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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 186507, 14 pages
Research Article

A Numerical Method for Preserving Curve Edges in Nonlinear Anisotropic Smoothing

1School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
2School of Computer Science, Sichuan Normal University, Chengdu 610066, China
3Institute of Medical Information and Technology, School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China

Received 28 January 2011; Accepted 18 February 2011

Academic Editor: Ming Li

Copyright © 2011 Shaoxiang Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.