We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. By incorporating edges found at multiple scales via an adaptive edge detector-based indicator function, the proposed scheme removes noise while respecting salient boundaries. We create a s...

Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures...

Nonnegative directional splittings of anisotropic diffusion operators in the divergence form are investigated. Conditions are established for nonnegative directional splittings to hold in a neighborhood of an arbitrary interior point. The result is used to construct monotone finite difference schemes for the boundary value problem of anisotropic diffusion operators. It is shown that such a mono...

This paper describes a method to enhance line structures in a gray level image. For this purpose, we blur the image using anisotropic gaussian filters along the directions of each line structures. In a line structure region the gradients of image gray levels have a uniform direction. To find such line structures, we evaluate the uniformity of the directions of the local gradients. Before this e...

Gaussian filters are widely used for image smoothing but it is well known that this type of filters blur the image features (e.g., edges). Anisotropic filtering draws more and more attention for its ability of featurepreserving smoothing. However, most existing anisotropic filters are quite time-consuming. In this report I will discuss the combination of anisotropic filtering and recursive impl...

Gaussian filter is widely used for image smoothing but it is well known that this type of filters blur the image features (e.g., edges). Two extensions of Gaussian filters will be discussed in this survey. One is the anisotropic filtering (bilateral filtering or PDE-based anisotropic diffusion) for feature-preserving smoothing and the other is the recursive implementation of various filters tha...

In this paper, novel second order and fourth order diffusion models are proposed for image denoising. Both models are based on the gradient vector convolution (GVC) model. The second model is coined by incorporating the GVC model into the anisotropic diffusion model and the fourth order one is by introducing the GVC to the You-Kaveh fourth order model. Since the GVC model can be implemented in ...

A theory is presented which incorporates the effect of dielectric anisotropy in random multiple scattering media. It predicts anisotropic diffusion, and a deflection of the diffuse energy flow in anisotropic slabs in the direction parallel to the slab. The transmittance integrated over all incoming and outgoing directions scales with the transport mean free path along the surface normal. The es...