We propose a PDE-based method to create textured representations of dense tensor-valued fields, for visualization purposes. Within the framework of anisotropic diffusion PDE’s, we focus on the general trace-based expressions (that we previously investigated in [39]) that are particularly well adapted to control the local smoothing performed by the regularization processes. Using this formalism,...

Diffusion tensor MRI (DT-MRI) is an image modality that is gaining clinical importance. After some preliminaries that describe the fundamentals of this imaging modality, we present a new technique to interpolate the diffusion tensor field, preserving boundaries and the constraint of positive-semidefiniteness. Our approach is based on the use of the inverse of the local structure tensor as a met...

We introduce a novel approach to the cerebral white matter connectivity mapping from diffusion tensor MRI. DT-MRI is the unique non-invasive technique capable of probing and quantifying the anisotropic diffusion of water molecules in biological tissues. We address the problem of consistent neural fibers reconstruction in areas of complex diffusion profiles with potentially multiple fibers orien...

We present a method for segmenting the thalamus and its subnuclei from Diffusion Tensor Magnetic Resonance Images(DT-MRI) using coupled, region based, level sets in 3D. Each surface, formed from the zero’th level set of the level set function, is associated with the most representative tensor contained within the surface. All neighboring voxels are then assigned to a region by finding the surfa...

We present a method for segmenting white matter as well as the gray matter structures from diffusion tensor magnetic resonance images (DT-MRI). The segmentation is done evolving a set of coupled level set functions. The zero level set of each level set function forms a surface in 3D that is driven by the region-based force including all tensors belonging to a certain region. The region-based fo...

The Nonlocal Data and Smoothness (NDS) filtering framework for greyvalue images has been recently proposed by Mrázek et al. This model for image denoising unifies M-smoothing and bilateral filtering, and several well-known nonlinear filters from the literature become particular cases. In this article we extend this model to so-called matrix fields. These data appear, for example, in diffusion t...

Most of the previous efforts on enhancing the DT-MRI estimation/smoothing have been based on “what is assumed to be correct”; and there are only very few studies concentrating on the validation of these approaches. This project presents our current efforts and observations for a validation framework. In the scope of this framework, high resolution fluoroscopy slices obtained from the brain stem...

Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is a non-invasive and in vivo medical imaging technique that allows neural tissue architecture to be probed at a microscopic scale. This is possible due to the diffusion of hydrogen atoms within water molecules in the imaging body; thus capturing the microstructure of the underlying tissues. DW-MRI adds to conventional MRI the capability of...

There has recently been increased interest in developing tensor data processing methods for the new medical imaging modality referred to as diffusion tensor magnetic resonance imaging (DT-MRI). This paper proposes a method for interpolating the primary vector fields from human cardiac DT-MRI, with the particularity of achieving interpolation and denoising simultaneously. The method consists of ...

Tensors are nowadays an increasing research domain in different areas, especially in image processing, motivated for example by DT-MRI (Diffusion Tensor Magnetic Resonance Imaging). Up to now, algorithms and tools developed to deal with tensors were founded on the assumption of a matrix vector space with the constraint of remaining symmetric positive definite matrices. On the contrary, our appr...