494 research outputs found

    Higher-Order Tensors and Differential Topology in Diffusion MRI Modeling and Visualization

    Get PDF
    Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is a noninvasive method for creating three-dimensional scans of the human brain. It originated mostly in the 1970s and started its use in clinical applications in the 1980s. Due to its low risk and relatively high image quality it proved to be an indispensable tool for studying medical conditions as well as for general scientific research. For example, it allows to map fiber bundles, the major neuronal pathways through the brain. But all evaluation of scanned data depends on mathematical signal models that describe the raw signal output and map it to biologically more meaningful values. And here we find the most potential for improvement. In this thesis we first present a new multi-tensor kurtosis signal model for DW-MRI. That means it can detect multiple overlapping fiber bundles and map them to a set of tensors. Compared to other already widely used multi-tensor models, we also add higher order kurtosis terms to each fiber. This gives a more detailed quantification of fibers. These additional values can also be estimated by the Diffusion Kurtosis Imaging (DKI) method, but we show that these values are drastically affected by fiber crossings in DKI, whereas our model handles them as intrinsic properties of fiber bundles. This reduces the effects of fiber crossings and allows a more direct examination of fibers. Next, we take a closer look at spherical deconvolution. It can be seen as a generalization of multi-fiber signal models to a continuous distribution of fiber directions. To this approach we introduce a novel mathematical constraint. We show, that state-of-the-art methods for estimating the fiber distribution become more robust and gain accuracy when enforcing our constraint. Additionally, in the context of our own deconvolution scheme, it is algebraically equivalent to enforcing that the signal can be decomposed into fibers. This means, tractography and other methods that depend on identifying a discrete set of fiber directions greatly benefit from our constraint. Our third major contribution to DW-MRI deals with macroscopic structures of fiber bundle geometry. In recent years the question emerged, whether or not, crossing bundles form two-dimensional surfaces inside the brain. Although not completely obvious, there is a mathematical obstacle coming from differential topology, that prevents general tangential planes spanned by fiber directions at each point to be connected into consistent surfaces. Research into how well this constraint is fulfilled in our brain is hindered by the high precision and complexity needed by previous evaluation methods. This is why we present a drastically simpler method that negates the need for precisely finding fiber directions and instead only depends on the simple diffusion tensor method (DTI). We then use our new method to explore and improve streamsurface visualization.<br /

    Converting Neuroimaging Big Data to information: Statistical Frameworks for interpretation of Image Driven Biomarkers and Image Driven Disease Subtyping

    Get PDF
    Large scale clinical trials and population based research studies collect huge amounts of neuroimaging data. Machine learning classifiers can potentially use these data to train models that diagnose brain related diseases from individual brain scans. In this dissertation we address two distinct challenges that beset a wider adoption of these tools for diagnostic purposes. The first challenge that besets the neuroimaging based disease classification is the lack of a statistical inference machinery for highlighting brain regions that contribute significantly to the classifier decisions. In this dissertation, we address this challenge by developing an analytic framework for interpreting support vector machine (SVM) models used for neuroimaging based diagnosis of psychiatric disease. To do this we first note that permutation testing using SVM model components provides a reliable inference mechanism for model interpretation. Then we derive our analysis framework by showing that under certain assumptions, the permutation based null distributions associated with SVM model components can be approximated analytically using the data themselves. Inference based on these analytic null distributions is validated on real and simulated data. p-Values computed from our analysis can accurately identify anatomical features that differentiate groups used for classifier training. Since the majority of clinical and research communities are trained in understanding statistical p-values rather than machine learning techniques like the SVM, we hope that this work will lead to a better understanding SVM classifiers and motivate a wider adoption of SVM models for image based diagnosis of psychiatric disease. A second deficiency of learning based neuroimaging diagnostics is that they implicitly assume that, `a single homogeneous pattern of brain changes drives population wide phenotypic differences\u27. In reality it is more likely that multiple patterns of brain deficits drive the complexities observed in the clinical presentation of most diseases. Understanding this heterogeneity may allow us to build better classifiers for identifying such diseases from individual brain scans. However, analytic tools to explore this heterogeneity are missing. With this in view, we present in this dissertation, a framework for exploring disease heterogeneity using population neuroimaging data. The approach we present first computes difference images by comparing matched cases and controls and then clusters these differences. The cluster centers define a set of deficit patterns that differentiates the two groups. By allowing for more than one pattern of difference between two populations, our framework makes a radical departure from traditional tools used for neuroimaging group analyses. We hope that this leads to a better understanding of the processes that lead to disease and also that it ultimately leads to improved image based disease classifiers

    Diffusion-adapted spatial filtering of fMRI data for improved activation mapping in white matter

    Get PDF
    Brain activation mapping using fMRI data has been mostly focused on finding detections in gray matter. Activations in white matter are harder to detect due to anatomical differences between both tissue types, which are rarely acknowledged in experimental design. However, recent publications have started to show evidence for the possibility of detecting meaningful activations in white matter. The shape of the activations arising from the BOLD signal is fundamentally different between white matter and gray matter, a fact which is not taken into account when applying isotropic Gaussian filtering in the preprocessing of fMRI data. We explore a graph-based description of the white matter developed from diffusion MRI data, which is capable of encoding the anisotropic domain. Based on this representation, two approaches to white matter filtering are tested, and their performance is evaluated on both semi-synthetic phantoms and real fMRI data. The first approach relies on heat kernel filtering in the graph spectral domain, and produced a clear increase in both sensitivity and specificity over isotropic Gaussian filtering. The second approach is based on spectral decomposition for the denosing of the signal, and showed increased specificity at the cost of a lower sensitivity.Novel approach to white matter filtering We introduced new advanced methods for filtering brain scans. Using them, we managed to improve the detection of activity in the white matter of the brain

    Dynamic Multivariate Simplex Splines For Volume Representation And Modeling

    Get PDF
    Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects. The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation

    Fast Fourier Transform at Nonequispaced Nodes and Applications

    Full text link
    The direct computation of the discrete Fourier transform at arbitrary nodes requires O(NM) arithmetical operations, too much for practical purposes. For equally spaced nodes the computation can be done by the well known fast Fourier transform (FFT) in only O(N log N) arithmetical operations. Recently, the fast Fourier transform for nonequispaced nodes (NFFT) was developed for the fast approximative computation of the above sums in only O(N log N + M log 1/e), where e denotes the required accuracy. The principal topics of this thesis are generalizations and applications of the NFFT. This includes the following subjects: - Algorithms for the fast approximative computation of the discrete cosine and sine transform at nonequispaced nodes are developed by applying fast trigonometric transforms instead of FFTs. - An algorithm for the fast Fourier transform on hyperbolic cross points with nonequispaced spatial nodes in 2 and 3 dimensions based on the NFFT and an appropriate partitioning of the hyperbolic cross is proposed. - A unified linear algebraic approach to recent methods for the fast computation of matrix-vector-products with special dense matrices, namely the fast multipole method, fast mosaic-skeleton approximation and H-matrix arithmetic, is given. Moreover, the NFFT-based summation algorithm by Potts and Steidl is further developed and simplified by using algebraic polynomials instead of trigonometric polynomials and the error estimates are improved. - A new algorithm for the characterization of engineering surface topographies with line singularities is proposed. It is based on hard thresholding complex ridgelet coefficients combined with total variation minimization. The discrete ridgelet transform is designed by first using a discrete Radon transform based on the NFFT and then applying a dual-tree complex wavelet transform. - A new robust local scattered data approximation method is introduced. It is an advancement of the moving least squares approximation (MLS) and generalizes an approach of van den Boomgard and van de Weijer to scattered data. In particular, the new method is space and data adaptive

    BRDF Representation and Acquisition

    Get PDF
    Photorealistic rendering of real world environments is important in a range of different areas; including Visual Special effects, Interior/Exterior Modelling, Architectural Modelling, Cultural Heritage, Computer Games and Automotive Design. Currently, rendering systems are able to produce photorealistic simulations of the appearance of many real-world materials. In the real world, viewer perception of objects depends on the lighting and object/material/surface characteristics, the way a surface interacts with the light and on how the light is reflected, scattered, absorbed by the surface and the impact these characteristics have on material appearance. In order to re-produce this, it is necessary to understand how materials interact with light. Thus the representation and acquisition of material models has become such an active research area. This survey of the state-of-the-art of BRDF Representation and Acquisition presents an overview of BRDF (Bidirectional Reflectance Distribution Function) models used to represent surface/material reflection characteristics, and describes current acquisition methods for the capture and rendering of photorealistic materials

    Anisotropy Across Fields and Scales

    Get PDF
    This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018

    BRDF representation and acquisition

    Get PDF
    Photorealistic rendering of real world environments is important in a range of different areas; including Visual Special effects, Interior/Exterior Modelling, Architectural Modelling, Cultural Heritage, Computer Games and Automotive Design. Currently, rendering systems are able to produce photorealistic simulations of the appearance of many real-world materials. In the real world, viewer perception of objects depends on the lighting and object/material/surface characteristics, the way a surface interacts with the light and on how the light is reflected, scattered, absorbed by the surface and the impact these characteristics have on material appearance. In order to re-produce this, it is necessary to understand how materials interact with light. Thus the representation and acquisition of material models has become such an active research area. This survey of the state-of-the-art of BRDF Representation and Acquisition presents an overview of BRDF (Bidirectional Reflectance Distribution Function) models used to represent surface/material reflection characteristics, and describes current acquisition methods for the capture and rendering of photorealistic materials
    corecore