A Numerical Method for Preserving Curve Edges in Nonlinear Anisotropic Smoothing

Abstract

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.