FEM based Numerical Approximation Model for the Ambrosio–Tortorelli Energy Model and the Numerical Simulation of the Edge Detection and Image Denoising

Abstract

We propose a FEM (Finite Element Method) based semi implicit simulation scheme for the Ambrosio–Tortorelli energy functional for the denoising and segmentation of noisy images. Our main goal is to detect the corners in noisy as well as noise free images. The fast converging semi implicit iterative numerical scheme is derived for the numerical solution of nonlinear partial differential equation which is obtained from the minimization of given energy functional using direct methods from the calculus of variations. The scaling parameters are used as regularization weights; these local adaptive smoothness parameters generally play a crucial role as regularization devices in the variational techniques for the image processing and computer vision research.