A novel approach is presented in this paper for improving anisotropic diffusion PDE models, based on the Perona–Malik equation. A solution is proposed from an engineering perspective to adaptively estimate the parameters of the regularizing function in this equation. The goal of such a new adaptive diffusion scheme is to better preserve edges when the anisotropic diffusion PDE models are applie...

In this paper a PDE based hybrid method for image denoising is introduced. The method is a bi-stage filter with anisotropic diffusion followed by wavelet based bayesian shrinkage. Here efficient denoising is achieved by reducing the convergence time of anisotropic diffusion. As the convergence time decreases, image blurring can be restricted and will produce a better denoised image than anisotr...

Spectral methods have recently gained popularity in many domains of computer graphics and geometry processing, especially shape processing, computation of shape descriptors, distances, and correspondence. Spectral geometric structures are intrinsic and thus invariant to isometric deformations, are efficiently computed, and can be constructed on shapes in different representations. A notable dra...

Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes with more than one diffusion coefficient, an average description by the mean squared displacement is often not sufficient. Hence, in this paper, we use the dist...

This paper presents a high-resolution numerical method for solving mass transport problems involving advection and anisotropic diffusion in shallow water based on unstructured mesh. An alternating operator-splitting technique is adopted to advance the numerical solution with advection and diffusion terms solved separately in two steps. By introducing a new r-factor into the Total Variation Dimi...

Abstract. In this paper, we consider anisotropic diffusion with decay, which takes the form α(x)c(x) − div[D(x)grad[c(x)]] = f(x) with decay coefficient α(x) ≥ 0, and diffusivity coefficient D(x) to be a second-order symmetric and positive definite tensor. It is well-known that this particular equation is a second-order elliptic equation, and satisfies a maximum principle under certain regulari...

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer–Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent ‘eddy diffusion’. W...

A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion–reaction problem with a diffusion parameter tending to zero. To solve numerically the singularly perturbed diffusion– reaction problem, monotone approximations are employed. Numerical examples are presented f...

This paper proposes new enhancement models to the methods of nonlinear anisotropic diffusion to greatly reduce speckle and preserve image features in medical ultrasound images. By incorporating local physical characteristics of the image, in this case scatterer density, in addition to the gradient, into existing tensorbased image diffusion methods, we were able to greatly improve the performanc...

This paper provides a detailed analysis of how anisotropic diffusion filters work on seismic data. The conventional trace mixing filter is shown to be an implementation of a specific d i ffusion process. Diffusion filters have diff e rent forms, ranging from the simplest linear isotropic (L-I) diffusion to the most complex nonlinear anisotropic (NL-AI) diffusion. The NL-AI diffusion filter can ...