Abstract: A discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes is developed and studied. The unknowns of this scheme are the values at the center of the control volumes and at some internal interfaces, chosen because of some irregularity of the diffusion tensor. If the tensor is regular enough, the values on the interfaces may be deduced from the ...

We develop, apparently for the first time, an automatic criterion to choose when to stop the iteration in anisotropic diffusion signal reconstruction.

This paper discusses the effects that partitioning has on the convergence rate of Domain Decomposition. When Finite Elements are employed to solve a second order elliptic partial differential equation with strong convection and/or anisotropic diffusion, the shape and alignment of a partition’s parts significantly affect the Domain Decomposition convergence rate. Given a PDE, if b is the directi...

Texture analysis is an important field of investigation that has received a great deal of interest from computer vision community. In this paper, we propose a novel approach for texture modeling based on partial differential equation (PDE). Each image f is decomposed into a family of derived sub-images. f is split into the u component, obtained with anisotropic diffusion, and the v component wh...

In this paper, we propose a two-stage level set segmentation framework to extract vascular tree from magnetic resonance angiography(MRA). First, we smooth the isosurface of MRA by anisotropic diffusion filter. Then this smoothed surface is treated as the initial localization of the desired contour, and used in the following geodesic active contours method, which provides accurate vascular struc...

On the one hand, anisotropic diffusion is a well-established concept that has improved numerous computer vision approaches by permitting direction-dependent smoothing. On the other hand, recent applications have uncovered the importance of second order regularisation. The goal of this work is to combine the benefits of both worlds. To this end, we propose a second order regulariser that allows ...

Ultrasound images provide the clinician with non-invasive, low cost, and real-time images that can help them in diagnosis and plannnig and therapy. However, although the human eye is able to derive the meaningful information from these images, automatic processing is very difficult because of the noise and artefacts present in the image. In this work, we propose to extend the current anisotropi...

We study low-order reconstruction operators on polyhedral meshes, providing a unified framework for degrees of freedom attached to vertices, edges, faces, and cells. We present two equivalent sets of design properties and draw links with the literature. In particular, the two-level construction based on a P0consistent and a stabilization part provides a systematic way of designing these operato...

Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numeric...

Breast cancer is one of the leading causes of cancer death among women worldwide. The proposed approach comprises three steps as follows. Firstly, the image is preprocessed to remove speckle noise while preserving important features of the image. Three methods are investigated, i.e., Frost Filter, Detail Preserving Anisotropic Diffusion, and Probabilistic Patch-Based Filter. Secondly, Normalize...