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Journal of Information Science and Engineering, Vol. 23 No. 5, pp. 1565-1578 (September 2007)

Combining Bidirectional Flow Equation and Fuzzy Sets for Adaptive Image Sharpening*

Shujun Fu1,2, Qiuqi Ruan2, Wenqia Wang1 and Jingnian Chen3
1School of Mathematics and System Sciences
Shandong University
Jinan, 250100, China
E-mail: shujunfu@163.com
2Institute of Information Science
Beijing Jiaotong University
Beijing, 100044, China
3School of Arts and Science
Shandong University of Finance
Jinan, 250014, China

In this paper, a region-based fuzzy bidirectional flow process is presented for image noise removal and edge sharpening. An image is divided into three-type different regions according to image features: edges, textures and details, and flat areas. For edges, a shock-type backward diffusion is performed in the gradient direction to the isophote line (edge), incorporating a forward diffusion in the isophote line direction; while for textures and details, a fuzzy backward diffusion is done to enhance image features preserving a natural transition. Moreover, an isotropic diffusion is used to smooth flat areas simultaneously. Finally, a shock capturing scheme with a special limiter function is developed to speed the process with numerical instability. Experiments on real images show that this method produces better visual results of the enhanced images than some related equations.

Keywords: bidirectional diffusion, edge sharpening, fuzzy membership function, image enhancement, noise removal, shock filters

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Received June 21, 2005; revised November 7, 2005 & January 19, 2006; accepted January 23, 2006.
Communicated by Pau-Choo Chung.
*This work was supported by the Natural Science Fund of Shandong Province, P.R. China (No. Y2006G08); the researcher fund for the special project of Beijing Jiaotong University, P.R. China; the open project of the National Laboratory of Pattern Recognition at the Institute of Automation of the Chinese Academy of Sciences, P.R. China; the general program project of School of Mathematics and System Sciences of Shandong University, P.R. China (No. 306002).