scholarly journals Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion to Preserve Singularities and Delete Isolated Points in Image Smoothing

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Zhiwu Liao ◽  
Shaoxiang Hu ◽  
Dan Sun ◽  
Wufan Chen
Keyword(s):  
Anisotropic Diffusion ◽  
Laplacian Operator ◽  
Image Smoothing ◽  
Unified Framework ◽  
Discretization Schemes ◽  
Edge Points ◽  
Isolated Points ◽  
Discretization Errors ◽  
Nonlinear Anisotropic Diffusion

Existing Nonlinear Anisotropic Diffusion (NAD) methods in image smoothing cannot obtain satisfied results near singularities and isolated points because of the discretization errors. In this paper, we propose a new scheme, named Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion (ELONAD), which allows us to provide a unified framework for points in flat regions, edge points and corners, even can delete isolated points and spurs. ELONAD extends two diffusion directions of classical NAD to eight or more enclosed directions. Thus it not only performs NAD according to modules of enclosed directions which can reduce the influence of traction errors greatly, but also distinguishes isolated points and small spurs from corners which must be preserved. Smoothing results for test patterns and real images using different discretization schemes are also given to test and verify our discussions.

scholarly journals A Numerical Method for Preserving Curve Edges in Nonlinear Anisotropic Smoothing

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Shaoxiang Hu ◽  
Zhiwu Liao ◽  
Dan Sun ◽  
Wufan Chen
Keyword(s):  
Numerical Method ◽  
Anisotropic Diffusion ◽  
Digital Images ◽  
New Method ◽  
Image Smoothing ◽  
Time And Space ◽  
Curve Edge ◽  
Nonlinear Anisotropic Diffusion ◽  
Anisotropic Smoothing

We focus on nonlinearity for images and propose a new method which can preserve curve edges in image smoothing using nonlinear anisotropic diffusion (NAD). Unlike existing methods which diffuse only among the spatial variants, the new method suggests that the diffusion should be performed both among the time variants and spatial variants, named time and space nonlinear anisotropic diffusion (TSNAD). That is, not only the differences of the spatial variants should be estimated by the nearby spatial points but also the differences of the time variants should be approximated by the weighted time differences of nearby points, according to the differences of gray levels between them and the consideration point. Since the time differences of nearby points using NAD can find more points with similar gray levels which form a curve belt for the center pixel on a curve edge, TSNAD can provide satisfied smoothing results while preserving curve edges. The experiments for digital images also show us the ability of TSNAD to preserve curve edges.

A nonlinear anisotropic diffusion equation for image restoration with forward-backward diffusivities

2021 ◽  
Vol 14 ◽  
Author(s):  
Santosh Kumar ◽  
Nitendra Kumar ◽  
Khursheed Alam
Keyword(s):  
Image Processing ◽  
Anisotropic Diffusion ◽  
Diffusion Models ◽  
Smoothing Kernel ◽  
Proposed Model ◽  
Invariant Kernel ◽  
Nonlinear Anisotropic Diffusion ◽  
Anisotropic Diffusion Equation ◽  
Frequent Problem ◽  
Deblurring And Denoising

Background: In the image processing area, deblurring and denoising are the most challenging hurdles. The deblurring image by a spatially invariant kernel is a frequent problem in the field of image processing. Methods: For deblurring and denoising, the total variation (TV norm) and nonlinear anisotropic diffusion models are powerful tools. In this paper, nonlinear anisotropic diffusion models for image denoising and deblurring are proposed. The models are developed in the following manner: first multiplying the magnitude of the gradient in the anisotropic diffusion model, and then apply priori smoothness on the solution image by Gaussian smoothing kernel. Results: The finite difference method is used to discretize anisotropic diffusion models with forward-backward diffusivities. Conclusion: The results of the proposed model are given in terms of the improvement.

scholarly journals An automatic stopping criterion for nonlinear anisotropic diffusion

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
César Bustacara-Medina ◽  
Leonardo Flórez-Valencia
Keyword(s):  
Anisotropic Diffusion ◽  
Stopping Criterion ◽  
Nonlinear Anisotropic Diffusion

Volumetric Nonlinear Anisotropic Diffusion on GPUs

2012 ◽  
pp. 62-73 ◽  
Author(s):  
Andreas Schwarzkopf ◽  
Thomas Kalbe ◽  
Chandrajit Bajaj ◽  
Arjan Kuijper ◽  
Michael Goesele
Keyword(s):  
Anisotropic Diffusion ◽  
Nonlinear Anisotropic Diffusion
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