An overview of the edge detection techniques based on partial differential equations (PDE) is presented in this work. Nonlinear anisotropic diffusion-based boundary extraction approaches, like influential Perona- Malik model and some improved variants it, are described first. Anisotropic schemes using mean curvature motion nonlinear PDE-based approaches combining diffusion to bilateral filter t...

We study a finite-difference discretization of an ill-posed nonlinear parabolic partial differential equation. The PDE is the one-dimensional version of a simplified two-dimensional model for the formation of shear bands via anti-plane shear of a granular medium. For the discretized initial value problem, we derive analytically, and observed numerically, a two-stage evolution leading to a stead...

A novel approach is presented in this paper for improving anisotropic diffusion PDE models, based on the Perona–Malik equation. A solution is proposed from an engineering perspective to adaptively estimate the parameters of the regularizing function in this equation. The goal of such a new adaptive diffusion scheme is to better preserve edges when the anisotropic diffusion PDE models are applie...

We consider both second order and fourth order TV-based PDEs for image processing in one space dimension. A general class of nonlinear regularizations of the TV functional result in well-posed uniformly parabolic equations in two dimensions. However the fourth order analogue (Osher et. al. Multiscale Methods and Simulation 1(3) 2003) based on a total variation minimization in an H−1 norm, has v...

Image restoration has been an active research area. Dierent formulations are eective in high qualityrecovery. Partial Dierential Equations (PDEs) have become an important tool in image processingand analysis. One of the earliest models based on PDEs is Perona-Malik model that is a kindof anisotropic diusion (ANDI) lter. Anisotropic diusion lter has become a valuable tool indierent elds of image...