We introduce the coarsening of finite element computational grid strategy into the method proposed by Kačur and Mikula in [11] for the numerical solution of the Perona–Malik model modified in the sense of Catté, Lions, Morel and Coll. It improves the efficiency of the method, while the solution tends to be more flat during the selective smoothing process applied to the image. The numerical appr...

In this paper a new approach to the problem of edge preserving smoothing is proposed and evaluated. The new algorithm is based on the combined forward and backward anisotropic diffusion with incorporated time dependent cooling process. This method is able to efficiently remove image noise while preserving and enhancing image edges, lines and corners. The new method has been applied for the deno...

This paper presents an approach for reducing speckle in ultrasound images using Coupled Partial Differential Equation (CPDE) which has been obtained by uniting secondorder and the fourth-order partial differential equations. Using PDE to reduce the speckle is the noise-smoothing methods which is getting attention widely, because PDE can keep the edge well when it reduces the noise. We also intr...

In this paper, the gradient vector flow fields are introduced in the image anisotropic diffusion, and the shock filter, mean curvature flow and Perona-Malik equation are reformulated respectively in the context of this flow fields. Many advantages over the original models can be obtained, such as numerical stability, a large capture range, and computational simplification etc. In addition, the ...

in a domain Ω ⊂ IR accompanied with homogeneous Neumann boundary conditions and an initial condition. Equation (1.1) is useful in image processing for selective smoothing of images and shapes. Numerical experiments in processing of 2D and 3D images are presented in [10]. Here, we present analysis of a special semidiscrete scheme for solving (1.1). Equation (1.1) is a degenerate parabolic equati...

Abstract Image denoising approaches based on partial differential modeling have attracted a lot of attention in image processing due to their high performance. The nonlinear anisotropic diffusion equations, specially Perona–Malik model, are powerful tools that improve the quality by removing noise while preserving details and edges. In this paper, we propose accurate local meshless algorithm so...