A second order tensor is usually used to describe the diffusion of water for each voxel within Diffusion Tensor
Magnetic Resonance (DT-MR) images. However, a second order tensor approximation fails to accurately
represent complex local tissue structures such as crossing fibers. Therefore, higher order tensors are used to
represent more complex diffusivity profiles. In this work we examine and compare segmentations of both second
order and fourth order DT-MR images using the Random Walker segmentation algorithm with the emphasis of
pointing-out the shortcomings of second order tensor model in segmenting regions with complex fiber structures.
We first adopt the Random Walker algorithm for segmenting diffusion tensor data by using appropriate tensor
distance metrics and then demonstrate the advantages of performing segmentation on higher order DT-MR
data. The approach proposed takes advantage of all the information provided by the tensors by using suitable
tensor distance metrics. The distance metrics used are: the Log-Euclidean for the second order tensors and
the normalized L2 distance for the fourth order tensors. The segmentation is carried out on a weighted graph
that represents the image, where the tensors are the nodes and the edge weights are computed using the tensor
distance metrics. Applying the approach to both synthetic and real DT-MRI data yields segmentations that are
both robust and qualitatively accurate.
Image segmentation is a method of separating an image into regions of interest, such as separating an object
from the background. The random walker image segmentation technique has been applied extensively to scalar
images and has demonstrated robust results. In this paper we propose a novel method to apply the random walker
method to segmenting non-scalar diffusion tensor magnetic resonance imaging (DT-MRI) data. Moreover, we
used a non-parametric probability density model to provide estimates of the regional distributions enabling the
random walker method to successfully segment disconnected objects. Our approach utilizes all the information
provided by the tensors by using suitable dissimilarity tensor distance metrics. The method uses hard constraints
for the segmentation provided interactively by the user, such that certain tensors are labeled as object or
background. Then, a graph structure is created with the tensors representing the nodes and edge weights
computed using the dissimilarity tensor distance metrics. The distance metrics used are the Log-Euclidean and
the J-divergence. The results of the segmentations using these two different dissimilarity metrics are compared
and evaluated. Applying the approach to both synthetic and real DT-MRI data yields segmentations that are
both robust and qualitatively accurate.
Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been
extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI).
It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and
stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite
its extensive use in DT-MRI community, however, not much attention has been given to the mathematical
correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space.
But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector
space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and
robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean
and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor,
its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively
that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically
show that it has a higher signal to noise ratio than fractional anisotropy.
In this paper, we propose an adaptive seeding strategy for visualization of diffusion tensor magnetic resonance
imaging (DT-MRI) data using streamtubes. DT-MRI is a medical imaging modality that captures unique water
diffusion properties and fiber orientation information of the imaged tissues. Visualizing DT-MRI data using
streamtubes has the advantage that not only the anisotropic nature of the diffusion is visualized but also the
underlying anatomy of biological structures is revealed. This makes streamtubes significant for the analysis of
fibrous tissues in medical images. In order to avoid rendering multiple similar streamtubes, an adaptive seeding
strategy is employed which takes into account similarity of tensors in a given region. The goal is to automate
the process of generating seed points such that regions with dissimilar tensors are assigned more seed points
compared to regions with similar tensors. The algorithm is based on tensor dissimilarity metrics that take into
account both diffusion magnitudes and directions to optimize the seeding positions and density of streamtubes
in order to reduce the visual clutter. Two recent advances in tensor calculus and tensor dissimilarity metrics
are utilized: the Log-Euclidean and the J-divergence. Results show that adaptive seeding not only helps to cull
unnecessary streamtubes that would obscure visualization but also do so without having to compute the culled
streamtubes, which makes the visualization process faster.
An important problem in medical image analysis is the segmentation of anatomical regions of interest. Once
regions of interest are segmented, one can extract shape, appearance, and structural features that can be analyzed
for disease diagnosis or treatment evaluation. Diffusion tensor magnetic resonance imaging (DT-MRI) is
a relatively new medical imaging modality that captures unique water diffusion properties and fiber orientation
information of the imaged tissues. In this paper, we extend the interactive multidimensional graph cuts segmentation
technique to operate on DT-MRI data by utilizing latest advances in tensor calculus and diffusion tensor
dissimilarity metrics. The user interactively selects certain tensors as object ("obj") or background ("bkg") to
provide hard constraints for the segmentation. Additional soft constraints incorporate information about both
regional tissue diffusion as well as boundaries between tissues of different diffusion properties. Graph cuts are
used to find globally optimal segmentation of the underlying 3D DT-MR image among all segmentations satisfying
the constraints. We develop a graph structure from the underlying DT-MR image with the tensor voxels
corresponding to the graph vertices and with graph edge weights computed using either Log-Euclidean or the
J-divergence tensor dissimilarity metric. The topology of our segmentation is unrestricted and both obj and bkg
segments may consist of several isolated parts. We test our method on synthetic DT data and apply it to real
2D and 3D MRI, providing segmentations of the corpus callosum in the brain and the ventricles of the heart.
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