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Beltrami flow in Hilbert space with applications to image denoising

[+] Author Affiliations
Zhizheng Liang

China University of Mining and Technology, School of Computer Science, Xuzhou 221116, China

Youfu Li

City University of Hong Kong, Department of Manufacturing Engineering and Engineering Management, Hong Kong, China

J. Electron. Imaging. 21(4), 043019 (Dec 12, 2012). doi:10.1117/1.JEI.21.4.043019
History: Received May 4, 2012; Revised November 2, 2012; Accepted November 13, 2012
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Abstract.  The Beltrami flow is an effective tool for dealing with images in many image-processing tasks. However, the important issue of how to set a proper embedding space is not solved in the Beltrami framework. We attempt to find a suitable embedding space by a nonlinear map. First, the image space is mapped into a high-dimensional feature space whose dimensionality may be infinite. It is found that directly dealing with the Beltrami flow in Hilbert space is impractical due to the unknown mapping function. Fortunately, using the well-known kernel methods, one can obtain the Beltrami flow in Hilbert space by performing inner products in the feature space. We refer to this flow as the kernel Beltrami flow. In addition, we also extend the kernel Beltrami flow to deal with vector-valued images. Finally, we show the effectiveness of the proposed method on gray-level and color images.

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© 2012 SPIE and IS&T

Citation

Zhizheng Liang and Youfu Li
"Beltrami flow in Hilbert space with applications to image denoising", J. Electron. Imaging. 21(4), 043019 (Dec 12, 2012). ; http://dx.doi.org/10.1117/1.JEI.21.4.043019


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