Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 749456, 15 pages
Research Article

Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion to Preserve Singularities and Delete Isolated Points in Image Smoothing

1Key Laboratory of Land Resources Evaluation and Monitoring in Southwest (Sichuan Normal University), Ministry of Education, Chengdu 610066, China
2School of Computer Science, Sichuan Normal University, Chengdu 610066, China
3School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
4Institute of Medical Information and Technology, School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China

Received 19 January 2011; Accepted 13 February 2011

Academic Editor: Ming Li

Copyright © 2011 Zhiwu Liao 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.


Existing Nonlinear Anisotropic Diffusion (NAD) methods in image smoothing cannot obtain satisfied results near singularities and isolated points because of the discretization errors. In this paper, we propose a new scheme, named Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion (ELONAD), which allows us to provide a unified framework for points in flat regions, edge points and corners, even can delete isolated points and spurs. ELONAD extends two diffusion directions of classical NAD to eight or more enclosed directions. Thus it not only performs NAD according to modules of enclosed directions which can reduce the influence of traction errors greatly, but also distinguishes isolated points and small spurs from corners which must be preserved. Smoothing results for test patterns and real images using different discretization schemes are also given to test and verify our discussions.