The Bloch-Torrey Partial Differential Equation (PDE) can be used to model the diffusion Magnetic Resonance Imaging (dMRI) signal in biological tissue. In this paper, we derive an Anisotropic Diffusion Transmission Condition (ADTC) for the Bloch-Torrey PDE that accounts for anisotropic diffusion inside thin layers. Such diffusion occurs, for example, in the myelin sheath surrounding the axons of...

Roussos and Maragos proposed a method for image interpolation in “Reversible interpolation of vectorial images by an anisotropic diffusion-projection PDE.” An earlier version was also published in conference paper (Roussos and Maragos, “Vector-Valued Image Interpolation by an Anisotropic Diffusion-Projection PDE,” 2007). Given a discretely sampled image v, the method finds an image u such that ...

Texture analysis techniques are being increasingly used for surface inspection, in which small defects that appear as local anomalies in textured surfaces must be detected. Traditional surface inspection methods mainly focus on homogeneous textures that contain periodical, repetitive patterns. In this paper, we study defect detection in sputtered glass substrates that involve inhomogeneous text...

Multigrid methods provide a means with which to accelerate the solution of many problems derived from multidimensional linear and nonlinear Partial Differential Equations. A multigrid approach is applied to anisotropic diffusion, a process that is useful for image smoothing and edge strengthening. It is demonstrated to improve the response of the diffusion process by smoothing stubborn low-freq...

We cast the problem of inferring the 3D shape of a scene from a collection of defocused images in the framework of anisotropic diffusion. We propose a novel algorithm that can estimate the shape of a scene by inferring the diffusion coefficient of a heat equation. The method is optimal, as we pose it as the minimization of a certain cost functional based on the input images, and fast. Furthermo...

We show that standard algorithms for anisotropic diffusion based on centered differencing (including the recent symmetric algorithm) do not preserve monotonicity. In the context of anisotropic thermal conduction, this can lead to the violation of the entropy constraints of the second law of thermodynamics, causing heat to flow from regions of lower temperature to higher temperature. In regions ...

The cover image shows a thresholded nonwoven fabric image which was processed by applying a coherence-enhancing anisotropic diffusion filter (see Section 5.2 for more details). The goal was to visualize the quality relevant adjacent fibre structures , so-called stripes. The displayed equations describe the basic structure of nonlinear diffusion filtering in the continuous, semidiscrete, and ful...

In this paper, two models for curvelet-regularized nonlinear diffusion are proposed for discontinuity-preserving denoising, using a new tight frame of curvelets and a nonlinear diffusion scheme. Numerical experiments show their good performance to recover the shape of edges and some important detailed components of the image while we use less iterations, in comparison to traditional methods. Ma...

Multi-resolution image analysis utilizes subsampled image representations for applications such as image coding, hierarchical image segmentation and fast image smoothing. An anti-aliasing filter may be used to insure that the sampled signals adequately represent the frequency components/features of the higher resolution signal. Sampling theories associated with linear anti-aliasing filtering ar...

BACKGROUND AND PURPOSE The various stages of multiple sclerosis (MS) are characterized by de- and remyelination as well as by inflammation. Diffusion MR imaging is sensitive to tissue water motion, which might correspond to these pathologic processes. Our purpose was to demonstrate differences in apparent diffusion coefficient (ADC) and diffusion tensor anisotropy in acute and chronic MS plaque...