Nonlinear diffusion filter and triangle method used for noise removal from polygonal shapes

2008 ◽  
Author(s):  
V. Zeljkovic ◽  
C. Tameze ◽  
R. Vincelette ◽  
E. Izquierdo
Keyword(s):  
Nonlinear Diffusion ◽  
Noise Removal ◽  
Diffusion Filter ◽  
Triangle Method

Nonlinear Diffusion Filters Combined with Triangle Method Used for Noise Removal from Polygonal Shapes

2014 ◽  
pp. 89-113
Keyword(s):  
Nonlinear Diffusion ◽  
Experimental Tests ◽  
Noise Removal ◽  
Experimental Results ◽  
Step Process ◽  
Diffusion Filter ◽  
Triangle Method ◽  
Excellent Preservation ◽  
Successful Removal ◽  
Polygonal Shape

A two-step process for removing noise from polygonal shapes is presented in this chapter. A polygonal shape is represented as its turning function and then a nonlinear diffusion filter and triangle method is applied. In the first step, several different nonlinear diffusion filters are applied to the turning function that identify dominant vertices in a polygon and remove those vertices that are identified as noise or irrelevant features. The vertices in the turning function which diffuse until the sides that immediately surround them approach the same turning function are identified as noise and removed. The vertices that are enhanced are preserved without changing their coordinates, and they are identified as dominant ones. In the second step, the vertices that form the smallest area triangles are removed. Obtained experimental results demonstrate that the proposed two-step process successfully removes vertices that should be dismissed as noise while preserving dominant vertices that can be accepted as relevant features and give a faithful description of the shape of the polygon. In experimental tests of this procedure successful removal of noise and excellent preservation of shape is demonstrated thanks to appropriate emphasis of dominant vertices.

A highly stable explicit scheme for a fourth-order nonlinear diffusion filter

2020 ◽  
Vol 11 (04) ◽  
pp. 2050030
Author(s):  
Mahipal Jetta
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Fourth Order ◽  
Nonlinear Diffusion ◽  
Splitting Scheme ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Diffusion Filter ◽  
Spatial Derivatives

The standard finite difference scheme (forward difference approximation for time derivative and central difference approximations for spatial derivatives) for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results. The alternating directional implicit (ADI) splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size. In this paper, we develop [Formula: see text] stencils for the approximation of second-order spatial derivatives based on the finite pointset method. We then make use of these stencils for approximating the fourth-order partial differential equation. We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme, without compromising on the quality of the filtered image. Further, we demonstrate through numerical simulations that the proposed scheme is more efficient, in obtaining quality filtered image, than an ADI splitting scheme.

Noisy Image Compressive Sensing Based on Nonlinear Diffusion Filter

2014 ◽  
Vol 510 ◽  
pp. 278-282 ◽  
Author(s):  
Ying Zhu ◽  
Yong Xing Jia ◽  
Yuan Wang ◽  
Chuan Zhen Rong ◽  
Yu Yang
Keyword(s):  
Compressive Sensing ◽  
Nonlinear Diffusion ◽  
Noisy Image ◽  
Diffusion Filter ◽  
Reconstruction Image

In the theory of compreesive sensing, the small amount of signal values can be reconstructed when signal is sparse or compressible.But the reconstruction of noisy image isnt very satisfied.In order to improve the quality of reconstruction image,the nonlinear diffusion filter is used in this paper.From the experiment results,the images reconstructed after nonlinear diffusion filter are better,and the value of PSNR is improved.

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