric provides both a cost function for registration and a proper distance for comparison. Experimental results on real data have shown that we can cluster fiber pathways correctly by evaluating correlations between BOLD signals and stimuli, temporal variations and power spectra of them.

This paper presents a novel Riemannian framework for shape analysis of parameterized surfaces. In particular, it provides efficient algorithms for computing geodesic paths which, in turn, are important for comparing, matching, and deforming surfaces. The novelty of this framework is that geodesics are invariant to the parameterizations of surfaces and other shape-preserving transformations of surfaces. The basic idea is to formulate a space of embedded surfaces (surfaces seen as embeddings of a unit sphere in IR3) and impose a Riemannian metric on it in such a way that the reparameterization group acts on this space by isometries. Under this framework, we solve two optimization problems. One, given any two surfaces at arbitrary rotations and parameterizations, we use a path-straightening approach to find a geodesic path between them under the chosen metric. Second, by modifying a technique presented in [25], we solve for the optimal rotation and parameterization (registration) between surfaces. Their combined solution provides an efficient mechanism for computing geodesic paths in shape spaces of parameterized surfaces. We illustrate these ideas using examples from shape analysis of anatomical structures and other general surfaces.

Intensity inhomogeneity often occurs in real-world images, which presents a considerable challenge in image segmentation. The most widely used image segmentation algorithms are region-based and typically rely on the homogeneity of the image intensities in the regions of interest, which often fail to provide accurate segmentation results due to the intensity inhomogeneity. This paper proposes a novel region-based method for image segmentation, which is able to deal with intensity inhomogeneities in the segmentation. First, based on the model of images with intensity inhomogeneities, we derive a local intensity clustering property of the image intensities, and define a local clustering criterion function for the image intensities in a neighborhood of each point. This local clustering criterion function is then integrated with respect to the neighborhood center to give a global criterion of image segmentation. In a level set formulation, this criterion defines an energy in terms of the level set functions that represent a partition of the image domain and a bias field that accounts for the intensity inhomogeneity of the image. Therefore, by minimizing this energy, our method is able to simultaneously segment the image and estimate the bias field, and the estimated bias field can be used for intensity inhomogeneity correction (or bias correction). Our method has been validated on synthetic images and real images of various modalities, with desirable performance in the presence of intensity inhomogeneities. Experiments show that our method is more robust to initialization, faster and more accurate than the well-known piecewise smooth model. As an application, our method has been used for segmentation and bias correction of magnetic resonance (MR) images with promising results.

We consider 3-D brain structures as continuous parameterized surfaces and present a metric for their comparisons that is invariant to the way they are parameterized. Past comparisons of such surfaces involve either volume deformations or nonrigid matching under fixed parameterizations of surfaces. We propose a new mathematical representation of surfaces, called q-maps, such that L² distances between such maps are invariant to re-parameterizations. This property allows for removing the parameterization variability by optimizing over the re-parameterization group, resulting in a proper parameterization-invariant distance between shapes of surfaces. We demonstrate this method in shape analysis of multiple brain structures, for 34 subjects in the Detroit Fetal Alcohol and Drug Exposure Cohort study, which results in a 91% classification rate for attention deficit hyperactivity disorder cases and controls. This method outperforms some existing techniques such as spherical harmonic point distribution model (SPHARM-PDM) or iterative closest point (ICP).

In this paper we introduce a novel Riemannian framework for shape analysis of parameterized surfaces. We derive a distance function between any two surfaces that is invariant to rigid motion, global scaling, and re-parametrization. It is the last part that presents the main difficulty. Our solution to this problem is twofold: (1) we define a special representation, called a q-map, to represent each surface, and (2) we develop a gradient-based algorithm to optimize over different re-parameterizations of a surface. The second step is akin to deforming the mesh on a fixed surface to optimize its placement. (This is different from the current methods that treat the given meshes as fixed.) Under the chosen representation, with the L2metric, the action of the re-parametrization group is by isometries. This results in, to our knowledge, the first Riemannian distance between parameterized surfaces to have all the desired invariances. We demonstrate this framework with several examples using some toy shapes, and real data with anatomical structures, and cropped facial surfaces. We also successfully demonstrate clustering and classification of these objects under the proposed metric.

Magnetic resonance diffusion tensor imaging is being widely used to reconstruct brain white matter fiber tracts. To characterize structural properties of the tracts, reconstructed fibers are often grouped into bundles that correspond to coherent anatomic structures. For further group analysis of fiber bundles, it is desirable that corresponding bundles from different studies are coregistered. To address these needs simultaneously, a unified fiber bundling and registration (UFIBRE) framework is proposed in this work. The framework is based on maximizing a posteriori Bayesian probabilities using an expectation maximization algorithm. Given a set of segmented template bundles and a whole-brain target fiber set, the UFIBRE algorithm optimally bundles the target fibers and registers them with the template. The bundling component in the UFIBRE algorithm simplifies fiber-based registration into bundle-to-bundle registration, and the registration component in turn guides the bundling process to find bundles consistent with the template. Experiments with in vivo data demonstrate that the estimated bundles have an approximately 80% consistency with ground truth and the root mean square error between their bundle medial axes is less than one voxel. The proposed algorithm is highly efficient, offering potential routine use for group analysis of white matter fibers.

Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions at a controllable scale. A data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation with a level set regularization term, from which a curve evolution equation is derived for energy minimization. Due to a kernel function in the data fitting term, intensity information in local regions is extracted to guide the motion of the contour, which thereby enables our model to cope with intensity inhomogeneity. In addition, the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function. Experimental results for synthetic and real images show desirable performances of our method.

Local image information is crucial for accurate segmentation of images with intensity inhomogeneity. However, image information in local region is not embedded in popular region-based active contour models, such as the piecewise constant models. In this paper, we propose a region-based active contour model that is able to utilize image information in local regions. The major contribution of this paper is the introduction of a local binary fitting energy with a kernel function, which enables the extraction of accurate local image information. Therefore, our model can be used to segment images with intensity inhomogeneity, which overcomes the limitation of piecewise constant models. Comparisons with other major region-based models, such as the piece-wise smooth model, show the advantages of our method in terms of computational efficiency and accuracy. In addition, the proposed method has promising application to image denoising.

To improve the accuracy of tissue structural and architectural characterization with diffusion tensor imaging, an anisotropic smoothing algorithm is presented for reducing noise in diffusion tensor images efficiently and effectively. The presented algorithm is based on previous anisotropic diffusion filtering, which is implemented with a straightforward but inefficient explicit numerical scheme. The main contribution of this paper is to improve the performance of the previous method considerably by using unconditionally stable and second order time accurate semi-implicit scheme. Our new method needs only few or even one iteration to achieve better smoothed images than what is generated by tens of iterations of the previous method, which makes it more attractive to practical use. Experiments with simulated and in vivo data have demonstrated the advantage of our new algorithm for denoising diffusion tensor images in terms of efficiency and effectiveness.

It is of significant interest for neurological studies to determine and visualize neuronal fiber pathways in the human brain. By exploiting the capability of diffusion tensor magnetic resonance imaging to detect local orientations of neuronal fibers, we have developed a system of algorithms to reconstruct, visualize and quantify neuronal fiber pathways in vivo. Illustrative results show that the system is a promising tool for visual analysis of fiber connectivity and quantitative studies of neuronal fibers.

The measurement, analysis and visualization of plant growth is of primary interest to plant biologists. We are developing software tools to support such investigations. There are two parts in this investigation, namely growth visualization of (i) a plant root and (ii) a plant stem. For both domains, the input data is a stream of images taken by cameras. The tools being developed make it possible to measure various time-varying quantities, such as differential growth. For both domains, the plant is modeled by using flexible templates to represent non-rigid motions.