Finite element approximation of a forward and backward anisotropic diffusion model in image denoising and form generalization

2008 ◽  
Vol 24 (2) ◽  
pp. 646-662 ◽  
Author(s):  
Carsten Ebmeyer ◽  
Jens Vogelgesang
Keyword(s):  
Finite Element ◽  
Image Denoising ◽  
Diffusion Model ◽  
Anisotropic Diffusion ◽  
Finite Element Approximation ◽  
Element Approximation

Mixed Finite Element Approximation for Bivariate Perona–Malik Model Arising in 2D and 3D Image Denoising

3D Research ◽  
2018 ◽  
Vol 9 (3) ◽  
Author(s):  
Amal Hjouji ◽  
Mostafa Jourhmane ◽  
Jaouad EL-Mekkaoui ◽  
Mohammed Es-sabry
Keyword(s):  
Finite Element ◽  
Image Denoising ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
3D Image ◽  
2D And 3D

An Angular Finite Element Method for the Solution of the Even-Parity Equation

2009 ◽  
Author(s):  
R. Becker ◽  
R. Koch ◽  
M. F. Modest ◽  
H.-J. Bauer
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Basis Functions ◽  
New Method ◽  
Discrete Ordinates ◽  
Test Case ◽  
Element Approximation ◽  
Promising Alternative ◽  
Element Discretization ◽  
Spatial Coordinates

The present article introduces a new method to solve the radiative transfer equation (RTE). First, a finite element discretization of the solid angle dependence is derived, wherein the coefficients of the finite element approximation are functions of the spatial coordinates. The angular basis functions are defined according to finite element principles on subdivisions of the octahedron. In a second step, these spatially dependent coefficients are discretized by spatial finite elements. This approach is very attractive, since it provides a concise derivation for approximations of the angular dependence with an arbitrary number of angular nodes. In addition, the usage of high-order angular basis functions is straightforward. In the current paper the governing equations are first derived independently of the actual angular approximation. Then, the design principles for the angular mesh are discussed and the parameterization of the piecewise angular basis functions is derived. In the following, the method is applied to two-dimensional test cases which are commonly used for the validation of approximation methods of the RTE. The results reveal that the proposed method is a promising alternative to the well-established practices like the Discrete Ordinates Method (DOM) and provides highly accurate approximations. A test case known to exhibit the ray effect in the DOM verifies the ability of the new method to avoid ray effects.

Finite Element Approximation of the p-Laplacian

1993 ◽  
Vol 61 (204) ◽  
pp. 523 ◽  
Author(s):  
John W. Barrett ◽  
W. B. Liu
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation
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