Fiber tract mapping from diffusion tensor MRI

Vemuri, Baba C.; Chen, Y.; Rao, Murali; McGraw, Tim; Wang, Z.; Mareci, Thomas H.

doi:10.1109/vlsm.2001.938885

Cited by 69 publications

(51 citation statements)

References 31 publications

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“…There exist two main classes of techniques. Nonspectral methods are based on a direct anisotropic smoothing of the diffusion weighted data (Vemuri et al, 2001) or consider each tensor as six scalar coordinates. This method suffers from the fact that the eigenvalues tend to diffuse faster than eigenvectors.…”

Section: Diffusion Tensor Regularizationmentioning

confidence: 99%

Variational, geometric, and statistical methods for modeling brain anatomy and function

et al. 2004

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We survey the recent activities of the Odyssée Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases. D

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Section: Diffusion Tensor Regularizationmentioning

confidence: 99%

Variational, geometric, and statistical methods for modeling brain anatomy and function

et al. 2004

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“…We would like to emphasise that we focus on methods for genuine tensor processing. Thus we do not consider scalar-or vector-valued PDE methods working on the eigensystem or filtering channels that are measured prior to computing tensors [11,28,29].…”

Section: Introductionmentioning

confidence: 99%

PDEs for Tensor Image Processing

Weickert

Feddern

Welk

et al. 2006

Mathematics and Visualization

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Methods based on partial differential equations (PDEs) belong to those image processing techniques that can be extended in a particularly elegant way to tensor fields. In this survey paper the most important PDEs for discontinuity-preserving denoising of tensor fields are reviewed such that the underlying design principles becomes evident. We consider isotropic and anisotropic diffusion filters and their corresponding variational methods, mean curvature motion, and selfsnakes. These filters preserve positive semidefiniteness of any positive semidefinite initial tensor field. Finally we discuss geodesic active contours for segmenting tensor fields. Experiments are presented that illustrate the behaviour of all these methods.

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“…These are a) directly smoothing the diffusion weighted images (DWIs) before computing the tensors [11,8], b) separately smoothing the eigenvectors and eigenvalues of the tensors [2,3,5], and c) smoothing whole tensors [1,7]. In the first method, one borrows techniques from classical gray-scale image processing to smooth the DWIs before estimation of the diffusion tensors.…”

Section: Introductionmentioning

confidence: 99%

“…In the first method, one borrows techniques from classical gray-scale image processing to smooth the DWIs before estimation of the diffusion tensors. For instance, Parker et al [11] applied the Perona-Malik algorithm to perform nonlinear smoothing of the raw DWIs, while Vemuri et al [8] used a smoothing scheme based on the weighted total variation norm. The main drawback of this first group of methods is that the DWIs are smoothed independently without any constraints imposed by the tensors.…”

Section: Introductionmentioning

confidence: 99%

Tensor MRI Regularization via Graph Diffusion

Zhang¹,

Hancock²

2006

Procedings of the British Machine Vision Conference 2006

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A new method for diffusion tensor (DT) image regularization is presented that relies on heat diffusion on discrete structures. We represent a DT image using a weighted undirected graph, where the weights of the edges are determined from the geometry of the white matter fiber pathways. Diffusion across this weighted graph is captured by the heat equation, and the solution, i.e. the heat kernel, is found by exponentiating the Laplacian eigen-system with time. DT image regularization is accomplished by convolving the heat kernel with each component of the diffusion tensors, and its numerical implementation is realized by using the Krylov subspace technique. The algorithm is tested and analyzed both on synthetic and real DT images.

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Fiber tract mapping from diffusion tensor MRI

Cited by 69 publications

References 31 publications

Variational, geometric, and statistical methods for modeling brain anatomy and function

Variational, geometric, and statistical methods for modeling brain anatomy and function

PDEs for Tensor Image Processing

Tensor MRI Regularization via Graph Diffusion

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