A new anisotropic diffusion method, application to partial volume effect reduction

The partial volume effect is a significant limitation in medical imaging that results in blurring when the boundary between two structures of interest falls in the middle of a voxel. A new anisotropic diffusion method allows one to create interpolated 3D images corrected for partial volume, without enhancement of noise. After a zero-order interpolation, we apply a modified version of the anisotropic diffusion approach, wherein the diffusion coefficient becomes negative for high gradient values. As a result, the new scheme restores edges between regions that have been blurred by partial voluming, but it acts as normal anisotropic diffusion in flat regions, where it reduces noise. We add constraints to stabilize the method and model partial volume; i.e., the sum of neighboring voxels must equal the signal in the original low resolution voxel and the signal in a voxel is kept within its neighbor's limits. The method performed well on a variety of synthetic images and MRI scans. No noticeable artifact was induced by interpolation with partial volume correction, and noise was much reduced in homogeneous regions. We validated the method using the BrainWeb project database. Partial volume effect was simulated and restored brain volumes compared to the original ones. Errors due to partial volume effect were reduced by 28% and 35% for the 5% and 0% noise cases, respectively. The method was applied to in vivo "thick" MRI carotid artery images for atherosclerosis detection. There was a remarkable increase in the delineation of the lumen of the carotid artery

Seismic Fault Preserving Diffusion

This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non linear diffusion filtering leading to a better detection of seismic faults. The non linear diffusion approaches are based on the definition of a partial differential equation that allows us to simplify the images without blurring relevant details or discontinuities. Computing the structure tensor which provides information on the local orientation of the geological layers, we propose to drive the diffusion along these layers using a new approach called SFPD (Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor are fixed according to a confidence measure that takes into account the regularity of the local seismic structure. Results on both synthesized and real 3-D blocks show the efficiency of the proposed approach.Comment: 10 page

Modeling anisotropic diffusion using a departure from isotropy approach

There are a large number of finite volume solvers available for solution of isotropic diffusion equation. This article presents an approach of adapting these solvers to solve anisotropic diffusion equations. The formulation works by decomposing the diffusive flux into a component associated with isotropic diffusion and another component associated with departure from isotropic diffusion. This results in an isotropic diffusion equation with additional terms to account for the anisotropic effect. These additional terms are treated using a deferred correction approach and coupled via an iterative procedure. The presented approach is validated against various diffusion problems in anisotropic media with known analytical or numerical solutions. Although demonstrated for two-dimensional problems, extension of the present approach to three-dimensional problems is straight forward. Other than the finite volume method, this approach can be applied to any discretization method

A Phase Field Model for Continuous Clustering on Vector Fields

A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.

Adaptive Nonlocal Filtering: A Fast Alternative to Anisotropic Diffusion for Image Enhancement

The goal of many early visual filtering processes is to remove noise while at the same time sharpening contrast. An historical succession of approaches to this problem, starting with the use of simple derivative and smoothing operators, and the subsequent realization of the relationship between scale-space and the isotropic dfffusion equation, has recently resulted in the development of "geometry-driven" dfffusion. Nonlinear and anisotropic diffusion methods, as well as image-driven nonlinear filtering, have provided improved performance relative to the older isotropic and linear diffusion techniques. These techniques, which either explicitly or implicitly make use of kernels whose shape and center are functions of local image structure are too computationally expensive for use in real-time vision applications. In this paper, we show that results which are largely equivalent to those obtained from geometry-driven diffusion can be achieved by a process which is conceptually separated info two very different functions. The first involves the construction of a vector~field of "offsets", defined on a subset of the original image, at which to apply a filter. The offsets are used to displace filters away from boundaries to prevent edge blurring and destruction. The second is the (straightforward) application of the filter itself. The former function is a kind generalized image skeletonization; the latter is conventional image filtering. This formulation leads to results which are qualitatively similar to contemporary nonlinear diffusion methods, but at computation times that are roughly two orders of magnitude faster; allowing applications of this technique to real-time imaging. An additional advantage of this formulation is that it allows existing filter hardware and software implementations to be applied with no modification, since the offset step reduces to an image pixel permutation, or look-up table operation, after application of the filter

Random noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections

The empirical origin of random noise is described, its influence on DTI variables is illustrated by a review of numerical and in vivo studies supplemented by new simulations investigating high noise levels. A stochastic model of noise propagation is presented to structure noise impact in DTI. Finally, basics of voxelwise and spatial denoising procedures are presented. Recent denoising procedures are reviewed and consequences of the stochastic model for convenient denoising strategies are discussed