In a number of disciplines, directional data provides a fundamental source of information. A novel framework for isotropic and anisotropic di usion of directions is presented in this paper. The framework can be applied both to regularize directional data and to obtain multiscale representations of it. The basic idea is to apply and extend results from the theory of harmonic maps in liquid cryst...

In this work we propose a compact cell-centered Galerkin method with subgrid stabilization for anisotropic heterogeneous di usion problems on general meshes. Both essential theoretical results and numerical validation are provided.

The article is concerned with eÆcient edge-preserving numerical techniques for noise removal via anisotropic di usion. New minimum-biased (MB) nite di erence formulas are introduced to minimize di usion on both the piecewise smooth portions and their boundaries. Locally one-dimensional time-stepping algorithms are analyzed and a formula for eÆcient timestep sizes is suggested, to remove the hig...

Visual tasks often require a hierarchical representation of shapes and images in scales ranging from coarse to ne. A variety of linear and nonlinear smoothing techniques, such as Gaussian smoothing, anisotropic di usion, regularization, etc. , have been proposed, leading to scalespace representations. We propose a geometric smoothing method based on local curvature in shapes and images. This de...

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the innitesimal covariance give...

This paper proposes a new class of nonlinear PDEs called the Gibbs Reaction And Di usion Equation GRADE for a variety of applications in computer vision image processing and graphics In two previous papers the authors have been studying a minimax entropy theory based on which a new class of Gibbs distributions are learned in a fully non parametric form from a set of observed images such as text...

A simple and e€ective numerical method is proposed for simulating the temporal di€usive mass transport process through a microstructure with arbitrary complexity described by a phase-®eld approach. The mass di€usion through a given microstructure is modeled by a di€usion equation with a variable di€usion coecient, which is solved by an ecient and accurate semi-implicit spectral method. It is ...

In this paper we use the di usion-limit expansion of transport equations developed earlier [23] to study the limiting equation under a variety of external biases imposed on the motion. When applied to chemotaxis or chemokinesis, these biases produce modi cation of the turning rate, the movement speed or the preferred direction of movement. Depending on the strength of the bias, it leads to anis...

Abstract In this paper an algebraic substructuring preconditioner is considered for nonconforming nite element approximations of second order elliptic problems in D domains with diagonal anisotropic di usion tensor Using a block Gauss elimination and a substructuring idea part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent matrix Whe...

Abstract In this paper an algebraic substructuring preconditioner is considered for nonconforming nite element approximations of second order elliptic problems in D domains with diagonal anisotropic di usion tensor Using a block Gauss elimination and a substructuring idea part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent matrix Whe...